Who Has Impacted Your Life the Most Free Essays

There are sure individuals, when we got some information about who sway your life’s, they for the most part referenced their folks. In any case, my folks gave me the endowment of life. They showed me how to talk and walk. We will compose a custom paper test on Who Has Impacted Your Life the Most or on the other hand any comparative point just for you Request Now They are consistently here for me when I need something. I can't live without their recommendation. My folks are ideal instances of allowed me to have great instruction and better life. In the first place, my dad is my direction with all that I had done. I can't postponed his encourage to me. I generally discover him in the position where I need him. For instance, my choice of concentrating in the United State or concentrating in Saudi Arabia. He urge me to go to the United State on the grounds that as teacher working in the college. He disclosed to me that instructing in America better for you. Indeed, even idea he is instructing on college in Saudi Arabia. Besides, he allowed me to pick whether I need to concentrate in Saudi Arabia or America. In conclusion, I decided to concentrate in the U. S, and he was with me for the in case landmark of supporting me and offering me guidance until I showed up to the U. S. Second, my mom is the best mother on the planet since she gave the impassible thing that no body can give me, is the endowment of live. She generally help me with whatever I need. She never compels me to do whatever I don't prefer to do. She needed for me to have the best training in all my years. She likewise upheld me and offered me guidance to my excursion to the U. S. I recall that she disclosed to me that â€Å"nobody was destined to know† on the grounds that I feared learning English. What's more, who will be the existence with various culture. In this circumstance, she said to me you are going to congruity with others there and don't be apprehensive, the life is simple. The most effective method to refer to Who Has Impacted Your Life the Most, Essays

Medea monologue from the play by Euripides Essay Paper Example For Students

Medea monolog from the play by Euripides Essay Paper A monolog from the play by Euripides NOTE: This monolog is reproduced from The Plays of Euripides in English, vol. ii. Trans. Shelley Dean Milman. London: J.M. Mark Sons, 1922. MEDEA: O my children! My children! ye have a city and a house Where, abandoning hapless me, without A mother ye for ever will live. Yet, I to different domains an outcast go, Ere any assistance from you I could infer, Or on the other hand observe you fortunate; the hymeneal pageantry, The lady of the hour, the cheerful lounge chair, for you enhance, Also, in these hands the fueled light support. How pitiable am I through my own backwards nature! You, O my children, I then futile have supported, Futile have drudged, and, squandered with weakness, Endured the pregnant matrons shocking pains. On you, in my distresses, numerous expectations I established erst: that ye with devout consideration Would cultivate my mature age, and on the casket Broaden me after deathmuch begrudged part Of humans; however these satisfying on edge musings Are evaporated now; for, losing you, an actual existence Of sharpness and anguish will I lead. Be that as it may, concerning you, my children, with those dear eyes Destined no more your mom to view, Consequently are ye hurrying to a world obscure. For what reason do ye look on me with such a look Of delicacy, or wherefore grin? for these Are your last grins. Ok pitiable, vomited me! What will I do? My goals comes up short. Shining with delight now I their looks have seen, My companions, I can no more. To those past plans I say farewell, and with me from this land My youngsters will pass on. For what reason should I cause A twofold part of pain to fall On my own head, that I may lament the sire By rebuffing his children? This will not be: Such advice I excuse. However, in my motivation What implies this change? Would i be able to favor disparagement, What's more, without risk of punishment grant the adversary To scape? My most extreme mental fortitude I should awaken: For the proposal of these delicate contemplations Continues from an exhaust heart. My children, Enter the majestic house. With respect to those Who regard that to be available were unholy While I the ordained casualties offer up, Let them make sure. This inspired arm Will never recoil. Oh! tsk-tsk! my spirit Submit not such a deed. Troubled lady, Stop and extra thy kids; we will live Together, they in outside domains will cheer Thy oust. No, by those avenging beasts Who abide with Pluto in the domains underneath, This will not be, nor will I ever leave My children to be offended by their adversaries. They surely amazing; at that point they should, I bore and I will kill them: is a deed Settled on, nor my motivation will I change. Full well I realize that now the illustrious lady of the hour Wears on her head the enchantment diadem, What's more, in the variegated robe lapses: Be that as it may, rushed on by destiny, I track a way Of absolute wretchedness, and them will plunge Into one yet increasingly pitiable. To my children Fain would I say: O stretch forward your correct hands Ye youngsters, for your mom to grasp. O dearest hands, ye lips to me generally dear, Drawing in highlights and open looks, May ye be fortunate, yet in a different universe; For by the tricky direct of your sire Are ye dispossessed of this world offered. Goodbye, sweet kissestender appendages, goodbye! What's more, fragrant breath! I never more can manage To look on you, my youngsters. My distresses Have vanquished me; I currently am very much aware What violations I adventure on: however rage, the reason Of hardships generally unfortunate to humankind, Over my better explanation hath won.

Day 0 from DC to Quito

Day 0 from DC to Quito January 10 On the plane from Panama to Quito What a goofy immigration card. I dont think I know my Date of Bird? My alarm went off at 4am. I submitted my very last application at 2am, couldnt fall asleep until 3am (you know that post-essay adrenaline rush?) and couldnt drag my body out of bed until 4:40. I discovered that the clothes I left out to dry were still SOAKED, and applied the hairdryer treatment with minimal success. Oh well…hopefully theres no mold when I open my suitcase in February. Raphael very kindly woke up extra early to help me pack, since I told him that I would be up late. We staggered around packing my things for an hour. I eventually had to give up on ever fitting my laptop into my suitcase; hopefully Eric can fit it into his backpack. At 6 or so, we went to the lobby to check out and get a cab to the airport. I was very grumpy, and my grumpiness was exacerbated by the very slow pace at which the rest of the world was moving. After listening to a very involved discussion about perks of hotel membership, we finally stored my bags and took a very sketchy cab ride* to the airport. I made a quick trip to Erics room to slide the luggage tags under his door. I hope I see my laptop again *Well, Raphael says it was sketchy. I was fast asleep and didnt notice that the driver was tailing other cars in icy slippery conditions. My morning became even less cheerful when we learned that a taxi to the airport costs $70. Fortunately the NRAO and MIT are covering travel expenses! Dunkin Donuts bagels then a 5-ish hour flight to Panama. I remember pretty much none of it (including take-off) except for the delicious ravioli (I woke up in time for lunch :)). Raphael woke me up when we were landing, so that I wouldnt miss the beautiful view. Panama Airport: humid, crowded, modern, indistinguishable from any other big transfer airport. After some discussion with French and American travelers about whether the water from the water fountain was safe to drink, we opted to buy a bottle of water, which somehow cost $4.  A Dunkin Donuts bagel cost $8. Ugh. NOT  a fan of Panama Airport. Panama Airport was the site of the first (of what Im sure will be many) amusing Spanish attempts Raphael: Hola. Baño…hombres? Saleswoman: *point* Raphael: Merci! A for effort! Now, were sitting on the plane from Panama to Quito. Our neighbor here in Row 7 is named Isabel. She lives in Chicago and is visiting her home in Ecuador  for the first time in 2 years. She hasnt told her family that shes coming, and is excited to surprise them. We introduced ourselves and she looked delighted: apparently her dad is named Rafael and her mom is named Ana!  Maybe when you have a kid, she said, you will name her Isabel!!!! We laughed politely. Our names seemed to particularly endear us to her. She wrote down suggestions for how to get to our hostel from the airport (take the trolé) as well as for how to deal with taxi drivers trying to rip you off. She invited us to visit her house in the ecological reserve, a 4-hour trip from Quito.  She wrote down her phone number and offered to show us around, and said we could call her if anything came up. What a kind person! Definitely intending to take her up on that. Woah, we just broke through the clouds. GREEN! Lots of green. Mountains, denser houses than I had imagined. Lots of farmland at the foot of the mountains peak. So green.

College Tuition Should Be More Affordable - Free Essay Example

Sample details Pages: 2 Words: 716 Downloads: 9 Date added: 2019/08/08 Category Education Essay Level High school Tags: College Tuition Essay Did you like this example? College Tuition Should Be More Affordable College tuition costs in the United States keep increasing every year. In my opinion, college tuition rates should drop in price. When I was seventeen, I had the fortune of meeting several college students that were enrolled in various institutions. Don’t waste time! Our writers will create an original "College Tuition Should Be More Affordable" essay for you Create order I was curious about continuing my education, and I asked them what the worst part of college was? Their response was the high tuition costs and the student loans with ten percent or more interest rates on top of their already ten to fifteen thousand dollar a semester college tuition. I believe college tuition rates should lower in order to decrease the stress on the student, ease the financial burden on the parent, and help a student finish college in hopes of obtaining a career. Stress on college students can be overwhelming and stressful. Many of them are away from home for the first time, unaware of the copious hours of studying, and hard work college classes require compared to high school, and are starting in a new area with unfamiliar surroundings. What many are unaware of however is the financial stress that comes with procuring a college degree. It costs on average of $9,410 a year for in state students in tuition at a public four year college (College Costs FAQs). That is $37,640 over a four year span! Due to the high cost of education, many turn to grants and scholarships to avoid paying outrageous interest fees that come with student loans. Unfortunately, grants and scholarships are both forms of unguaranteed funds. Anyone can apply, but not everyone receives money. Due to this many opt to accept student loans. The average student loan interest rate is 3.76% (Interest Rates and Fees). So when all is said and done, the total cost for a student using nothing but student loans to pay for education. Student loans coupled with college tuition is $39,055.26, almost $40,000 dollars. Knowing these facts, I believe college tuition rates should be more affordable, so that students do not have to incur a massive amount of debt before they have a chance to graduate. Parents of college students sometimes pay their college tuition. Many even put money aside from the students birth till they graduate high school in order to pay some or all of the tuition. The average cost of raising a child from birth to age of eighteen is $233,610 (Gajanan). So on top of the costly amount it takes to raise a child, a parent must also worry about setting their child up with money for tuition, so that they may continue their education and have a chance at a better future. By lowering the cost of tuition nationwide would help ease the financial burden on the parent of sending their child to college. Some students do not finish college and drop out due to the financial strain college tuition puts on them. Only 46% of college students complete school once starting it (Waldren). The cost of tuition in 1985 for tuition and fees at a four year institution per year was $2,784. Fast forward to 2007 and the cost has skyrocketed to $10,913 (U.S. Department of Education), almost five times the original amount! A student dropping out of college because of not being able to afford it is a travesty. It is expected by 2020 that 65% of Americas workforce will need either a bachelors or an associates degree (Carnavale 5). However if education becomes better funded and tuition rates drop due to it, then it is logical to believe that college dropout rates will decrease as well. As a result, more students will have a better chance of finishing their degree plan, have better odds of competing, and making a living wage in the career of their choosing. In conclusion, high tuition fees are negatively affecting students and their families. If fees were to drop, making education more affordable and accessible, not only would students stress levels be lowered, but their families would also reap the positive effects of not being financially burdened, while trying to ensure that students receive education. This would also give the student a better chance at accessing a higher paying career, rather than a lower paying job. For the student and the parent, there is nothing to lose by lowering college tuition, rather both gain peace of mind instead.

A Secret Weapon for Survey of Architecture Sample Essay Topics

A Secret Weapon for Survey of Architecture Sample Essay Topics Survey of Architecture Sample Essay Topics: the Ultimate Convenience! Do in-depth research When exploring your subject, you might need to study critical reviews regarding your topic. Closed-ended questions incorporate a list alternatives to pick from. If you're confused with a number of interesting topics to research on the web, it's much better to choose what interests you the most. The social issues research papers may appear easy to write in comparison with different topics, but still it demands an extremely creative strategy, a big quantity of curiosity and capacity to think beyond the box and search info in unconventional sources. The New Angle On Survey of Architecture Sample Essay Topics Just Released You may be requested to compose an essay about technology, education, media, family members, or another subject. Social networking is a cheap but efficient advertizing channel. The survey was piloted in a ne ighborhood university that provides graduate courses. If you are searching for assistance with your essay then we provide a comprehensive writing service offered by fully qualified academics in your area of study. Definitions of Survey of Architecture Sample Essay Topics You are able to likewise do the essays offered in the very first section of each one of the tests in the Official Study Guide. Writing the ideal survey questions for your paper is critical if you need to collect the info you're searching for. Information for this paper should come from a number of sources. Academic papers can't contain any signals of plagiarism. Selecting a research topic is something which everyone mostly goes about in the incorrect way. To make sure that you will see a complete answer to every question, we've got a support team that is always online. Open-ended questions usually ask people to compose some sort of short answer and don't provide respondents with a set of choices to select fr om. Closed-ended questions supply a list of alternatives for folks to pick from. What the In-Crowd Won't Tell You About Survey of Architecture Sample Essay Topics It is not important to us, whether you're too busy on the job concentrating on a passion undertaking, or simply tired of a seemingly infinite stream of assignments. A masterpiece is the consequence of simple and refined work. Fortunately, it's also somewhat less common. Instead, you've got to think of your own subject from a huge pool of possibilities. The Pain of Survey of Architecture Sample Essay Topics Paraphrasing the question at the beginning of the introduction signals that the writer of an Architecture essay intends to produce the work relevant from the start all the way through the finish. You will discover details about ways to select a topic and about architecture and its relationship with different arts. Architecture is the heart of life as it's critical for our modern times. The Secret to Survey of Architecture Sample Essay Topics Overall there are a lot of issues which may have resulted in the original defect in the property like a leak, damp, an issue with the gutters or rainwater goods, no matter how the remedy has to be found to the original problem or it might recur. While others wish to just demonstrate a subject. In the event you can't find your subject here, don't hesitate to have a talk with our staff and put an order for a customized history essay on your specific subject. Apparently, you don't need to babble, but I mean write about just 1 subject at one time. The topography of the website has to be assessed. The subjects listed on this page are somewhat universal and might not get the job done so great if you wish to develop a flawless history essay. You ought to be certain to understand everything clearly once you go for an essay topic. If you make your essay correctly, it will leave readers with a durable impression. If you wish to compose the essay yourself, we believe it would be best to pick a universal subject or issue. You should understand completely that you're not writing a descriptive essay. There's an amount of mathematical intuition an individual should know about when designing buildings and tall structures. Inside this way it's possible to collect important information about the wellness of a structure during construction and during its lifetime from a remote site. If you would like to have the own hard-earned volume of architecture then, you've got to compose a great architecture thesis. If for instance, you study architecture, there are several things which you could address in your final document. 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Augustinian Theodicy Free Essays

The Augustinian Theodicy From Augustine in his booke ‘Confessions’ in 397AD. His argument was that God is good and created a world perfectly good and free from defection, evil suffering. Based on Genesis 1-3 ‘Either God cannot abolish evil, or he will not. We will write a custom essay sample on Augustinian Theodicy or any similar topic only for you Order Now If he cannot, he is not all-powerful, if he will not he is not all-good. ‘ Augustine ‘The believer must have, in a cool moment, a solution to the problem of evil. If he does not, his faith is not rational†¦ ‘ Richard Swinburne The perfect world – â€Å"God saw all that he had made and saw that it was good. Genesis – Evil is a privation of good as darkness is a privation of light. – Humanity has free will to choose good over evil. The Fall – Natural moral evil exist because things fell short of what God intended. – â€Å"The penalty of sin corrects the dishonour of sin† Augustine. – God shouldn’t intervene because evil is the price of freedom. Humans can’t overcome the inevitably of them sinning. – The fall marks the entrance of evil into the world. (The fall being Adam’s mistake). – Humanity has an inherent guilt as descendants of Adam Eve (original sin). We have to ‘put up with’ what we have indirectly done to the Universe. The punishment for the original sin is ‘seminally present’. Intervention – There is hope through Jesus for all. This is a God given opportunity for those with good intentions to find a selfish reason for doing good. – Augustine’s theodicy is soul-deciding. Meaning we have a choice of path metaphorically in life. In this way Augustine tries to prove the righteousness of God. By showing that God was right not to intervene when we chose to do wrong against God. And that giving us the choice of giving our life to christ is a act of generosity. However this contradicts the idea of him being all-loving as this theodicy tells us that God would let there be a way to bring evil suffering into the world. But if he did not mean this, it either contradicts the fact that he is all-knowing or all-powerful. Basically†¦ God made a perfect world (is this true? ), humans committed the original sin (God does not have control), evil took the world, God didn’t intervene (as a just punishment), but he gave us a way to desire to be perfect. Natural evil – came through the loss in nature after ‘the fall’ Moral evil – came through the new knowledge of good and evil which was discovered through disobedience. Punishments: Separation from God. Expulsion from the garden of Eden. They must now live in a fallen world. Pain in childbirth. Struggle with the earth to yield a harvest. Tension between man and woman. Physical death. Old testament – God sends the law prophets to try and restore the relationship between humans and God. But these methods fail, leading to Jesus. New Testament – God sends Jesus. In Augustine’s eyes this was the best God had to offer. How to cite Augustinian Theodicy, Papers

Mendelian Genetics Lab Report Essay Example

Mendelian Genetics Lab Report Paper Its also the framework for the modern research that is making inroads in treating diseases previously believed to be incurable. In this era of genetic engineering the incorporation of foreign DNA into chromosomes of unrelated species?it easy to lose sight of the basics of the process that makes it all possible. These were his conclusions: The hereditary determinants are of a particulate nature. These determinants are called genes. Each parent has a gene pair in each cell for each trait studied. The Fl from a cross of two pure lines contains one allele or the dominant phenotype and one for the recessive phenotype. These two alleles comprise the gene pair. One member of the gene pair segregates into a gamete, thus each gamete only carries one member of the gene pair. Gametes unite at random and irrespective of the other gene pairs involved. (Carlson) The purpose of this lab is to teach students how traits of an organism can be predicted with a dibber cross using the recessive and dominant traits. Using a dibber cross given the phenotype and genotype of Fl (parents), the traits f offspring should be predictable with ratios derived from the dibber cross. Materials and Methods: Part A- Materials furnished are containers of green and albino seedlings. Count the number of green and albino seedlings, and add total number of seedlings. Then Calculate the ratio of green to albino seedlings. (stalagmite) Part B- A corn of ear was furnished, the ear of corn contains four different traits. We will write a custom essay sample on Mendelian Genetics Lab Report specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Mendelian Genetics Lab Report specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Mendelian Genetics Lab Report specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Each kernel can be one of two colors purple or yellow, each kernel can either be wrinkled or smooth (purple, yellow, wrinkled, smooth). Then determine the ratios in which each of the character traits is found and also what possible genotypes the parents might be. (stalagmite) Results: Part A- Observed Ratios of Green to Albino Seedlings # of green seedlings #balloon seedlings Ratio of green to albino seedlings 71 18 0. 83. 1, Total: 89 This graph shows that there is a ratio of green to albino seedlings. There were 71 green seedlings, and 18 albino seedlings, with a total of 89 seedlings.

Homeschool Stress

Homeschool Stress Homeschooling is a big responsibility and commitment. It can be stressful, but far too often we homeschooling parents make it more stressful than it has to be.   Are you guilty of stressing out yourself or your kids unnecessarily with any of the following? Expecting Perfection Expecting perfection in yourself or your children is certain to put unnecessary stress on your family. If you’re  transitioning from public school to homeschool, it’s important to remember that it takes time to adjust to your new roles. Even if your children have never  attended a traditional school, transitioning to  formal learning  with young children  requires a period of adjustment. Most veteran homeschooling parents would agree that this period of adjustment can  take 2-4 years. Don’t  expect perfection right out of the gate. You may be caught in the trap of  expecting academic perfection. is a  popular phrase among homeschooling parents. The idea is that you’ll stick with a topic, skill, or concept until it is completely mastered. You may hear homeschooling parents state that their children get straight A’s because they don’t move on until the skill is mastered. There is nothing wrong with that concept  Ã¢â‚¬â€œ in fact, being able to work on a concept until a child fully understands it is one of the benefits of homeschooling. However, expecting 100% from your child all of the time can be frustrating for you both. It doesn’t allow for simple mistakes or an off day. Instead, you may wish to decide on a percentage goal. For example, if your child scores 80% on his paper, he clearly understands the concept and can move on. If there is a certain type of problem that caused a grade less than 100%, spend some time going back over that concept. Otherwise, give yourself and your child the freedom to move on. Trying to Finish All the Books We homeschooling parents are also often guilty of operating under the assumption that we have to complete every single page of every piece of curriculum that we use. Most homeschool curricula contain enough material for a typical 36-week school year, assuming a 5-day school week. This doesn’t account for field trips, co-op, alternative schedules, illness, or a myriad of other factors that could result in not completing the entire book. It’s okay to finish most of the book. If the subject is one that is built on previously-learned concepts, such as math, chances are that the first several lessons of the next level are going to be review. In fact, that’s often one of my kids’ favorite aspects of starting a new math book  Ã¢â‚¬â€œ it seems easy at first because it’s material they’ve already learned. If it’s not a concept-based subject  Ã¢â‚¬â€œ history, for example -  chances are, you’ll come back around to the material again before your kids graduate. If there is material that you feel you simply must cover and you’re clearly not going to have time, you may want to consider skipping around in the book, dropping some of the activities, or covering the material in a different way, such as listening to an audiobook on the topic while running errands or watching an engaging documentary during lunch.​ Homeschooling parents may also be guilty of expecting their child to complete every problem on every page. Most of us can probably remember how happy we were when one of our teachers told us to complete only the odd-numbered problems on the page. We can do that with our children. Comparing Whether you’re comparing your homeschool to your friend’s homeschool (or to the local public school) or your kids to someone else’s kids, the comparison trap puts everyone under unnecessary stress. The problem with comparison is that we tend to compare our worst to someone else’s best. That causes self-doubt as we focus on all the ways we don’t measure up rather than capitalizing on what we’re going well. If we want to produce cookie-cutter kids, what’s the point of homeschooling? We can’t tout individualized instruction as a homeschool benefit, then get upset when our kids aren’t learning exactly what someone else’s kids are learning. When you’re tempted to compare, it helps to look at the comparison objectively. Is this something your child should probably know or be doing?Is it something that would benefit your homeschool?Is it a good fit for your family?Is your child physically, emotionally, or developmentally capable of performing this task or accomplishing this skill? Sometimes, comparing helps us identify skills, concepts, or activities that we would like to incorporate in our homeschools, but if it’s something that doesn’t benefit your family or your student, move on. Don’t let unfair comparisons add stress to your home and school. Not Allowing Your Homeschool to Evolve We may start out as staunchly school-at-home parents, but later learn that  our  educational philosophy is more  in line with Charlotte Mason. We  may  begin  as radical unschoolers  only to discover that our children prefer textbooks. It is not uncommon for a family’s homeschooling style to change over time, becoming more relaxed as they get more comfortable with homeschooling or becoming more structured as their  children grow older. Allowing your homeschool to evolve is normal and positive. Trying to hold on to methods, curricula, or schedules that no longer make sense for your family will likely put undue stress on you all. Homeschooling comes with its own set of stress-inducers. Theres no need to add more to it. Let go of unrealistic expectations and unfair comparisons, and let your homeschool adapt as your family grows and changes.

Explore These Free Online Macroeconomics Textbook Resources

Explore These Free Online Macroeconomics Textbook Resources Today, there are more resources available for economics students than ever before. This new knowledge-rich environment has opened the possibility for enriched learning and has made research more easily and readily accessible to the average economics student. Whether you are seeking to supplement your university studies, dig deeper into your economic research for a project, or drive your self-study of economics, we at About.com have compiled a series of excellent economics resources and assembled them into a comprehensive online macroeconomics textbook. Introduction to About.coms Online Macroeconomics Textbook About.coms online macroeconomics textbook is presented as a set of links to various resources and articles on key macroeconomics topics that are perfect for the economics beginner, undergraduate student, or someone just trying to brush up on the basic macroeconomics concepts. These resources present much of the same information as the classic hardcover textbooks listed on university course syllabi, but  in an easily accessible format that encourages fluid navigation. Also like those expensive economics textbooks that undergo revisions and updates as they are published in subsequent editions, our online macroeconomics textbook resources are always being updated with the latest and most useful information some of which is driven by readers like you!   While every undergraduate-level macroeconomics textbook covers the same core material within its many pages, each does so in a different order depending on the publisher and how the authors choose to present the information. The order we have chosen to present our macroeconomics resources is adapted from Parkin and Bades quintessential text,  Economics. Complete Online Macroeconomics Textbook CHAPTER 1: What is Macroeconomics? Compilation of articles that strive to answer this seemingly simple question, what is economics? CHAPTER 2: Unemployment An examination of the macroeconomics issues surrounding unemployment including, but not limited to, productivity and income growth, supply and demand of labor, and wages. CHAPTER 3: Inflation and Deflation A look at the basic macroeconomics concepts of inflation and deflation, including examinations of price levels, demand-pull inflation, stagflation, and the Phillips curve. CHAPTER 4: Gross Domestic Product Learn about the concept of gross domestic product or GDP, what it measures, and how it is calculated. CHAPTER 5: The Business Cycle Discover one of the keys to understanding how periodic but irregular fluctuations in the economy, what they are, what they mean, and what economic indicators are involved. CHAPTER 6: Aggregate Demand Supply Supply and demand at the macroeconomic level. Learn about aggregate supply and demand and how it influence economic relationships. CHAPTER 7: Consumption Saving Learn to analyze the economic behaviors of consumption versus saving. CHAPTER 8: Fiscal Policy Discover the policies and actions of the United States government that influence the American economy. CHAPTER 9: Money Interest Rates Money makes the world, or rather, the economic go round. Explore the various money-related economic factors that drive the economy. Be sure to check out this chapters subsections for a deeper exploration:- Money- Banks- Demand For Money- Interest Rates CHAPTER 10: Monetary Policy Like federal fiscal policy, the United Statess government also directs monetary policy that impacts the economy.   CHAPTER 11: Wages Unemployment Looking deeper into the drivers of wages and unemployment, be sure to check out the subsections of this chapter for further discussion:- Productivity Income Growth- Demand Supply of Labor- Wages Employment- Unemployment CHAPTER 12: Inflation Looking deeper into the drivers of inflation, be sure to check out the subsections of this chapter for further discussion:- Inflation Price Level- Demand-Pull Inflation- Stagflation- Phillips Curve CHAPTER 13: Recessions Depressions The phases of the business cycle are exaggerated with the occurrence of recessions and depressions. Learn about these deep falls in the economy. CHAPTER 14: Government Deficit Debt Discover the impact government debt and deficit spending has on the economy. CHAPTER 15: International Trade In todays global economy, globalization and international trade along with its concerns regarding tariffs, sanctions, and exchanges rates are consistently among the most debated issues. CHAPTER 16: Balance of Payments Explore the balance of payments and the role it plays in the international economy. CHAPTER 17: Exchange Rates Exchange rates are ever more important to an economys health as international trade continues to be a great influence on domestic economies. CHAPTER 18: Economic Development Beyond the borders of the United States, explore the economic issues faced by developing countries and the third world.

Law Assignment Example | Topics and Well Written Essays - 1000 words - 2

Law - Assignment Example Traditional dating was when a man asked a woman out several days prior to the day they were supposed to go dating if she was interested. The innovations made dating more casual that it was before. However, the question that bugs many people is; are hookups good or bad for women’s rights? According to England and Thomas, hook ups are when two people go out dancing, for movies and later on retire to a more private place for sexual encounters. Such encounters are aided with a lot of drinking. From the research that was carried out, more men enjoyed hookups than women did. The rates of satisfaction in women were low and many were not happy with their en counters. Many of the men hooked up with women that they had never seen before and in the morning, they could not remember their partners. Taking to perspective the fragile nature of the women emotions, it is then appropriate to say that hook ups are not in the best interests of the women. Many of the women leave the encounters emotionally bruised and the fact that they have not achieved the intended felling’s makes it more frustrating for women. As much as there is dating, hooking up or any other form of interaction people need to live together. This is what is called cohabitation; a living arrangement that is facilitated by agreement between two parties. Mostly this happens in members of the opposite sex. According to England and Thomas, the increase in heterosexual cohabitation has led to delayed marriages and an increase in divorce and caused one of the most significant changes in family life, as we have known it. It is believed that cohabitation had decreased the committed that is associated with marriage. Marriage used to be the foundation of sexual relations, living together among many other family related matters. Today people are joining up to live together without even being married. They are having children and even giving themselves names husbands and wives without

The World Film joural Essay Example | Topics and Well Written Essays - 1250 words

The World Film joural - Essay Example The film’s characters  exist  in  reality  making it more  real  and  intense; in fact, some of the cast resided in Rio de Janeiro at the time of shooting this film. City of God focuses on the tagline that if one chooses to  run,  the  beast  catches up with  them and, if they choose to  stay, the  beast  eats them. This is a moral dilemma which faces the characters in the film, who have to  choose  to either leave the crime-infested suburb or stay put and become affected by the organized crime. The film has received much acclaim on different aspects ranging from receiving four Academy Award nominations, the best writing (adaptation), directing, editing and cinematography. The film opens by chickens  being prepared  for a meal, but one of the chickens manages to escape and  is chased  by a  gang  member who meet Rocket, a  youth  who seems to  believe  that the gang is out to kill him. The film’s  excellent  cine matography comes out when the chicken halts between the Rocket and the armed gang member showing the  confusion  being witnessed  in the area by most young persons, unsure of which side to  follow; either the  bunch  of criminals or the  ordinary  person. Suddenly, we  are taken  back to Rocket’s childhood days where he is playing  soccer; here, we learn how the City of God  was established  in the late 1960s. ... This, in turn, endears the trio to the citizens, who  protect  the  former  and some young men even  idolize  them as heroes and saviors of the community. However, such idolization has detrimental effects for some of the boys in the City of God as seen through Li’l Dice, who manages to talk his counterparts into raiding a motel and robbing its occupants off their valuables. Being too young, Li’l Dice  is tasked  to serve as a lookout for the police, a move that angers Li’l Dice, who subsequently uses his issued gun to kill all the motel occupants. In the City of God, induction into the life of crime and gangs takes place at a tender age as evident through Li’l Dice  being given  a gun to  warn  his  crew  of police’ arrival. The law enforcement agencies  are brought  into the limelight upon the occurrence of the motel massacre. In the story, the police have a laid back attitude towards  criminal  gangs, choosing t o wait until a crime as grave as the massacre occurs before they  act  ((Lins and Entrekin, p. 113). Cohesion among members of criminal gangs is minimal as they  turn  against one another upon the slightest provocation. Li’l Dice, who appears to have enjoyed the act of killing, shots down his friend Goose after stealing from him. The film leaps forward into the 1970s where we note that Rocket has since joined a group of  youthful  hippies, the â€Å"Groovies†, who take part in smoking marijuana. Rocket’s  infatuation  with a girl draws him further towards his interest in photography.  However, his efforts of getting closer to the girl  are squashed  by â€Å"the Runts†, a group of young trouble seekers under the leadership of Li’l Dice who now refers to himself as Li’l Ze. Li’l Dice’s  evolution  into a drug king results in his wanton

Modelling Tool for Photonic Crystal Device Issues

Modelling Tool for Photonic Crystal Device Issues Chapter 4 SIMULATION DETAILS OF THE PROJECT In the past 10 years, photonic crystals (PCs) have attracted much scientific and commercial interest. The research and design work for PCs starts from accurate modal analysis of the device. Once the modes are found, structure can be simulated for that particular mode and the results of power spectra can be observed at the detector. In this chapter we will discuss about the modelling tool used for solving various problems related to photonic crystal device mentioned in next chapters. In our work, Opti-FDTD v11.0, a proprietary of Optiwave is used as a simulating tool to fulfill this purpose. 4.1 Introduction to FDTD Opti-FDTD is a user-friendly graphical interface that allows the designing of photonic devices in an efficient manner. It provides accurate computer aided simulations with the proper analysis of results. It is a powerful and highly integrated software package which is based on the finite-difference time-domain (FDTD) method. FDTD technique implies the solution of maxwell equations with finite-difference expressions for the space and time derivatives. FDTD schemes are especially promising for the investigation of PBG structures, as they provide an opportunity of analyzing the spatial distribution of the electromagnetic field in PBG structure. Opti-FDTD enables to design, analyze and test nonlinear photonic components for wave propagation, scattering, reflection, diffraction and other nonlinear phenomenon. The method allows for the effective simulation and analysis of structures with sub-micron details. Such fine scale implies high degree of light confinement and a large refractive ind ex contrast of materials to be used in design. Since FDTD method calculates electric and magnetic field at all points of computational domain, it is required for the domain to be finite. For this purpose, artificial boundaries are inserted in the simulation space. In FDTD perfectly matched layer (PML) acts as a absorbing layer for wave equations. In numerical methods, it truncates the computational regions while simulating problems. 4.2 Design Tools of Opti-FDTD Opti-FDTD is used to design photonic devices, simulate and analyze results. Design tools are available in toolbars and menu options. These tools include waveguide primitives, editing and manipulation tools, and special layout regions. Fig 4.1. Main layout of Opti-FDTD Designer Design tools of Opti-FDTD include designer, simulator and analyzer. 4.2.1 Opti-FDTD Designer This section created the desired layout on a wafer that is saved in a file with the extension .fdt. Opti-FDTD designer is opened from the start menu. This section enables a user to work on multiple layouts of project at the same time. One can store and retrieve projects using .fdt files. In addition to the standard cut, copy, and paste editing functions, we can: Scale elements or groups of elements swap overlapping elements snap elements to a grid of the layout zoom into or out of the project layout link elements together The main elements required to perform simulation of layout design include wafer, waveguide and input field. Wafer is the work area of design in Opti-FDTD. Each layout consists of only one wafer. It is a planar substrate on which we place and design the waveguides and cavities. The option of wafer properties is found in edit menu to modify the length, width and material of the wafer. Light wave propagates in Z-direction i.e. along the horizontal path on the screen. Discretization mesh is formed along the X-direction which corresponds to vertical path on the screen. Wafer is a necessary element for running a simulation. While starting a new project, the default material of wafer is air. Fig 4.2. Wafer coordinate system Waveguides are the building blocks of photonic circuits. Path perpendicular to the waveguide center defines the width of the waveguide. The default waveguide profile is air which can be changed while creating a new design. One can resize, rotate and move waveguides anywhere in the layout. Waveguide changes its color after selection. The orientation and shape of a waveguide can also be changed by dragging start/end handles. Properties of a waveguide can be viewed by double clicking it in the project layout. This opens the dialog box of waveguide properties where user can make required changes. Some major waveguide options provided by software include circular, elliptical and linear waveguides. From user point of view, waveguides can also be created by making some cells off in the photonic structure. Such a waveguide allows propagation of electromagnetic wave with minimum attenuation. The input field is an essential element in design to allow simulation to run. Its position is at an input plane which can be moved throughout the layout. It defines the light that enters the simulated structure. Geometric position of the input field and its orientation can be defined in the input field dialog box. Options available for input fields in the software are modal, gaussian, rectangular and user defined. The concept of input field is purely geometrical. It is a position and direction which defines a plane completely. Multiple input fields can be positioned on multiple input fields simultaneously. In a 2D design, input plane can be horizontal (perpendicular to X-axis) or can be vertical (perpendicular to Z-axis). Input field parameters must be defined carefully. The time domain parameters of input field can be specified as continuous wave or gaussian modulated continuous wave. Both the cases demand an input wavelength for the carrier wave. In Opti-FDTD all dimensions are defined in units of ÃŽ ¼m. Multiple input planes are distinguished with the help of ‘label’ facility provided by the software. Input wave can move in positive or negative direction depending on the option selected in the tab of wave configuration. An enable input field check box selects the input plane to be considered in calculation. Figures below show the placement of vertical and horizontal input plane. Fig 4.3. A vertical input plane for 2-D photonic crystal structure Fig 4.4. A horizontal input plane for 2-D photonic crystal structure Layout design in Opti-FDTD software includes profile designer, initial properties and layout designer. Profile designer define the material properties (refractive index of material) and channel profile. Initial properties set initial simulation domain properties including dimensions and material. Layout designer help to draw the lattice type (rectangular or hexagonal) and define the properties of the structure. 4.2.2 Opti-FDTD Simulator Opti-FDTD provides two types of FDTD simulations 32-bit simulation (performed by 32-bit simulators) 64-bit simulation (performed by 64-bit simulators) Opti-FDTD simulator monitors the progress, while the simulation is running. The simulation results are stored in a file with extension (.fda). After launching a 2-D simulation from Opti-FDTD designer, Opti-FDTD simulator displays the results of 2-D simulation. Fig. 4.5 shows the results of 2-D simulation for the structure shown in Fig. 4.3. Fig 4.5. 2-D simulation results (image map) in Opti-FDTD simulator Opti-FDTD simulator window contains output window and graph window. 4.2.2.1 Graph Window While running a 2-D simulation, a simulation window with several tabs appears. The first tab is the refractive index tab (Refr_Idx). Fig. 4.6 shows the refractive index distribution for the structure in Fig. 4.3. Fig 4.6. Refractive index distribution (image map) with palette Opti-FDTD simulator provides several types of views for graphs that include height plot and image map. Fig. 4.5 shows the image map of simulated field Ey. The height plot of the refractive index distribution of structure is shown in Fig. 4.7. Fig 4.7. Height plot of refractive index distribution 4.2.2.2 Output Window The output window contains notification and error tabs which display notifications regarding the status of simulations or any error that occur during simulation. Opti-FDTD simulator does not show this window by default. It can be accessed from tools menu. Figure below shows an example of output window. Fig 4.8. Output Window Simulation parameters can be accessed in Opti-FDTD_Simulator by selecting simulation > simulation parameters. For changing any of the parameters one should use Opti-FDTD_Designer. These parameters can’t be changed in simulator. Observation points can be used to obtain DFT and FFT transform. Observation line is used to observe power spectrum of the transmitted electromagnetic field. Opti-FDTD simulator provides the facility of PWE (plane wave expansion) solver. Fig 4.9. Simulation parameters dialog box Fig. 4.9. Simulation parameters dialog box The simulator provides tools for post-processing data analysis. Structure below shows the workflow of PBG structure analysis. Waveguide layout designer which provides necessary tools for designing a PBG crystal structure. After designing, PWE band solver simulation parameters are configured and PWE calculation is launched. After calculations results are automatically saved in .PND file and data is used for post-processing analysis. Fig. 4.10. Flow chart of PBG structure analysis The PWE band solver contains two windows including band diagram graph window and processing image window. PWE band solver graph window displays data of each eigen values based on each k-vector. During simulation, data is updated continuously from currently running calculations. Progress of calculations can be seen in the window. After completion of calculations, band diagram can be plotted either as band-gap data graph or line-connected data point graph. Fig. 4.11 shows a PWE band solver graph display for the structure shown in Fig. 4.3. Fig. 4.11. PWE band solver graph window Processing message window consist of notification and error tabs. This window displays textual information related to the activities performed in band solver. It provides notification on the k-vector value, tolerance, iteration number and time and date when results were being observed. Fig. 4.12 shows the notification window for the above-mentioned band solver. Error window displays notifications about processing errors. Fig. 4.12. Processing message window 4.2.3 Opti-FDTD Analyzer Opti-FDTD provides the facility to view power spectrum. Observation points are used for this purpose. To view the spectrum, observation area analysis can be accessed from tools menu. Fig. 4.13 shows the observation area analysis dialog box. Fig. 4.13. Observation area analysis dialog box The flow chart below summarizes the full procedure of designing, simulating and analyzing. Following algorithm is used to generate the flow chart. Create a new project Open Opti-FDTD designer Initialize the project Open waveguide profile designer Define the material Define 2-D channel profile Set up initial properties Create a design Draw a PBG crystal structure Set up the lattice properties Insert input plane Set up the input plane Insert observation lines Observe refractive index distribution Observe the refractive index distribution Set up observation lines Run the simulation Set up the simulation parameters Run 32-bit simulation Fig. 4.14. Flow chart of processing of photonic crystal structure using Opti-FDTD [ Courtesy: Ref. [28] ] Analyze the simulation results Open Opti-FDTD analyzer Observe power spectrum Export results The block diagram illustration of the same is depicted in Fig. 4.15. Fig. 4.15. Opti-FDTD block diagram [ Courtesy: Ref. [28] ] Opti-FDTD analyzer first loads the files and processes it to simulator. Simulator runs the proposed design and exports data to other file formats [30]. Further chapters provide the methodology to improve the performance of photonic crystal biosensors. They also explain the application of such device in the emerging field of DNA photonics. A comparative account is also prepared between the performances of photonic crystal biosensor and surface plasmon resonance biosensor which proves the superiority of PC biosensors over SPR devices.

Daily Routines

Your Daily Routines: Then and Now Day| Before College| After College| Sunday| My daily routine before college on a Sunday was to attend church service and was to decide what our Sunday dinner plans were. | My daily routine now that I am enrolled in college on a Sunday are to attend church service, decide what our Sunday dinner plans are, and to make sure that all of my assignments and discussion questions are submitted, and all participation posts are completed for the week. .| Monday| My daily routine before college on Mondays were to go to work and come home to watch my favorite TV shows to wind down from my day. My daily routine now that I am enrolled in college on a Monday is to go to work try to complete a participation post or a discussion question during my lunch break, and then come home and make dinner while studying. | Tuesday| My daily routine before college on Tuesdays were to go to work and come home to watch my favorite TV shows to wind down from my day. | My daily rout ine now that I am enrolled in college on a Tuesday is to go to work try to complete a participation post or a discussion question during my lunch break, and then come home and make dinner while studying. Wednesday| My daily routine before college on Wednesdays go to work and come home to watch my favorite TV shows to wind down from my day. | My daily routine now that I am enrolled in college on a Wednesday is to go to work try to complete a participation post or a discussion question during my lunch break, and then come home and make dinner while studying. | Thursday| My daily routine before college on Thursdays were go to work and come home to watch my favorite TV shows to wind down from my day. My daily routine now that I am enrolled in college on a Thursday is to go to work try to complete a participation post or a discussion question during my lunch break, and then come home and make dinner while studying. | Friday| My daily routine before college on Fridays were go to work and come and decide what our weekend plans were with our friends are and maybe have a date night. | My daily routine now that I am enrolled in college on a Friday is to go to work try to complete a participation post or a discussion question during my lunch break, and then come home to spend time with my husband. Saturday| My daily routine before college on a Saturday was to sleep in late, make a nice lunch fore my husband and then go out with friends and enjoy each others company later that night. | My daily routine now that I am enrolled in college on a Saturay is to wake up a bit earlier than usual to try to complete a participation post or a discussion question before cleaning my house and going out with friends. | What are the major differences in your daily routine now that you are in school? The major differnces that I see now that I am back in school are that I have a more structured schedule and am able to focus on completeing assignments before doing extracuricular activities. Have you included enough time into your schedule for academics? What information in the chart demonstrates evidence to support your answer? I have included enought time into my schedule for academics by cutting out alot of television watching and minimizing the activites I do with friends prior to completeing my class work. The information on the chart that demonstrates evidence of this is there not being any extra activites or television watching during the week or prior to completeing assignments. Do you have an effective balance in the use of your time and your priorities? Why or why not? I do feel that I have an effective balance in the use of my time and my priorities by my cutting out the things that will not assist me in acgieving my goal of and education and earning my diploma. I have substituted watching television by watching the web tutorials. What are some time management strategies you have learned this week that you can implement to make your daily routine effective? A time management strategy I have learned this week is to learn to comprimise with myself I have to buckle down and do my works on certain days so that I can reward myself and be afforded the time for fun activities on other days when my classwork has been completed.

Use of sandwich structures - Free Essay Example

Sample details Pages: 27 Words: 8221 Downloads: 6 Date added: 2017/06/26 Category Statistics Essay Did you like this example? CHAPTER 1 INTRODUCTION 1.1 Introduction The use of sandwich structures has been increasing in recent years because of their lightweight and high stiffness. Commonly, the naval industry and transportation uses the E-glass fibers while the aerospace industry uses composite structures such as carbon fiber. The use of sandwich panels with composite facesheet in the naval industry is particularly appealing because they have better corrosion and environmental resistance and reduced magnetic signatures when compared to double-hull construction steel ships. Don’t waste time! Our writers will create an original "Use of sandwich structures" essay for you Create order On the other hand, composite sandwich panels are easily susceptible to damage by a strange object impact. The damage may be visible, penetration or perforation, or invisible, internal delamination and debonding. Both types of damages will result in stiffness and strength reduction. It is then important to study the impact behavior of composite sandwich panels. Failure in composite structures can be caused by low, high and extremely high or localized impact. An impact caused by a foreign body initiates two waves from impact point in a panel: a through-thickness wave and a transverse shear wave. Whether or not these waves play an important role in the impact response of the panel depends on the actual contact duration between the projectile and panel and the time it takes the transverse shear wave to reach the panel boundary. Figures 1.1 (a)-(c) show three-impact scenarios: low-velocity, high-velocity and ballistic impact. In low-velocity impact, the contact force duration is long compared to the time it takes the transverse shear wave travel to reach the plate boundary. Many waves reflect back and forth across the side dimension of the panel. In high-velocity impact, the contact force duration is much shorter than the transverse shear wave travel time through the panel. Usually high-velocity impact is the same with perforation and localized damage of the panel. Ballistic impact deals only with through-thickness wave propagation. During ballistic impact, there is complete perforation of the panel with little or no panel deformation. The contact force duration is approximately the wave travel time through the panel thickness. Ballistic impact usually involves the study of penetration mechanics. Low-velocity High-velocity Ballistic Impact The projectile to panel mass ratio will control whether wave propagation effect dominates the panel impact response and then suggested that a mass ratio be use as a parameter to determine impact response. It was shown that small mass impacts produce more damage than high-mass impacts having same kinetic energy. While small-mass impacts were defined by wave-controlled response, large mass impacts were defined by boundary-controlled response. Common examples of low-velocity impact are of bird strikes, collision with floating object, and dropped tools, may cause damage. Underwater blast or debris from a faraway explosion and air was considered as a high-velocity impact situation. Examples of ballistic impact would be a bullet or fragments from a nearby explosion hitting the panel. Another important factor governing the impact on composite structures is the ballistic limit. The ballistic limit is defined as the highest velocity of the projectile to cause perforation. When the residual velocity (exit) of the projectile is zero, then the initial velocity of the projectile that causes perforation is the ballistic limit of the sandwich panel. The ballistic limit may be calculate analytically or determined experimentally. In the experimental method, sandwich panels are shoot with projectiles over narrow range of velocities to either just cause penetration or to just perforate the panel. There exists a striking velocity at which 50% of the panels are completely perforate above this value and remaining 50% are partly penetrate below this value. This striking velocity is expresse as V50, which is the ballistic limit of the panel. In the analytical approach, the ballistic limit is determined by the conservation of energy principle. The approach is complex because it inc ludes a variety of factors like core thickness, facesheet thickness, shape of the projectile, core crushing stress, and so on. 1.2 Problem Statement This topic was an expansion of the Wan Awis research. He has done only an experimental work. For impact application, we need to predict skin and core material thickness. Since impact phenomena depend on numerous parameters such as material properties or projectile geometry, a numerical model, validated experimentally, is necessary to allow the study of the influence of several parameters without making costly experimental tests. This will definitely enhance the development of our military technology and achievements in the future because of the ability of this software to cut production cost and time consuming of the experimental work. The numerical figures have been compared to modal test results aiming mainly to validate the studies. Simulation based on finite element analysis (FEA) must not exceed 15% error or this simulation could be claimed not acceptable. 1.3 Objective To simulate the damage of composite sandwich structures subjected to high-velocity impact using finite element analysis. To determine the energy absorption capability of the components on the behavior of the sandwich panel under impact load using ANSYS AUTODYN 13.0 To validate a numerical model with actual experiment. 1.4 Scope of Works To characterize a mechanical behavior of carbon fiber panel by using tensile and determine the fiber volume force and density. Design and validate the numerical model. Conduct a ballistic impact test simulation. Using the experiments data to calculate the energy absorption on the impact. CHAPTER 2 LITERATURE REVIEW 2.1Introduction A great deal of research has been conducted in the area of impact of composite structures. In this chapter, previous work done on the impact response of laminated composite plates and composite sandwich panels will be reviewed. 2.2Impact of Composite Laminates A detail study of impact of composite laminates in the three impact regimes ballistic impact, low-velocity and high-velocity is presented in this section. 2.2.1Low-velocity Impact Abrate, 1998 give a specific review on different analytical models of impact on composite laminates. He classified impact models into four groups: impact on infinite plate model, energy balance models, spring-mass models, and complete models. In the energy balance model, the initial kinetic energy of the projectile is used to calculate the deformation of the composite laminate. The velocity of the projectile reaches zero at the maximum deflection of the composite laminate. At this point, all of the kinetic energy of the projectile is converted to strain energy needed to deform the composite laminate. Energy balance model assumes that the structure behaves in quasi-static manner. The time history of force and deflection are obtained using the spring-mass model representing the composite laminate. The model shown in Figure 2.1 consists of nonlinear contact stiffness (K), one spring representing the linear stiffness of the structure (Kbs), another spring for the nonlinear membrane stiff ness (Km), effective mass of the structure (M2) as well as the mass of the projectile (M1). Equations of motion are written from a free body diagram. The infinite plate model is used when the deformation wavefront has not reached the boundary but if the wave reaches the plate boundary then this model is not an appropriate one to use. In the complete model, the dynamics of the structure and projectile are taken into explanation. Appropriate plate theory has to be selected and used. In many cases the classical plate theory can be used but when transverse shear deformations become significant, higher-order theories must be used. One of the earliest studies on the impact of composite laminates was by Goldsmith et al, 1995, who conducted high-velocity and quasi-static impact tests on carbon-fiber laminates by using a cylindro-conical projectile. Three different specimen of varying thickness were considered. Energy balance principle was used to predict the dynamic penetration energy, static penetration energy, and also the ballistic limit of the composite laminate. The fiber failure accounted for most of the energy absorbed. The predicted theoretical energy was in good agreement with measured energy for thin laminates but not for the thick laminates. This was approved to the fact that transverse shear deformation played an important responsibility in thick laminates subjected to low-velocity impact. The effect of transverse shear deformation was not dominant due to its quick occurrence in the high-velocity impact of laminates. Therefore, the predicted energy in the dynamic case was always close to but less than the measured energy for the thin and thick laminates. The predicted ballistic limit was less than measured values due to the nonlinear factors. Cantwell, 2007 studied the influence of target geometry in the low-velocity impact of composite laminate. The tests were performed on GFRP plates with hemispherical indenter on either circular or square supports. He used energy-balance model to predict the plate deflection and the delamination area of the laminated structure. His study stated that there is little or no influence of target geometry on the failure modes. It also suggested that delamination was dependent on interlaminar shear stress and increasing the plate diameter required more energy for damage initiation. Hou et al., 2000 predicted impact damage in composite laminates using LSDYNA 3D. The numerical results were compared to experimental results on low-velocity impact on composite laminate with an initial velocity of 7.08 m/s The Chang-Chang failure criteria was modified taking the shear stress into consideration and the model was implemented in DYNA 3D. 2.2.2 High-velocity Impact In 1988, Cantwell performed high-velocity impact tests of CFRP laminates with 6 mm diameter, 1g steel ball as the projectile. The influence of fiber stacking sequence and target geometry was study. The experiments reveal that varying the target geometry had no significance on initial damage caused. While the damage initiated in the distal facesheet in thin laminates, however, in thick laminates it initiated from incident facesheet. Zhao et al., 2007 investigated the failure modes in composite laminates subjected to high-velocity impact. Three different laminates were subject to impact by hemispherical projectile in the range of 10-300 m/s. An energy balance was considered and equations for residual velocity for the laminates were given in terms of the mass of the projectile and striking velocity. The thickness and stacking sequence were finding to play an important role in the energy absorption. Cheng et al., 2007 developed an analytical model based on the spring-mass model for high-velocity impact of a blunt ended and a sharp-ended projectile on thick composite laminates. They considered the effect of moving boundary due to the propagation of shear wave. The analysis was modeled using series of quasi-static events. At the end of each quasi-static step, the failed layers were remove based on punch shear damage and fiber damage criteria, and the wave front was moved outwards. While the first spring stiffness constant was measure based on the penetration depth of the projectile, the second spring stiffness constant was measured based on the bottom node of the plate. 2.2.3 Ballistic Impact Silva et al., 2005 performed numerical simulations of ballistic impact on thin Kevlar 29 composite laminates using a fragment-simulating projectile. The laminate material model was simulating using AUTODYN and the projectile was modeled using Johnson-Cook strength model. Finite element mesh for both laminate and projectile was generating using True Grid. Accurate predictions of ballistic limit (V50) and the failure modes were made. Ballistic limit is the minimum velocity of impact at which a given projectile just perforates a given target. On occasion, the term is also used to identify the maximum impact velocity at which the projectile can penetrate into the target with perforation. It is often defined statistically as the impact velocity for which the projectile has a 50% probability of perforating the target; it is then denoted by V50. Guild et al., 2007 conducted numerical simulations of ballistic impact on composite laminates and compared them with experimental results. The laminates were made of E-glass/vinyl ester resin with varying thickness and ball bearings of varying mass were use as projectiles. The damage modes included fiber failure, matrix failure, penetration, and delamination. Hashin failure criteria was use to determine the damage mode. Delamination was modeled using an interface between the two plies. As the force increased between two nodes above the specified value, the nodes were untied and the delamination increased. The ballistic limit from experiments was in good agreement with numerical results Naik et al., 2008 studied the ballistic impact behavior of thick composites. E-glass/epoxy laminates of varying thickness were subject to high-velocity impact. The effects of projectile diameter, projectile mass and laminate thickness on the ballistic limit were studied. Wave theory and an energy balance were use to predict the ballistic limit of the laminate. The contact duration of the projectile with the laminate was maximum when the initial velocity was equal to ballistic limit and decreased when the initial velocity increased beyond the ballistic limit. Deka et al., 2008 conducted ballisitic impact on E-glass/polypropylene composite laminates with cylinder-shaped projectiles. The experimental results were validating with numerical analysis using LS-DYNA. Although the laminate was modeling in Hypermesh, LS-DYNA was used to analyze failure mechanisms. The analytical model was base on energy conservation and failure in the numerical analysis was predicted based on Hashins failure criteria. 2.3 Impact of Composite Sandwich Panels In this section, a detail study of impact of composite sandwich panels in the three impact regimes low-velocity, high-velocity and ballistic impact is presented. 2.3.1 Low-velocity Impact Mines et al., 1998 investigated quasi-static loading and low-velocity impact behavior on two different composite sandwich panels. While the first panel was made up of E-glass/vinyl ester skin and Coremat core, the second panel was made of Eglass/epoxy skin and aluminium honeycomb core. The first panel with Coremat core had failed in the sequence of core shear, debonding, and distal facesheet damage and incident facesheet failure. The second panel failed by core shear, debonding, incident facesheet failure and then distal facesheet failure later. In the low-velocity impact tests, the failure pattern remained the same in both the panels as of the quasi-static tests. The core properties and impact velocity govern the energy absorption capability of the sandwich panel. Wen et al., 1998 investigated the penetration and perforation of composite laminates and sandwich panels under quasi-static, drop-weight and ballistic impact tests by flat-faced, hemispherical-ended and conical-nosed indenters/projectiles. They categorized the impact on laminates and sandwich panels into low-velocity impact and wave-dominated (high-velocity/ballistic impact) response. It was also stated in the research that sandwich panels subjected to low-velocity impact have similar load-displacement characteristics as of quasi-static loading case. The perforation energy required by flat faced projectile was more than hemispherical-ended and conical shaped projectiles in high-velocity impact. Schubel et al., 2005 investigated quasi-static and low-velocity impact behavior of sandwich panels with woven carbon/epoxy facesheets and PVC foam. The low-velocity impact model behaved similar to quasi-static loading case when loads and strain levels were same. The static indentation response was compared to the numerical results obtained using ABAQUS and were in good agreement. A membrane solution, assuming membrane in the core affected region and plate on elastic foundation in the rest of sandwich panel was in poor agreement with the numerical results. Hoo Fatt et al., 2001, developed static and dynamic models of sandwich panels subjected to low-velocity impact. They investigated the behavior of sandwich panels having carbon/epoxy skins and a Nomex honeycomb core with a hemispherical indenter under various support conditions such as simply supported, fully clamped, and rigidly supported. Spring-mass models were considered to determine the load-displacement curve. They also investigated the damage initiation of sandwich panels under low-velocity impact loading. The initial mode of damage depended upon the panel support conditions, projectile nose shape, geometry of the specimens, and material properties of the facesheet and core. Various failure patterns were studied and solutions based on them were derived separately. The analytical solution for the ballistic limit was also found and results for thick laminates were in better agreement than thin laminates. Suvorov et al., 2005 performed numerical analysis on sandwich panels with foam core and studied the effect of interlayer in between the top facesheet and foam core. The foam core was modeled as crushable foam in ABAQUS. While the polyurethane (PUR) interlayer reduced the deformations in both the core and the composite facesheets, the elastomeric foam (EF) interlayer offered a better protection for the foam core alone. Besant et al., 2001 performed numerical analysis on sandwich panels with aluminium honeycomb core. The metal honeycomb core was modeled as elastic perfectly plastic material. A quadratic yield criterion was proposed for the core material, which included both normal and transverse shear stresses. The importance of core plasticity in finite element analysis was explained. 2.3.2 High-velocity Impact A great deal of work has been done in the area of low-velocity impact of laminates and sandwich panels and high-velocity impact of laminates but limited work has been presented in the domain of high-velocity and ballistic impact of sandwich panels. The following describes some recent studies on the high-velocity impact of composite sandwich panels Velmurugan et al., 2006 studied the projectile impact on composite sandwich panels in the range of 30-100 m/s. The sandwich models in this study were not the typical sandwich panels in the conventional sense. They had a core height comparable to the facesheet thickness and acted as a bonding agent between the facesheets. Energy-balance model was used to determine the ballistic limit of three different sandwich panels. They assumed the sandwich panel as a single plate since the foam layer was thin and comparable to facesheet thickness. Also uniform failure mechanism along the through thickness direction was assumed in their model. Skvortsov et al., 2003 developed an analytical model using energy-balance principle to determine the ballistic limit of composite sandwich panels subjected to high velocity impact. Two different sandwich panels were subjected to high velocity impact using three different projectiles. These tests were conducted on simply supported and rigidly supported boundary conditions, and the initial velocity was varied in the range of 70-95 m/s. The predicted panel energy was close to the experimental values and the error was due to the strain-rate effects, plastic behavior, and hardening phenomena, which are not consider in the analysis. 2.3.3 Ballistic Impact Kepler et al., 2007 conducted ballistic impact on sandwich panels consisting of GFRP plates and Divinycell H80 core, with three different projectiles. Lumped spring mass model was use to calculate force histories and panel response. Concentric rings connected by shear springs represented the sandwich panel. In this model, core shear deformation was assumed as the single significant contributor to the sandwich panel stiffness. The facesheet orthotropic was neglected in the panel response. Four different force histories: constant force, triangular force, sine series, and combination of sine and triangular force were used to calculate the energy loss in the panel. Of these, triangular and combined force gave results in better agreement with experimental results. 2.4Aluminium Honeycomb For design and construction of lightweight transportation systems such as satellites, aircraft, high-speed trains and fast ferries, structural weight saving is one of the major considerations. To meet this requirement, sandwich construction is frequently use instead of increasing material thickness. This type of construction consists of thin two facing layers separated by a core material. Potential materials for sandwich facings are aluminium alloys, high tensile steels, titanium, and composites depending on the specific mission requirement. Several types of core shapes and core material are been applied to the construction of sandwich structures. Among them, the honeycomb core that consists of very thin foils in the form of hexagonal cells perpendicular to the facings is the most popular. A sandwich construction provides excellent structural efficiency, i.e., with high ratio of strength to weight. Other advantages offered by sandwich construction are elimination of welding, superior insulating qualities and design versatility. Even if the concept of sandwich construction is not very new, it has primarily been adopt for non-strength part of structures in the last decade. This is because there are a variety of problem areas to be overcome when the sandwich construction is applied to design of dynamically loaded structures. Other investigators have previously carried out noteworthy theoretical and experimental studies on linear elastic and nonlinear behavior of aluminium sandwich panels. Kelsey et al., 1985 derived simple theoretical expressions of the shear modulus of honeycomb sandwich cores. Witherell, 1977 performed an extensive theoretical study for structural design of an air cushion vehicle hull structure using aluminium honeycomb sandwich panels. Okuto et al., 1991 showed the validity of the so-called equivalent plate thickness method in which a honeycomb sandwich panel subjected to inplane loads is approximately replaced by a single skin panel with equivalent plate thickness. Kobayashi et al., 1994, studied Elasto plastic bending behavior of sandwich panels. An experimental study was undertaken by Yeh et al., 1991 to investigate the buckling strength characteristics of aluminium honeycomb sandwich panels in axial compression. Kunimo et al., 1989 both, have studied the characteristics of the energy absorption capacity of bare honeycomb cores under lateral crushing loads theoretically and experimentally. 2.5 Ballistic Limit The ballistic limit may also be defined as the maximum velocity at which a particular projectile is expected to consistently fail to penetrate armor of given thickness and physical properties at a specified angle of obliquity. Because of the expense of firing tests and the impossibility of controlling striking velocity precisely, plus the existence of a zone of mixed results in which a projectile may completely penetrate or only partially penetrate under apparently identical conditions, statistical approaches are necessary, based upon limited firings. Certain approaches lead to approximation of the V50 Point, that is, the velocity at which complete penetration and incomplete penetration are equally likely to occur. Other methods attempt to approximate the V0 Point, that is, the maximum velocity at which no complete penetration will occur 2.6 Energy Absorption Mechanism of Composite Materials The research was done by Naik and Shrirao at 2004. Impact loads can be categorized into three categories which is low-velocity impact, high-velocity impact and hyper-velocity impact. This classification is made because of change in projectiles velocity will result in different mechanisms in terms of energy transfer between projectile and target, energy dissipation and damage propagation mechanism. Basically, ballistic impact is considered as low-mass high velocity impact. In this impact event, a low-mass projectile is launched by source into target at high velocity. It is unlike low-velocity impact that involved high-mass impactor impacting a target at low velocity. In view of the fact that ballistic impact is high velocity event, the effect is localized and near to impact location. According to Naik et al. (2006), seven possible energy absorbing mechanisms occur at the target during ballistic impact. Those mechanisms are cone formation at the back face of the target, deformation of secondary yarns, tension in primary yarns/fibres, delamination, matrix cracking, shear plugging and friction between the projectile and the target. Then, the researchers formulated all these energies into equation whereby the total energy absorbed by the target is summation of kinetic energy of moving cone EKE, shear plugging ESP, deformation of secondary yarns ED, tensile failure of primary yarns ETF, delamination EDL, matrix cracking EMC and friction energy EF. ETOTALi = EKEi + ESPi + EDi + ETFi + EDLi + EMCi + EFi Mines et al. (1999) identified three modes of energy absorption when analysed the ballistic perforation of composites with different shape of projectile. These energy absorptions are local perforation, delamination and friction between the missile and the target. However, the contribution of friction between the missile and the target in energy absorption is low compared to the other two. In terms of local perforation, three through-thickness regimes can be identified, namely: I shear failure, II tensile failure and III tensile failure and delamination. Out of these three regimes, the through-thickness perforation failure is dominated by shear failure. Similar observation has been made by other researcher for thick graphite epoxy laminates whereby the perforation failure is dominated by shear failure. The third main energy absorption mechanism is delamination. Delamination can propagate under Mode I (tensile) and Mode II (shear) loading and each mode can dominate each other depen ding on structural configuration of the composite as well as material properties. Therefore, it can be predicted that the total perforation energy is a summation of energy absorption due to local perforation, delamination and friction between the missile and the target. Epred = Ef + Esh + Edl where Ef = friction between the missile and the target; Esh = local perforation; Edl = delamination Apart from that, Morye et al. (2000) has studied energy absorption mechanism in thermoplastic fibre reinforced composites through experimental and analytical prediction. They considered three mechanisms that involved in absorbing energy by composite materials upon ballistic impact. The three energy absorption mechanisms are tensile failure of primary yarns, elastic deformation of secondary yarns and the third mechanism is kinetic energy of cone formed at back face of composite materials. They concluded that kinetic energy of the moving cone had a dominant effect as energy absorption mechanism for composite materials. However, they neglected a delamination as one of the factor contributed to the failure of composite materials during ballistic impact. 2.7 Kinetic Energy Equation Kinetic energy (KE) attack is a penetration of the residual energy of a projectile. A projectile can give a certain amount of energy to attack and damage a vehicle if the projectile sufficient residual energy when it arrive at the target. This residual is very important to overmatch the capability and strength of the target material to resist penetration, and then it will penetrate. Kinetic energy shot can be presented with the simple law of physic. K.E = Mprojectile Vprojectile2 Increasing the mass (Mprojectile) of the shot increases its energy, but the real payoff comes from increasing its velocity (Vprojectile). If the diameter of the shot fills the whole gun barrel, the projectile becomes heavier and difficult to accelerate to required velocity with the length of the barrel. Additionally, a large diameter solid shot will provide more energy to penetrate the armour plate compared to a projectile which has the same mass but a smaller diameter. Consequently, the larger shot is not only less effective at the target but it is difficult to give it the necessary velocity. According to Chang et al., 1990, depth of penetration at the target will depend not only on residual energy, but also on shape and size of the projectile. The curve shape at the projectile head is more important, as it must not only able to pierce the armour but the shoulders of the shot must also support the remainder so that it does not break up on its way through the armour. If for given mass the diameter of the shot is reduced and is length increased, then for the same residual energy the shot will penetrate further, as it is working on a smaller cross section area of armour. The ratio of length-to-diameter is called slenderness ratio. Any projectile with ratio in excess of 7:1 cannot be spin stabilized it is not until they reach a ratio approximately 20:1 that they can call long rod. So, based on those discussions above, we can conclude that energy absorption can be performed by this relation Eabsor = Ein Eout = [ Mprojectile Vin2] [ Mprojectile Vout2] = Mprojectile (Vin2 Vout2) So, Eabsorbed = Mprojectile (Vin2 Vout2) 2.8 Tsai-Hill Failure Criterion Hill, 1950 proposed a yield criterion for orthotropic materials: G+H12+F+H22+F+G32-2H12-2G13-2F23+2L232+2M132+2N122=1 This orthotropic yield criterion will be used as an orthotropic strength or failure criterion in the spirit of both criteria being limits of linear elastic behavior. Thus, Hills yield stresses F, G, H, L, M and N will be regarded as failure strengths. Hills criterion is an extension of von Mises yield criterion. The von Mises criterion, in turn, can be related to the amount of energy that is used to distort the isotropic body rather than to change its volume. However, distortion cannot be separated from dilatation in orthotropic materials, so Equation 2.8 is not related to distortional energy. Unfortunately, some authors still mistakenly call the criterion of Tsai-Hill a distortional energy failure criterion. The failure strength parameters F, G, H, L, M and N were related to the usual failure strength X, Y, and S for a lamina by Tsai. If only 12 acts on the body, then, because its maximum value is S, 2N=1S2 Similarly, if only 1 acts on the body, then G+H=1X2 And if only 2 acts, then F+H=1Y2 If the strength in the 3-direction is denoted by Z and only 3 acts, then F+G=1Z2 Then, upon combination of Equations (2.10), (2.11) and (2.12), the following relations between F, G, H and X, Y, Z result: 2F=1Y2+1Z2-1X2 2G=1X2+1Z2-1Y2 2H=1X2+1Y2-1Z2 For plane stress in the 1-2 plane of a unidirectional lamina with fibers in the 1-direction, 3 = 13 = 23 = 0. However, from the cross sectional of such a lamina in Figure 2.3, Y = Z from the obvious geometrical symmetry of the material construction. Thus, Equation (2.8) leads to 12X2-12X2+22Y2+122S2=1 as the governing failure criterion in terms of the familiar lamina principal strengths X, Y, and S. And, the appropriate values of Xt or Xc and Yt or Yc must be used depending on the signs of 1, 2, 12 (except that the surface is symmetrical about the plane 12 = 0 because S has only one value). Finally, for the off-axis composite material example of Tsai-Hill failure criterion, substitution of the stress-transformation equations, 1=xcos2 2=xsin2 12=-xsincos In Equation (2.14) yields the Tsai-Hill failure criterion for uniaxial off-axis strength, cos4X2+1S2-1X2cos2sin2+sin4Y2=1X2 which is one criterion. Because a composite lamina usually has different strengths in tension and compression, the values of X and Y must take on the appropriate values depending on the quadrant of stress space consists of four different segments that are continuous in value but not in slope at the uniaxial strengths. The Tsai-Hill failure criterion appears to be much more applicable to failure prediction for this composite material than either the maximum stress criterion or the maximum strain failure criterion. Other less obvious advantages of the Tsai-Hill failure criterion are: The variation of strength with angle of lamina orientation is smooth rather than having cusps that are not seen in experimental results. The strength continuously decreases as grows from 0 rather than the rise in uniaxial strength that is characteristic of both the maximum stress and the maximum strain criteria. The maximum stress and strain criteria are incorrect by 100% at 30. Considerable interaction exists between the failure strengths X, Y, S in the Tsai-Hill failure criterion depends on whether the material being studied is ductile or brittle. Other composite materials might be better treated with the maximum stress or the maximum strain criteria or even some other criterion. 2.9 Finite Element Analysis This subheading starts with a brief introduction to AUTODYN and then follows this with an overview of the SPH implementation carried out. Aizawa et al., 1980 has conducted the research about the AUTODYN software. The AUTODYN software is widely used to simulate non-linear impact phenomena involving large strains and deformations, plasticity, fracture, and flow. The software, available on PCs to supercomputers, is packaged in an interactive, integrated environment wherein the pre- and post-processing and the analysis are contained in a single menu-driven architecture. The software encompasses a number of different numerical approaches for the analysis of impact problems. Within the software, Lagrange, Euler, ALE (Arbitrary Lagrange Euler), Shells, and SPH (Smooth Particle Hydrodynamics) numerical processors (solvers) are available. Impact processes ranging from equipment drop tests to the hypervelocity impact of space debris on a spacecraft can be modeled. Related study also been done by N.K.et al., 1987. The results of a number of analyses are present to highlight the advantages and disadvantages of each numerical technique for different classes of impact applications. It is shown that the selection of the appropriate numerical technique or combination of technique is critical to achieving both an accurate and computationally efficient solution. Impact case studies presented include: Hypervelocity impact of space debris on a shielded spacecraft Impact and penetration of ceramic armor by a steel projectile Oblique impact and ricochet of a steel sphere on RHA armor Impact and crush of a steel girder Explosive formation of an oil well perforator with subsequent impact and penetration on a layered steel/concrete structure The solutions illustrate the use of different numerical techniques with emphasis on efficiency and accuracy. Validation of results with available experimental data is shown. Animations of the numerically simulated impact phenomena can be shown directly from the AUTODYN software. CHAPTER 3 SIMULATION METHODOLOGY This chapter provides the detailed description of method of approach used in carrying out the present study. This includes the strategies that have been design to serve guidelines throughout the process of the study and to assist in achieving the desired objectives. An outline of the methodology is first present in a flow chart to provide an overview of the whole process, followed by detailed discussion of the outline and elaboration of key procedures and techniques employed in the simulations. Flow of my methodology consists the methods that been took in order to accomplish the expected results. Figure 3.1 showed the complete flow of methodology for this research. First thing to do is to make some researches about the topic chosen. All information was gathered through readings from related journals and thesis did some diggings through numerous interviews to get a clear figure about this topic. Next step, study and learn about the simulation program that is going to be used in this research, ANSYS AUTODYN and based on previous researches from literature reviews paper and results, we try to validate whether ANSYS AUTODYN really reliable to be used to continue this research. Then, we simulate in ANSYS AUTODYN. The comparison and analysis were done to validate simulated results with response to actual damage specimen. 3.1Simulation Tools Used Finite element analysis was conduct on the sandwich structure using ANSYS 2-D/3-D finite element model was developed and appropriate material properties were given to each component. For both the cases, ANSYS AUTODYN 2-D/3-D NONLINEAR hydrocode was used. It is an explicit numerical analysis code, where the equations of mass, momentum and energy conservation coupled with materials descriptions are solved. Alternative numerical processors are available and can be selectively used to model different regions of a problem. The currently available processors include Lagrange, Euler, Euler FCT, ALE and SPH. 3.2 Simulation Justification Based on much discussion about which software that are available that could conduct the simulation on sandwich structure subjected to high velocity impact, finally the findings showed that ANSYS AUTODYN is the one that is going to be used to simulate the test. So, to prove that this software is capable to conduct the simulation, some comparison on result between Lagrange solver with SPH solver of ANSYS AUTODYN on one of the literature review topic, Cylinder impacting a rigid wall (Taylor Test) was done. The comparison was on the results for cylindrical shape impact behavior to see whether results simulated with Lagrange solver showed the more or less the same graph as simulate in SPH solver. Figure 3.2 (a) showed the experimental deformation of rigid wall. Whereas Figure 3.2 (b) and (c) represent the resulting final deformations and plastic strain contours for the two analyses. The results which are summarized in Table 3.1 show that both simulations show satisfactory comparison with experiment. The SPH solution compares almost exactly with the Lagrange result. Experimental Deformation Lagrange Simulation Result SPH Simulation Result Table 3.1 Comparison of experimental and numerical Taylor Test results Experiment Lagrange SPH Cylinder Length (mm) 23.13 to 23.59 23.30 23.35 Impact Diameter (mm) 16.70 to 17.04 16.78 16.80 This validation illustrates that the SPH implementation also works well for cylindrical symmetry. It proved that no special unphysical techniques are used to treat particles close to the axis, or indeed anywhere else in the problem. 3.3 Simulation Setup In the numerical simulations presented, the projectile is made of steel. The steel material properties are from the AUTODYN material library and are shown in Table 3.2. The size and geometry of the projectile vary with different problems. The projectile was considered rigid. Lagrange solver was applied to the projectile. The laminated composite material was model by Lagrange method. In order to account for contact/penetration behavior between the Lagrange projectile and the Lagrange laminate, the gap interaction logic of AUTODYN has been activated between the Lagrange cells. AUTODYN has a state of art contact logic wherein objects use a small gap to determine if interaction exists. This gap defines a detection zone that exists around each interacting cell face or node. If a node enters the detection zone it is repelled by a force that is a function of the intrusion depth. AUTODYN also features another special function impact/penetration interface to avoid excessive noise on the impact surfaces. This feature is activated in all the simulations presented. The Lagrange solver has been implemented in both 2D and 3D. However, AUTODYN-2D is used here for simplicity and ease of demonstration. The laminated composite specimens for the penetration experiment were rectangular. In the AUTODYN simulations, an equivalent rectangular laminate plate was modeled in 3D analysis. The size of the rectangular laminate is equivalent to the experiment laminate plate The detail flow of simulation is shown in Figure 3.3. 3.4 Description of Model Consider the composite sandwich panel and rigid projectile as shown in Figure 3.4. The dimension of projectile is 23.10 mm in length and had a hemispherical head with 5.56 mm diameter. The effective material properties used in AUTODYN simulations for this material are shown in Table 3.3. The equation of state of the laminate is linear with a bulk modulus of 15.0 GPa. The laminate is treated as a linear elastic material. The sandwich panel consists of thin orthotropic facesheets of thickness h = 3 mm and isotropic crushable polymeric aluminium core of thickness H = 27 mm. 3.5 Failure Theory For a composite laminate, the Tsai-Hill Failure criteria are applied. Then, for the projectile, it is consider as rigid body. 3.6 Geometry Consider the composite sandwich panel shown in Figure 3.4. The core of the sandwich panel and the rigid projectile were created using *Part. The reference node for the rigid projectile was defined at the bottom of the projectile. The mass of the projectile was assigned automatically by the software 3.7 Material Properties Table 3.2 Material properties of steel projectile Properties Value Reference Density (g/cm3) 7.9 Bulk Modulus (GPa) 200 Shear Modulus (GPa) 90 Yield Stress (MPa) 200 Ultimate Strain 0.4 Erosion Strain 3.0 Table 3.3 Material properties of carbon fiber Properties Value E1 (GPa) 68.5 E2 (GPa) 68.5 E3 (GPa) 9 G12 (GPa) 3.7 v12 0.11 Xt (MPa) 860 Xc (MPa) 795 Yt (MPa) 860 Yc (MPa) 795 St (MPa) 98 1 (kg/m3) 1430 f 0.02 c (MPa) 60 Table 3.4 Mechanical properties of aluminium honeycomb core (Boyer et al., 1991) Properties Value Density (kg/m3) 77 Young Modulus (MPa) 69000 Poissons Ratio 0.33 Shear Modulus (MPa) 25000 Shear Strength (MPa) 120 3.8 Analysis Type An ANSYS AUTODYN Dynamic Explicit type analysis was performed for a time period of 0.15 ms. Non-linear geometry was switched on. All the required outputs such as displacements, velocities and stresses were defined in this module. 3.9 Mesh In finite element analysis, it is preferred to create a mesh with the least number of elements to keep analysis time reasonable while still getting accurate results. The facesheets and core were separate to get a very fine mesh towards the center of the sandwich structure. A biased ratio of 8.5 with 75 elements was defined in the first region of the panel and uniform mesh of 30 elements was defined in the second region. The facesheets had 2 elements through the thickness and the core had 25 elements. Both facesheets and core had default hourglass control and default distortion control. 3.10 Contact, Boundary Conditions The fixed boundary condition (transverse and radial velocity equal to zero) is applied on the outer boundary of the laminate. The velocity of the projectile is V0 = 287 m/s. 3.11 Simulation Analysis This simulation was performed using the Lagrange processor with erosion. Another approach available within AUTODYN is the SPH (Smooth Particle Hydrodynamics) solver wherein a gridless Lagrangian technique is used. Figure 3.9 are shown about the running-in-progress in simulation. Another figure of the simulation progress are shown at Appendix B CHAPTER 4 RESULT AND DISCUSSION 4.1Introduction This chapter is the one that showed all the actual experiment results that previous done and simulated results using ANSYS AUTODYN. The simulations that have been do by using Lagrange method. Comparison was done between the results and actual experiment result to see whether simulation results agreed well with the actual penetration done by Wan Awiss experiment. Data for penetration test were presented afterwards. 4.2Actual Penetration/Firing Test Results These are the data sheets of actual test handle by Wan Awis at 600m closed shooting range at STRIDE. Table 4.1 presents a Summary Penetration Test for Round 5.56mm Steel Core, the profile of specimen used and basic criteria for 5.56mm bullet for this penetration test. Results from this lot size of 5.56 mm bullets are shown in Table 4.2. This data will be compared with the simulated results. Table 4.1 Actual firing condition BALLISTIC IMPACT TEST Sample Hard Panel Test weapon 5.56 mm, 9 mm Test Gun Sample Type Sandwich Panel Shooting Distance 10m (honeycomb) and 5m (carbon fiber) Sample Size (mm) 100 x 100 x 3.3 Temperature 29.3C 31C Ammunition Calibre 5.56 45 mm Rel. Humidity 88% -93% Type of Projectile: FMJ (M855) Steel Core Shooting Angle: 0 obliquity Table 4.2 Test result on composite sandwich structure with 5.56 mm Caliber Range Type of specimen Depth of Penetration Entry diameter Exit diameter Entry Velocity Exit Velocity m mm mm mm m/s m/s 5.56mm 20 Composite 33.1 5.5 6.8 287 220.67 4.3 Simulation Results by ANSYS AUTODYN The simulation results were compared with the experimental ones to validate the finite element model. The variables selected to validate the numerical model were the residual velocity, the ballistic limit, and the contact time. The disadvantage of the experimental impact tests is the limited information concerning the development of the projectile during the impact. The experimental tests provided information only about the velocity of the projectile before the impact over the front skin and after the perforation of the back skin. However, the finite element model showed the progression of the projectile while it was crossing through the sandwich plate. Fig. 4.6 shows the progression of the projectile velocity during the impact (Vimp = 287 m/s). There are some pictures to show the results for this observation on penetration effect on specimen using ANSYS AUTODYN. The pictures was attached at the Appendix B. Simulation impact observations were done on projectiles back view, projectiles front view, and projectiles side view. The simulated results produced by ANSYS AUTODYN were done regarding difference parameters and values against time. The simulated results were presented in form of graph related to parameters specified. 4.3.1Residual Velocity The progress of the velocity shown in Figure 4.6 is representative of each impact. Plotted graphs were extracted from the same node in this simulated analysis. There are three different trends corresponding to the three components of the sandwich (front skin, core, and back skin). In the first region, the composite front skin caused a sudden drop in velocity at the beginning of the impact event, so that the projectile reached the honeycomb core at a velocity of nearly 250 m/s. Secondly, the velocity remained almost constant as the projectile went through the honeycomb core, when the projectile reached the back skin, its velocity was nearly 240 m/s. In the back skin, a new drop in velocity was observed for a residual velocity of over 210 m/s. 4.3.2 Energy Absorbed The projectile lost 46% of its impact kinetic energy, front and back skins absorbed 46% and 41% of the absorbed energy, respectively, and the honeycomb core absorbed 13%. This analysis was made on each numerical test, calculating the energy absorbed by the three components of the sandwich plate. Figure 4.8 specified the relation of absorbed energy against impact velocity. The skins were the main factor responsible for the energy absorption, while the energy absorbed by the honeycomb core was lower. The percentage of the energy absorbed by each component was almost constant for impact velocities higher than 250 m/s: the front skin absorbed 45%, back skin 40%, and core 15% of the absorbed energy by the composite panel (refer Figure 4.7). However, when the impact velocity was near the ballistic limit, the front skin absorbed most of the impact energy so that the projectile reached the back skin at a low-velocity. Thus, the energy absorbed by the back skin was reduced. The energy needed to break high strength carbon-fibres is very high, so the projectile underwent a sudden lost of kinetic energy when it penetrated a composite skin. The main energy-absorption mechanism of the honeycomb core was the plastic strain of the aluminium walls. The experimental tests indicated that the region of the honeycomb over which the projectile impacted had no influence on the results. The energy needed to deform a thin-walled cell of aluminium is very low, so the projectile crossed the honeycomb core with no major loss of kinetic energy. 4.3.3 Depth of Penetration Figure 4.9 shown the graph of displacement against time. The displacement (depth of penetration) is on specimens element that experienced the contact with 5.56 bullet projectile. Relation between those parameters was clearly explained by the above graph (refer Figure 4.9). The depth of penetration is increased by the time of penetration. The maximum displacement is about 3.3 cm which is equivalent to specimens thickness. 4.3.4 Contact Time Another analysis was done to see relation about contact time against the impact velocity (refer Figure 4.10). The contact time was determined as the time between the contact of the projectile with the front skin and the immediate at which the projectile fully penetrated the sandwich plate. 4.4 Velocity (mm/s) Against Time (s) Analysis The value of energy absorb during penetration can be calculated by using this formula Eabsorbed=12MprojectileVin2-Vout2 So, the value for impact velocity for simulated penetration test is 287m/s and value for after impact velocity is around 210 m/s (Figure 4.6) Eabsorbed=120.001782872-2102=34.06J The calculated value of energy absorbed during penetration for the front skin is equivalent with the value in the graph shown. (Figure 4.8) 4.5 Ballistic Limit The ballistic limit was defined as the minimum impact velocity required for the projectile to completely penetrate the sandwich plate. From the model, the ballistic limit calculated was 147 m/s. The experimental ballistic limit estimated was 139 4.2 m/s, by fitting the equation of Lambert et al., 1976 to the residual velocity versus impact velocity curve. A comparison of the results from the numerical model and the experimental test gave a difference of 6% in the ballistic limit. 4.6 Discussions The analysis done were clearly told us some methodology used on findings all required results about penetration test for 5.56 mm bullet projectile to the composite sandwich structure with honeycomb core. The value for each method that was performed based on equation involving simulated result. Table 4.3 contains the comparison between actual and simulation analysis (FEA) regarding the value of residual velocity, and amount of energy absorbed. This table could be highlighted as the final results for this final year degree project on topic Modeling of Sandwich Structure with Honeycomb Core Subjected to High Velocity Impact. Table 4.3 Table of results Data Source Impact velocity (m/s) Residual velocity (m/s) Energy Absorb (J) Actual test 287 220.67 34.06 Simulation Result 287 210 34.58 Percentage of error between results can be calculated using normal method used in many analyses. This percentage error value is very important in order to prove that the simulation software suggested for FEA in this research is reliable to conduct further study on this research in the future. A large difference of error indicates that the simulation doesnt meet it purpose and objective for this research. Error = [(findings actual) / actual] 100% So, based on this formula we can calculate percentage of errors (Eq 4.3) Simulation Results (Residual Velocity) Error = [(210 220.67)] / 220.67 100% = 4.84% Simulation Results (Energy Absorbed) Error = [(34.58- 34.06)] / 34.06 100% = 1.53% The percentage errors calculated were presented in Table 4.4. As we can clearly see, the percentage of error is in an acceptable range. The objectives for this research are relevant and proven scientifically using finite element analysis and engineering methods. Table 4.4 Percentage errors compare to actual penetration test Task Simulation Result (Residual Velocity) Simulation Result (Energy Absorbed) Percentage Error Between Actual Test and Simulation Analysis (%) 4.84 1.53 CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS 5.1 Conclusions In this study the perforation of composite sandwich panels subjected to high-velocity impact was analyzed using a three dimensional finite element model implemented in ANSYS AUTODYN. Experimental impact tests were carried out to validate the numerical model. Good agreement was found between numerical and experimental results; in particular, the numerical simulation was able to predict the energy absorption of the sandwich panel with a difference of 1.53% and the residual velocity of the sandwich panel with a different of 4.84%. The influence of both skins and the core in the energy-absorption capabilities of the sandwich panel was studied in a wide range of impact velocities. Most of the impact energy was absorbed by the skins. For impact velocities above 600 m/s, approximately 45% of the impact energy was absorbed by the front skin and 40% by the back skin. For impact velocities close to ballistic limit, the front skin absorbed almost the 60% of the energy. On the opposite, the honeycomb core absorbed between 10 and 20% of the impact energy by plastic strain, at all the impact velocities analyzed. Also, the energy-absorption mechanisms in both skins and the core were studied. The main mechanism in the skins was fibre breakage whereas in the core the mechanism was the plastic deformation of the aluminium wall. Both in the skins and the core, the damage was concentrated in a small area around the impact point.