Should Children Be Taught Sex Education In School Essay

Should Children Be Taught Sex Education In School - Essay Example Children are curious about sex.† (Student health service, 2010). Sex education in schools becomes even more warranted in cases where parents do not have appropriate education and resources to guide their children. In addition to schools, both family and society also need to contribute to educating children on reproductive health and well being. It is the moral right of every child, especially girls, to be provided with sex education as it will help to prevent unwarranted pregnancies, sexually transmitted diseases and conditions such as suicide (On the need, 2010). With the rapid growth in information, the term sex is being often used in today’s world. Thus it has become a matter of importance to teach young children about the correct concepts regarding sexual matters before they become misled by inappropriate information provided by the media and other resources (Student health service, 2010). It is vital to begin sex education programs before children reach puberty and it should continue as long as children are able to make correct judgments about sexual practices (Sex education that works, n.d). Many people have argued against detailed sex education for children with the fear that they may negatively influence them. However, frightening people about sex and sexual practices have not helped them to understand the morality of sex.

Consulting report Assignment Example | Topics and Well Written Essays - 2500 words

Consulting report - Assignment Example Using this equation a web portal can be created where the same loyal customers can enter details of their shopping and the same staff can pick it out for them and pack it up to save time. This will not only save time for both and affect inventory and logistics positively, but also increase sales. In a research (Park, 1998) it was concluded that hi-tech baby boomers and older/physically challenged people were more prone to shop online. Another research (Hiser, 1999) confirmed that consumers other than those having dual incomes were a viable market segment. On a general basis buying groceries online was not dependent on the number of people in the house or incomes or gender. On the other hand buying behavior is more likely to be linked to the penetration of Internet and its usability among the shoppers (Ward, 2000). In today’s age where there is an application for every website the company would be making more sales if people in the community are given the option of selecting their groceries on the go. Instead of traditional inventory management system, using the warehouse as the Master Organization and transferring all stocks from there on when stocks are out anywhere, RCE proposes to use a flexible and manageable system. Maintain a fixed stock at all stores for all or some inventories, while keeping all suppliers connected with the Master Organization. This helps put the customer in focus and also helps increase sales as projected to 1%. On an organizational level, if Bradford chooses to bring in revenue through a web portal, a managed inventory at all stores will speed up the process of picking and bagging the orders. For staff to be effective in managing the store of inventory on-site at each business unit(store), effective trainings can be given and management can be done with simple bar-code readers. Staff that has been stocking the locations and managing

Causes for the french revolution Essay Example for Free

Causes for the french revolution Essay There were many causes for the French Revolution, which started in 1789. However there were three main causes that affected the decision to have a revolution the most which were the weak economy, a bad harvest, and King Louis XVI and his wife Marie Antoinette. These were the main reasons that lead to the French Revolution because these events were the ones that affected France the most during 1789. The weak economy was one of the causes of the French Revolution because at that time France was in debt. France was in debt due to helping the colonist become independent from Britain in the American Revolution. For example, in The French Revolution Begins reading it states â€Å"And he borrowed heavily in order to help the American revolutionaries in their war against Great Britain, France’s chief rival. † This is one of the reasons that started the French Revolution because due to being in debt King Louis XVI’s solution was to raise the taxes on the nobles. This was surprised the 2nd estate which consist of the nobles because they paid the least taxes of the 3 estates. Due to this action the 2nd estate called a meeting called the Estates General. In these types of meetings each estate would usually only get one vote but due to the fact that it would be unfair to the 3rd estate. So for this reason every person who was at the Estates General would be granted a vote. The Estates General was to basically approve the new tax. This meeting then caused the National Assembly, which was what the third estate was now called. The third estate pledged a tennis court oath that stated that they wouldn’t leave until a new constitution was made. They drafted a new constitution, which now made France a constitutional monarchy. In conclusion, this is how being in depth was one of the reasons that started the French Revolution. Another cause for the French revolution was the bad harvest in the 1780’s. This was one of the causes for the French revolution because people could grow their food or grain, which is the ingredient to make bread. â€Å"The price of bread doubled in 1789, and many people faced starvation† (French Revolution Begins). In my opinion, I believe that this is one of the reasons to start the revolution because the people back then were poor. They were poor due to the reason that most of their money went to taxes so, if their money went to taxes and they barley had enough to pay for how much the bread used to be hoe are they expected to pay for bread when the price is doubled. I also believe that this is inequitable due to the fact that it isn’t their fault that there was bad weather I believe that the king was just trying to get money. Doubling the bread price made people not have enough money and many people died because of starvation. In conclusion, this is how a bad harvest was another one of the major causes to the French Revolution. The last main cause to the French Revolution had to do with King Louis XVI and his wife Marie Antoinette. This I believe was the main reason for the French Revolution because the king and his wife were spending money on unnecessary things. For example â€Å"†¦she spent so much money on gowns, jewels, gambling, and gifts†¦Ã¢â‚¬ (The French Revolution Begins). Based on this evidence we could see how the money was being misused and how the queen didn’t even care about the situation happening with the people. Another example showing how Antoinette was a bad queen was â€Å"One year she lost the equivalent of $1. 5 million gambling in card games† (The French Revolution Begins). This example shows us how the queen spent money and when it came to help people put they were in depth. An example of how King Louis XVI was being a bad king was â€Å"However he lacked the ability to make decisions† (The French Revolution). In my opinion I believe that this is how King Louis XVI was a cause to the French Revolution because this quote shows how he did not know what was right for the people and did not know how to deal with all of the things that were going on in France like people wanting a revolution. This was a good thing for France because they saw that the King could not make any good decisions so they saw that it was a good idea to overthrow the monarchy and become a limited monarchy. In conclusion there were many things that lead to the French Revolution but only 3 things were the main causes. The 3 main causes were the fact that the French were in depth due to the American Revolution. The fact that there was a bad harvest in the 1780’s. Lastly the fact that King Louis XVI and his wife Marie Antoinette were spending money in a useless way and that they were making bad decisions.

Kolb learning cycle

Kolb learning cycle KOLB LEARNING CYCLE Abstract: In this assignment, we discuss about learning, Kolbs learning cycle and different learning styles. And we get lot of knowledge how to become a good learner. Learning: In that environment that we are usually not going there before, or not have any idea about their rule and regularities, in that point we need to learn about the basic information for our survival. That is called learning. To prepare ourselves for the new challenges of life, no doubt, it is little bite hard, but we have to follow the rule and regularities about the specific needs. Learning is the first step for doing anything in life, because without learning in life we are not be able to do anything in life. Kolb: Kolb is one of the most potent investigators in the field because he gives a complete theoretical picture. According to kolb, learning is the way where we can gain lot of knowledge through different experiences. The theory describes a way of making and placing the syllabus and points in very beautiful way and tell us how the syllabus will be teach and how student can learn lot of knowledge. It indicates that learning is cyclical, takes four stages, sometimes related to as detection, watching, thinking and doing. An important characteristic of the theory is that the different stages are linked with clear-cut learning styles. Wherever, they feel comfortable that is the first stage for them learning. In the case of student there are different tasks where student can pass one by one, and become more wiser with practice and knowledge. Teachers also have different styles of teaching to the students with different new ideas. So everyone have different stages of learning. Kolbs experiential learning theory is one of the master piece of educational theories in higher education, and it has is own place in the literature on geography in higher education in the UK. However, estimating from published literature and the result of this theory is not really good impacting or less well geographers in north America. This is fairly surprising given that Kolb is an American organisational psychologist, whose work has targeted lot of care in north America, specially in the education management and psychology literature. Kolbs cycle have had very good impact on the work of teachers and students and new learners. Kolbs learning cycle: According to kolbs there are four elements which complete the learning cycle and they are very important, because these elements work one by one and very smoothly, they will take place each other. 1- Activist: Pretending, homework, analysis. What is new, i am part of anything, problem solving, small groups give and take equal feedback, trainer should be a icon of a professional, in this case we should give the new learner to chance to learn his own way with some criteria for relevance of stuffs. 2- Reflector: Diaries, logs, thinking. I like the way to think about this training thought. In this case lectures are play very important role to know the really personality of the person by Jude performance. 3- Theorist: Papers, inferences. How this thing is part of other thing. Training thought, case studies, theory readings and work with your own ideas will give you lot of help. Including talking with experts, is not encourage. 4- Pragmatist: Same work, laboratories, notices. How can i get the real advantage of this work? Training thought, equal feedback is helpful. In this case whatever you want to do, you must have proper qualification of the relevant field and complete knowledge. Help from the perfection will be better and boost your career. Different stages in the cycle: Not doubt, Kolbs learning cycle have four elements and they have individual importance. But the main important thing is that they also have appropriate at different stages in the cycle. In 1988 Gibbs take a full advantage and research on Kolbs learning cycle in the field of educational practice. He gets the result that all the elements have very close relationship with each other on different stages. In setting out logical significances of Kolbs theory Gibbs indicates. It is not complete just to do, and not is it complete just to think. Nor is it enough simply to do and think. Learning from excises necessary demand the doing and the thinking. in an opening public talk: Stage 1 (CE): Students one by one read complete takes out from three or four books that represent factors of living in necessary. At giving them a substitute building material. Stage 2 (RO): IN groups of 5-6, students take interest in key questions, like does it look that these experiences were change made by gender. In this stage student need to look back on their reading and also try to focus for the next stage. stage 3 (AC): In that stage 30 minute lecture on the relevant topic give them the idea what is basic need for specific topic and it will be solve. Stage 4 (AE): At this stage student know how to be going forward and present their own ideas. Which is revenant to the all previous stages. In the next class session: Stage 5 (CE): In this stage, students show their ideas and compare with other idea as well. (experience) Stage 6 (RO): In this stage, students discuss questions that help them to improve their ideas. In this stage teacher play very important role to give the student proper guideline. Which really help them a lot in future. (reflection) Stage 7 (AC): This stage is very important because in this stage teach show the students or give them their result and according to the requirement. (conceptualisation) Stage 8 (AE): In this stage, students are able to write their views correctly and according to the point. (experimentation) At this position the work or lesson move to another topic, where Kolbs theory may be used again to base learning experience. At this time students will look back and use the way of analysis (AE), Second time, they move (CE). Hopefully they tell the people (RO), and might give view that if they read this theory (AC), they get the result at the end differently and their experience might be automatically changed by that learning. http://www2.glos.ac.uk/GDN/discuss/kolb1.htm Personal Review of learning: In my opinion, everyone has different learning styles. Some people are mostly visual, auditory or kinaesthetic learner. Actually, everyone learns by variety of elements or styles. But there is always one style is more predominant in each person. In that a person may can increase his learning power, with the help of his predominant style, and become a successful person in his field. Different people choose different ways of learning. But I always choose that way, which, I can fully understand before doing. It means I usually take the from the checklists and quizzes etc. And main important thing is that currently, I am student, so usually learn a lot of knowledge from books, internet, novels, newspapers, different articles and main important thing, I get lot of knowledge my teachers. If I want to choose or develop my best learning way, i will prefer quizzes or checklist. Like I will put some multiple choice questions to know the opinion of people, which help us a lot to create a learning style. For example: Q1: I like to study A: with other people like play games and learn B: In 5-6 people groups where I can listen other people views C: OR alone in a peace full place Q2: I recall thing best if I A: make lists and write them in a page or diary B: record the knowledge and listen C: write down and read them back Q3: I like to learn using A: Rimes and tones that I make up B: pictures and diagrams C: labs and presentation Q4: sometimes when no one is near me I will A: perform out information B: do something else which give me boost to do C: make a photo In my homework, which help me in my work. Q5: I recall things most when I A: read them B: hear them C: say them Q6: I Have problem to recalling thing if I A: cant take about in class B: just read it dont discuss in class C: cant take or write in notebook Q7: I recall A: looks B: names C: both names and faces Q8: when I study for a exam I like to A: I like to draw a picture, charts in my work B: read thoroughly C: make a scheme Well, I thought so I Can create that type of learning style in the future, which help us a lot to know the personality of the person. Then we can give the same task which he / she can easily solve. And become a good learn or successful person, in their fields. Conclusion: In this assignment ,we learn a lot of information about who we can become a good learn, in different ways. And become a successful in future. Plus point is that all the ways are linked with each other, in very beautiful manner. So it every useful source of become a good learner, and get lot of advantages. References: http://www2.glos.ac.uk/GDN/discuss/kolb1.htm http://www.sos.net/~donclark/history/kolb.html http://homeworktips.about.com Cottrell, s. (2003) The Study Skills handbook, Palgrave study Guides

Cleopatra Essays -- essays research papers

When you think of Cleopatra you tend to think of Cleopatra, Queen of the Nile. Which isn’t far from the truth. Cleopatra was queen of Egypt, which is located on the Nile River. In her lifetime she had every luxury imaginable, which she used to gain the popularity of the roman authority. She was very important in terms of Egyptian history. However she was also very well known in terms of Roman history. She seduced some of most well known Roman men of her time. Cleopatra was a seductress. Who used her fame and fortune to seduce these men. Some of these men included such men as Julius Caesar and Marc Antony. Cleopatra was born in 69 BC She was the last Ptolemaic ruler. Her father was the Ptolemy XII. She was very, which added to her popularity of the Egyptian and Roman world. Cleopatra t...

Animal Testing Should Be Outlawed Essay -- Argumentative Persuasive 20

According to Biology Online, animal experimentation is defined as the use of animals in experiments and development projects usually to determine toxicity, dosing and efficacy of test drugs before proceeding to human clinical trials. Animal experimentation has been going on since ancient Greece when Aristotle and Hippocrates first made their model of the human body based on what they had observed through animal dissection. Then, Romans used animals to do more psychological tests on animals like pigs, monkeys and dogs. After that, the Renaissance period took up physiological studies. Since then, the 20th century had a huge increase in animal testing until 1980 when activists started standing up against the labs. Activists have not been very successful at protecting the animals’ rights in some cases and the past decades have seen a noticeable increase in animal testing for many reasons (Baumans). Today, despite activist’s efforts, animal testing is still commonly used. Ne vertheless, animal testing is unethical and should be outlawed. People in favor of animal testing believe that animals are needed for any sort of medical advancement. They believe that without testing on live animals, our medical field would not be able to make improvements. Scientists assume that humans would be hindered enormously if they did not test drugs on animals before they were released to the human world. They also think that animals are tested to do various behavioral and genetic testing. People in favor of animal testing are under the impression that the animals are a great help towards psychologists in finding out more about the brain and how the human brain works. They think that without the animals, nobody would be able to fully understand how the ... ...ety. aavs.org, 2010. Web. 16 Nov. 2010. . Bantwal, Natasha. "Arguments Against Animal Testing." Buzzle.com: Intelligent Life on the Web. Buzzle.com, 2010. Web. 16 Nov 2010. against-animal-testing.html>. Baumans, V. "Use of animals in experimental research: an ethical dilemma?." Gene Therapy (2004): S64–S66. Web. 9 Nov 2010. . Goldman, Laura. "New System May Replace Lab Rats with Robots." Change.org. Change.org, 08 Aug 2010. Web. 16 Nov 2010. . "Research Alternatives." CHAI Online. CHAI Online: Concern for Helping Animals In Israel , 2010. Web. 16 Nov 2010. .

Ansys Tutorial Release 12.1

 ® ANSYS Tutorial Release 12. 1 Structural & Thermal Analysis Using the ANSYS Release 12. 1 Environment Kent L. Lawrence Mechanical and Aerospace Engineering University of Texas at Arlington SDC PUBLICATIONS www. SDCpublications. com Schroff Development Corporation Visit the following websites to learn more about this book: ANSYS Tutorial 2-1 Lesson 2 Plane Stress Plane Strain 2-1 OVERVIEW Plane stress and plane strain problems are an important subclass of general threedimensional problems. The tutorials in this lesson demonstrate:  ¦Solving planar stress concentration problems. Evaluating potential inaccuracies in the solutions.  ¦Using the various ANSYS 2D element formulations. 2-2 INTRODUCTION It is possible for an object such as the one on the cover of this book to have six components of stress when subjected to arbitrary three-dimensional loadings. When referenced to a Cartesian coordinate system these components of stress are: Normal Stresses ?x, ? y, ? z Shear Stresses ? xy, ? yz, ? zx Figure 2-1 Stresses in 3 dimensions. In general, the analysis of such objects requires three-dimensional modeling as discussed in Lesson 4.However, two-dimensional models are often easier to develop, easier to solve and can be employed in many situations if they can accurately represent the behavior of the object under loading. 2-2 ANSYS Tutorial A state of Plane Stress exists in a thin object loaded in the plane of its largest dimensions. Let the X-Y plane be the plane of analysis. The non-zero stresses ? x, ? y, and ? xy lie in the X – Y plane and do not vary in the Z direction. Further, the other stresses (? z,? yz , and ? zx ) are all zero for this kind of geometry and loading.A thin beam loaded in its plane and a spur gear tooth are good examples of plane stress problems. ANSYS provides a 6-node planar triangular element along with 4-node and 8-node quadrilateral elements for use in the development of plane stress models. We will use both triangles and qua ds in solution of the example problems that follow. 2-3 PLATE WITH CENTRAL HOLE To start off, let’s solve a problem with a known solution so that we can check our computed results as well as our understanding of the FEM process. The problem is that of a tensile-loaded thin plate with a central hole as shown in Figure 2-2.Figure 2-2 Plate with central hole. The 1. 0 m x 0. 4 m plate has a thickness of 0. 01 m, and a central hole 0. 2 m in diameter. It is made of steel with material properties; elastic modulus, E = 2. 07 x 1011 N/m2 and Poisson’s ratio, ? = 0. 29. We apply a horizontal tensile loading in the form of a pressure p = -1. 0 N/m2 along the vertical edges of the plate. Because holes are necessary for fasteners such as bolts, rivets, etc, the need to know stresses and deformations near them occurs very often and has received a great deal of study.The results of these studies are widely published, and we can look up the stress concentration factor for the case s hown above. Before the advent of suitable computation methods, the effect of most complex stress concentration geometries had to be evaluated experimentally, and many available charts were developed from experimental results. The uniform, homogeneous plate above is symmetric about horizontal axes in both geometry and loading. This means that the state of stress and deformation below a Plane Stress / Plane Strain 2-3 orizontal centerline is a mirror image of that above the centerline, and likewise for a vertical centerline. We can take advantage of the symmetry and, by applying the correct boundary conditions, use only a quarter of the plate for the finite element model. For small problems using symmetry may not be too important; for large problems it can save modeling and solution efforts by eliminating one-half or a quarter or more of the work. Place the origin of X-Y coordinates at the center of the hole. If we pull on both ends of the plate, points on the centerlines will move al ong the centerlines but not perpendicular to them.This indicates the appropriate displacement conditions to use as shown below. Figure 2-3 Quadrant used for analysis. In Tutorial 2A we will use ANSYS to determine the maximum horizontal stress in the plate and compare the computed results with the maximum value that can be calculated using tabulated values for stress concentration factors. Interactive commands will be used to formulate and solve the problem. 2-4 TUTORIAL 2A – PLATE Objective: Find the maximum axial stress in the plate with a central hole and compare your result with a computation using published stress concentration factor data.PREPROCESSING 1. Start ANSYS, select the Working Directory where you will store the files associated with this problem. Also set the Jobname to Tutorial2A or something memorable and provide a Title. (If you want to make changes in the Jobname, working Directory, or Title after you’ve started ANSYS, use File > Change Jobname or Di rectory or Title. ) Select the six node triangular element to use for the solution of this problem. 2-4 ANSYS Tutorial Figure 2-4 Six-node triangle. The six-node triangle is a sub-element of the eight-node quadrilateral. 2.Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add > Structural Solid > Quad 8node 183 > OK Figure 2-5 Element selection. Select the triangle option and the option to define the plate thickness, otherwise a unit thickness is used. 3. Options (Element shape K1) > Triangle, Options (Element behavior K3) > Plane strs w/thk > OK > Close Plane Stress / Plane Strain 2-5 Figure 2-6 Element options. 4. Main Menu > Preprocessor > Real Constants > Add/Edit/Delete > Add > OK Figure 2-7 Real constants. Enter the plate thickness of 0. 01 m. ) >Enter 0. 01 > OK > Close Figure 2-8 Enter the plate thickness. 2-6 ANSYS Tutorial Enter the material properties. 5. Main Menu > Preprocessor > Material Props > Material Models Material Model Number 1, click Structural > Line ar > Elastic > Isotropic Enter EX = 2. 07E11 and PRXY = 0. 29 > OK (Close the Define Material Model Behavior window. ) Create the geometry for the upper right quadrant of the plate by subtracting a 0. 2 m diameter circle from a 0. 5 x 0. 2 m rectangle. Generate the rectangle first. . Main Menu > Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners Enter (lower left corner) WP X = 0. 0, WP Y = 0. 0 and Width = 0. 5, Height = 0. 2 > OK 7. Main Menu > Preprocessor > Modeling > Create > Areas > Circle > Solid Circle Enter WP X = 0. 0, WP Y = 0. 0 and Radius = 0. 1 > OK Figure 2-9 Create areas. Plane Stress / Plane Strain 2-7 Figure 2-10 Rectangle and circle. Now subtract the circle from the rectangle. (Read the messages in the window at the bottom of the screen as necessary. ) 8.Main Menu > Preprocessor > Modeling > Operate > Booleans > Subtract > Areas > Pick the rectangle > OK, then pick the circle > OK (Use Raise Hidden and Reset Picking as necessary. ) Figure 2-11 Geo metry for quadrant of plate. Create a mesh of triangular elements over the quadrant area. 9. Main Menu > Preprocessor > Meshing > Mesh > Areas > Free Pick the quadrant > OK Figure 2-12 Triangular element mesh. Apply the displacement boundary conditions and loads to the geometry (lines) instead of the nodes as we did in the previous lesson.These conditions will be applied to the FEM model when the solution is performed. 10. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the left edge of the quadrant > OK > UX = 0. > OK 2-8 ANSYS Tutorial 11. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the bottom edge of the quadrant > OK > UY = 0. > OK Apply the loading. 12. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Pressure > On Lines.Pick the right edge of the quadrant > OK > Pressure = -1. 0 > OK (A positive pressure would be a compressive load, so we use a nega tive pressure. The pressure is shown by the two arrows. ) Figure 2-13 Model with loading and displacement boundary conditions. The model-building step is now complete, and we can proceed to the solution. First, to be safe, save the model. 13. Utility Menu > File > Save as Jobname. db (Or Save as †¦. ; use a new name) SOLUTION The interactive solution proceeds as illustrated in the tutorials of Lesson 1. 14. Main Menu > Solution > Solve > Current LS > OKThe /STATUS Command window displays the problem parameters and the Solve Current Load Step window is shown. Check the solution options in the /STATUS window and if all is OK, select File > Close In the Solve Current Load Step window, select OK, and when the solution is complete, Close the ‘Solution is Done! ’ window. POSTPROCESSING We can now plot the results of this analysis and also list the computed values. First examine the deformed shape. 15. Main Menu > General Postproc > Plot Results > Deformed Shape > Def. + Undef. > OK Plane Stress / Plane Strain 2-9 Figure 2-14 Plot of Deformed shape.The deformed shape looks correct. (The undeformed shape is indicated by the dashed lines. ) The right end moves to the right in response to the tensile load in the X direction, the circular hole ovals out, and the top moves down because of Poisson’s effect. Note that the element edges on the circular arc are represented by straight lines. This is an artifact of the plotting routine not the analysis. The six-node triangle has curved sides, and if you pick on a mid-side of one these elements, you will see that a node is placed on the curved edge. The maximum displacement is shown on the graph legend as 0. 2e-11 which seems reasonable. The units of displacement are meters because we employed meters and N/m2 in the problem formulation. Now plot the stress in the X direction. 16. Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Stress > X-Component of stress > OK Use PlotCtrls > Symbols [/PSF] Surface Load Symbols (set to Pressures) and Show pre and convect as (set to Arrows) to display the pressure loads. Figure 2-15 Surface load symbols. Also select Display All Applied BCs 2-10 ANSYS Tutorial Figure 2-16 Element SX stresses.The minimum, SMN, and maximum, SMX, stresses as well as the color bar legend give an overall evaluation of the ? x (SX) stress state. We are interested in the maximum stress at the hole. Use the Zoom to focus on the area with highest stress. (Your meshes and results may differ a bit from those shown here. ) Figure 2-17 SX stress detail. Plane Stress / Plane Strain 2-11 Stress variations in the actual isotropic, homogeneous plate should be smooth and continuous across elements. The discontinuities in the SX stress contours above indicate that the number of elements used in this model is oo few to calculate with complete accuracy the stress values near the hole because of the stress gradients there. We will not accept this stress solu tion. More six-node elements are needed in the region near the hole to find accurate values of the stress. On the other hand, in the right half of the model, away from the stress riser, the calculated stress contours are smooth, and SX would seem to be accurately determined there. It is important to note that in the plotting we selected Element Solu (Element Solution) in order to look for stress contour discontinuities.If you pick Nodal Solu to plot instead, for problems like the one in this tutorial, the stress values will be averaged before plotting, and any contour discontinuities (and thus errors) will be hidden. If you plot nodal solution stresses you will always see smooth contours. A word about element accuracy: The FEM implementation of the truss element is taken directly from solid mechanics studies, and there is no approximation in the solutions for node-loaded truss structures formulated and solved in the ways discussed in Lesson 1.The continuum elements such as the ones for plane stress and plane strain, on the other hand, are normally developed using displacement functions of a polynomial type to represent the displacements within the element, and the higher the polynomial, the greater the accuracy. The ANSYS six-node triangle uses a quadratic polynomial and is capable of representing linear stress and strain variations within an element. Near stress concentrations the stress gradients vary quite sharply. To capture this variation, the number of elements near the stress concentrations must be increased proportionately.To obtain more elements in the model, return to the Preprocessor and refine the mesh, first remove the pressure. All elements are subdivided and the mesh below is created 17. Main Menu > Preprocessor > Loads > Define Loads > Delete > Structural > Pressure > On Lines. Pick the right edge of the quadrant. Main Menu > Preprocessor > Meshing > Modify Mesh > Refine At > All (Select Level of refinement 1. ) Figure 2-18 Global mesh refineme nt. 2-12 ANSYS Tutorial We will also refine the mesh selectively near the hole. 18.Main Menu > Preprocessor > Meshing > Modify Mesh > Refine At > Nodes. (Select the three nodes shown. ) > OK (Select the Level of refinement = 1) > OK Figure 2-19 Selective refinement at nodes. (Note: Alternatively you can use Preprocessor > Meshing > Clear > Areas to remove all elements and build a completely new mesh. Plot > Areas afterwards to view the area again. Note also that too much local refinement can create a mesh with too rapid a transition between fine and coarse mesh regions. ) Reapply the pressure loading, repeat the solution, and replot the stress SX. 9. Main Menu > Solution > Solve > Current LS > OK Save your work. 20. File > Save as Jobname. db Plot the stresses in the X direction. 21. Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Stress > X-Component of stress > OK Plane Stress / Plane Strain 2-13 Figure 2-20 SX stress contour after mesh refinement. Figu re 2-21 SX stress detail contour after mesh refinement. The element solution stress contours are now smooth across element boundaries, and the stress legend shows a maximum value of 4. 386 Pa, a 4. percent change in the SX stress computed using the previous mesh. To check this result, find the stress concentration factor for this problem in a text or reference book or from a suitable web site. For the geometry of this example we find Kt = 2. 17. We can compute the maximum stress using (Kt)(load)/(net cross sectional area). Using the pressure p = 1. 0 Pa we obtain. ? x MAX = 2. 17 * p * (0. 4)(0. 01) /[(0. 4 ? 0. 2) * 0. 01] = 4. 34 Pa 2-14 ANSYS Tutorial The computed maximum value is 4. 39 Pa which is around one percent in error, assuming that the value of Kt is exact. -5 THE APPROXIMATE NATURE OF FEM As mentioned above, the stiffness matrix for the truss elements of Lesson 1 can be developed directly and simply from elementary solid mechanics principles. For continuum problems in t wo and three-dimensional stress, this is generally no longer possible, and the element stiffness matrices are usually developed by assuming something specific about the characteristics of the displacements that can occur within an element. Ordinarily this is done by specifying the highest degree of the polynomial that governs the displacement distribution within an element.For h-method elements, the polynomial degree depends upon the number of nodes used to describe the element, and the interpolation functions that relate displacements within the element to the displacements at the nodes are called shape functions. In ANSYS, 2-dimensional problems can be modeled with six-node triangles, four-node quadrilaterals or eight-node quadrilaterals. Figure 2-22 Triangular and quadrilateral elements. The greater the number of nodes, the higher the order of the polynomial and the greater the accuracy in describing displacements, stresses and strains within the element. If the stress is constan t throughout a region, a very imple model is sufficient to describe the stress state, perhaps only one or two elements. If there are gradients in the stress distributions within a region, high-degree displacement polynomials and/or many elements are required to accurately analyze the situation. These comments explain the variation in the accuracy of the results as different numbers of elements were used to solve the problem in the previous tutorial and why the engineer must carefully prepare a model, start with small models, grow the models as understanding of the problem develops and carefully interpret the calculated results.The ease with which models can be prepared and solved sometimes leads to careless evaluation of the computed results. Plane Stress / Plane Strain 2-15 2-6 ANSYS FILES The files created during the solution were saved in step 20 of Tutorial 2A. Look in the working directory and you see Tutorial2A files with extensions BCS, db, dbb, esav, full, mntr, rst, and sta t. However, the Tutorial 2A problem can be reloaded using only Tutorial2A. db, so if you want to save disk space, you can delete the others. 2-7 ANSYS GEOMETRY The finite element model consists of elements and nodes and is separate from the geometry on which it may be based.It is possible to build the finite element model without consideration of any underlying geometry as was done in the truss examples of Lesson 1, but in many cases, development of the geometry is the first task. Two-dimensional geometry in ANSYS is built from keypoints, lines (straight, arcs, splines), and areas. These geometric items are assigned numbers and can be listed, numbered, manipulated, and plotted. The keypoints (2,3,4,5,6), lines (2,3,5,9,10), and area (3) for Tutorial 2A are shown below. (Your numbering may differ. ) Figure 2-23 Keypoints, lines and areas.The finite element model developed previously for this part used the area A3 for development of the node/element FEM mesh. The loads, displacement b oundary conditions and pressures were applied to the geometry lines. When the solution step was executed, the loads were transferred from the lines to the FEM model nodes. Applying boundary conditions and loads to the geometry facilitates remeshing the problem. The geometry does not change, only the number and location of nodes and elements, and at solution time, the loads are transferred to the new mesh.Geometry can be created in ANSYS interactively (as was done in the previous tutorial) or it can be created by reading a text file. For example, the geometry of Tutorial 2A can be generated with the following text file using the File > Read Input from command sequence. (The keypoint, line, etc. numbers will be different from those shown above. ) 2-16 ANSYS Tutorial /FILNAM,Geom /title, Stress Concentration Geometry ! Example of creating geometry using keypoints, lines, arcs /prep7 ! Create geometry k, 1, 0. 0, 0. 0 ! Keypoint 1 is at 0. 0, 0. 0 k, 2, 0. 1, 0. 0 , 3, 0. 5, 0. 0 k, 4, 0. 5, 0. 2 k, 5, 0. 0, 0. 2 k, 6, 0. 0, 0. 1 L, L, L, L, 2, 3, 4, 5, 3 4 5 6 ! Line from keypoints 2 to 3 ! arc from keypoint 2 to 6, center kp 1, radius 0. 1 LARC, 2, 6, 1, 0. 1 AL, 1, 2, 3, 4, 5 ! Area defined by lines 1,2,3,4,5 Geometry for FEM analysis also can be created with solid modeling CAD or other software and imported into ANSYS. The IGES (Initial Graphics Exchange Specification) neutral file is a common format used to exchange geometry between computer programs. Tutorial 2B demonstrates this option for ANSYS geometry development. -8 TUTORIAL 2B – SEATBELT COMPONENT Objective: Determine the stresses and deformation of the prototype seatbelt component shown in the figure below if it is subjected to tensile load of 1000 lbf. Figure 2-24 Seatbelt component. The seatbelt component is made of steel, has an over all length of about 2. 5 inches and is 3/32 = 0. 09375 inches thick. A solid model of the part was developed in a CAD system and exported as an IGES file. The f ile is imported into ANSYS for analysis. For simplicity we will analyze only the right, or ‘tongue’ portion of the part in this tutorial.Plane Stress / Plane Strain 2-17 Figure 2-25 Seatbelt ‘tongue’. PREPROCESSING 1. Start ANSYS, Run Interactive, set jobname, and working directory. Create the top half of the geometry above. The latch retention slot is 0. 375 x 0. 8125 inches and is located 0. 375 inch from the right edge. If you are not using an IGES file to define the geometry for this exercise, you can create the geometry directly in ANSYS with key points, lines, and arcs by selecting File > Read Input from to read in the text file given below and by skipping the IGES import steps 2, 3, 4, and 10 below. FILNAM,Seatbelt /title, Seatbelt Geometry ! Example of creating geometry using keypoints, lines, arcs /prep7 ! Create geometry k, 1, 0. 0, 0. 0 ! Keypoint 1 is at 0. 0, 0. 0 k, 2, 0. 75, 0. 0 k, 3, 1. 125, 0. 0 k, 4, 1. 5, 0. 0 k, 5, 1. 5, 0. 5 k, 6, 1. 2 5, 0. 75 k, 7, 0. 0, 0. 75 k, 8, 1. 125, 0. 375 k, 9, 1. 09375, 0. 40625 k, 10, 0. 8125, 0. 40625 k, 11, 0. 75, 0. 34375 k, 12, 1. 25, 0. 5 k, 13, 1. 09375, 0. 375 k, 14, 0. 8125, 0. 34375 2-18 L, L, L, L, L, L, L, L, ANSYS Tutorial 1, 2 3, 4 4, 5 6, 7 7, 1 3, 8 9, 10 11, 2 ! arc LARC, LARC, LARC, Line from keypoints 1 to 2 from keypoint 5 to 6, center kp 12, radius 0. 25, etc. 5,6, 12, 0. 25 8, 9, 13, 0. 03125 10, 11, 14, 0. 0625 AL,all ! Use all lines to create the area. 2. Alternatively, use a solid modeler to create the top half of the component shown above in the X-Y plane and export an IGES file of the part. To import the IGES file 3. Utility Menu > File > Import > IGES Select the IGES file you created earlier. Accept the ANSYS import default settings. If you have trouble with the import, select the alternate options and try again.Defeaturing is an automatic process to remove inconsistencies that may exist in the IGES file, for example lines that, because of the modeling or th e file translation process, do not quite join to digital precision accuracy. Figure 2-26 IGES import. Turn the IGES solid model around if necessary so you can easily select the X-Y plane. Plane Stress / Plane Strain 2-19 4. Utility Menu > PlotCtrls > Pan, Zoom, Rotate > Back, or use the side-bar icon. Figure 2-27 Seatbelt solid, front and back. 5.Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add > Solid > Quad 8node 183 > OK (Use the 8-node quadrilateral element for this problem. ) 6. Options > Plane strs w/thk > OK > Close Enter the thickness 7. Main Menu > Preprocessor > Real Constants > Add/Edit/Delete > Add > (Type 1 Plane 183) > OK > Enter 0. 09375 > OK > Close Enter the material properties 8. Main Menu > Preprocessor > Material Props > Material Models Material Model Number 1, click Structural > Linear > Elastic > Isotropic Enter EX = 3. 0E7 and PRXY = 0. > OK (Close Define Material Model Behavior window. ) Now mesh the X-Y plane area. (Turn on area numbers if it helps. ) 9. Main Menu > Preprocessor > Meshing > Mesh > Areas > Free. Pick the X-Y planar area > OK IMPORTANT NOTE: The mesh below was developed from an IGES geometry file. Using the text file geometry definition, may produce a much different mesh. If so, use the Modify Mesh refinement tools to obtain a mesh density that produces results with accuracies comparable to those given below. Computed stress values can be surprisingly sensitive to mesh differences. -20 ANSYS Tutorial Figure 2-28 Quad 8 mesh. The IGES solid model is no longer needed, and since its lines and areas may interfere with subsequent modeling operations, we can delete it from the session. 10. Main Menu > Preprocessor > Modeling > Delete > Volume and Below (Don’t be surprised if everything disappears. Just Plot > Elements to see the mesh again. ) 11. Utility Menu > PlotCtrls > Pan, Zoom, Rotate > Front front side of mesh. ) (If necessary to see the Figure 2-29 . Mesh, front view. Now apply displacement and pr essure boundary conditions.Zero displacement UX along left edge and zero UY along bottom edge. 12. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the left edge > UX = 0. > OK 13. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the lower edge > UY = 0. > OK The 1000 lbf load corresponds to a uniform pressure of about 14,000 psi along the ? inch vertical inside edge of the latch retention slot. [1000 lbf/(0. 09375 in. x 0. 75 in. )]. 14.Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Pressure > On Lines Plane Stress / Plane Strain 2-21 Select the inside line and set pressure = 14000 > OK Figure 2-30 Applied displacement and pressure conditions. Solve the equations. SOLUTION 15. Main Menu > Solution > Solve > Current LS > OK POSTPROCESSING Comparing the von Mises stress with the material yield stress is an accepted way of evaluating static load yielding for du ctile metals in a combined stress state, so we enter the postprocessor and plot the element solution of von Mises stress, SEQV. 16.Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Stress > (scroll down) von Mises > OK Zoom in on the small fillet where the maximum stresses occur. The element solution stress contours are reasonably smooth, and the maximum von Mises stress is around 118,000 psi. Further mesh refinement gives a stress value of approximately 140,000 psi. The small fillet radius of this geometry illustrates the challenges that can arise in creating accurate solutions, however you can easily come within a few percent of the most likely true result using the methods discussed thus far.Figure 2-31 Von Mises stresses. 2-22 ANSYS Tutorial Redesign to reduce the maximum stress requires an increase in the thickness or fillet radius. Look at charts of stress concentration factors, and you notice that the maximum stress increases as the radius of the str ess raiser decreases, approaching infinite values at zero radii. If your model has a zero radius notch, your finite-size elements will show a very high stress but not infinite stress. If you refine the mesh, the stress will increase but not reach infinity.The finite element technique necessarily describes finite quantities and cannot directly treat an infinite stress at a singular point, so don’t ‘chase a singularity’. If you do not care what happens at the notch (static load, ductile material, etc. ) do not worry about this location but examine the stresses and strains in other regions. If you really are concerned about the maximum stress in a particular location (fatigue loads or brittle material), then use the actual part notch radius however small (1/32 for this tutorial); do not use a zero radius.Also examine the stress gradient in the vicinity of the notch to make sure the mesh is sufficiently refined near the notch. If a crack tip is the object of the anal ysis, you should look at fracture mechanics approaches to the problem. (See ANSYS help topics on fracture mechanics. ) The engineer’s responsibility is not only to build useful models, but also to interpret the results of such models in intelligent and meaningful ways. This can often get overlooked in the rush to get answers. Continue with the evaluation and check the strains and deflections for this model as well. 7. Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Strain-total > 1st prin > OK The maximum principal normal strain value is found to be approximately 0. 004 in/in. 18. Main Menu > General Postproc > Plot Results > Contour Plot > Nodal Solu > DOF Solution > X-Component of displacement > OK Figure 2-32 UX displacements. Plane Stress / Plane Strain 2-23 The maximum deflection in the X direction is about 0. 00145 inches and occurs as expected at the center of the right-hand edge of the latch retention slot. -9 MAPPED MESHING Quadrilateral m eshes can also be created by mapping a square with a regular array of cells onto a general quadrilateral or triangular region. To illustrate this, delete the last line, AL,all, from the text file above so that the area is not created (just the lines) and read it into ANSYS. Use PlotCtrls to turn Keypoint Numbering On. Then use 1. Main Menu > Preprocessor > Modeling > Create > Lines > Lines > Straight Line. Successively pick pairs of keypoints until the four interior lines shown below are created. Figure 2-33 Lines added to geometry. 2.Main Menu > Preprocessor > Modeling > Create > Areas > Arbitrary > By Lines Pick the three lines defining the lower left triangular area. > Apply > Repeat for the quadrilateral areas. > Apply > OK Figure 2-34 Quadrilateral/Triangular regions. 3. Main Menu > Preprocessor > Modeling > Operate > Booleans > Glue > Areas > Pick All 2-24 ANSYS Tutorial The glue operation preserves the boundaries between areas that we will need for mapped meshing. 4. Main Men u > Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines Enter 4 for NDIV, No. lement divisions > OK All lines will be divided into four segments for mesh creation. Figure 2-35 Element size on picked lines. 5. Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add > Solid > Quad 8node 183 > OK (Use the 8-node quadrilateral element for the mesh. ) 6. Main Menu > Preprocessor > Meshing > Mesh > Areas > Mapped > 3 or 4 sided > Pick All The mesh below is created. Applying boundary and load conditions and solving gives the von Mises stress distribution shown.The stress contours are discontinuous because of the poor mesh quality. Notice the long and narrow quads near the point of maximum stress. We need more elements and they need to be better shaped with smaller aspect ratios to obtain satisfactory results. Plane Stress / Plane Strain 2-25 Figure 2-36 Mapped mesh and von Mises results. One can tailor the mapped mesh by specifying how many elements are to be plac ed along which lines. This allows much better control over the quality of the mesh, and an example of using this approach is described in Lesson 4. 2-10 CONVERGENCEThe goal of finite element analysis as discussed in this lesson is to arrive at computed estimates of deflection, strain and stress that converge to definite values as the number of elements in the mesh increases, just as a convergent series arrives at a definite value once enough terms are summed. For elements based on assumed displacement functions that produce continuum models, the computed displacements are smaller in theory than the true displacements because the assumed displacement functions place an artificial constraint on the deformations that can occur.These constraints are relaxed as the element polynomial is increased or as more elements are used. Thus your computed displacements usually converge smoothly from below to fixed values. Strains are the x and/or y derivatives of the displacements and thus depend o n the distribution of the displacements for any given mesh. The strains and stresses may change in an erratic way as the mesh is refined, first smaller than the final computed values, then larger, etc. Not all elements are developed using the ideas discussed above, and some will give displacements that converge from above. (See Lesson 6. In any case you should be alert to computed displacement and stress variations as you perform mesh refinement during the solution of a problem. 2-11 TWO-DIMENSIONAL ELEMENT OPTIONS The analysis options for two-dimensional elements are: Plane Stress, Axisymmetric, Plane Strain, Plane Stress with Thickness and Generalized Plane Strain. The two examples thus far in this lesson were of the third type, namely problems of plane stress in which we provided the thickness of the part. 2-26 ANSYS Tutorial The first analysis option, Plane Stress, is the ANSYS default and provides an analysis for a part with unit thickness.If you are working on a design problem in which the thickness is not yet known, you may wish to use this option and then select the thickness based upon the stress, strain, and deflection distributions found for a unit thickness. The second option, Axisymmetric analysis is covered in detail in Lesson 3. Plane Strain occurs in a problem such as a cylindrical roller bearing caged against axial motion and uniformly loaded in a direction normal to the cylindrical surface. Because there is no axial motion, there is no axial strain.Each slice through the cylinder behaves like every other and the problem can be conveniently analyzed with a planar model. Another plane strain example is that of a long retaining wall, restrained at each end and loaded uniformly by soil pressure on one or both faces. The Generalized Plane Strain feature assumes a finite deformation domain length in the Z direction, as opposed to the infinite value assumed for standard plane strain. 2-12 SUMMARY Problems of stress concentration in plates subject to in-plane loadings were used to illustrate ANSYS analysis of plane stress problems.Free triangular and quadrilateral element meshes were developed and analyzed. Mapped meshing with quads was also presented. Similar methods are used for solving problems involving plane strain; one only has to choose the appropriate option during element selection. The approach is also applicable to axisymmetric geometries as discussed in the next lesson. 2-13 PROBLEMS In the problems below, use triangular and/or quadrilateral elements as desired. Triangles may produce more regular shaped element meshes with free meshing.The six-node triangles and eight-node quads can approximate curved surface geometries and, when stress gradients are present, give much better results than the four-node quad elements. 2-1 Find the maximum stress in the aluminum plate shown below. Use tabulated stress concentration factors to independently calculate the maximum stress. Compare the two results by determining the percen t difference in the two answers. Convert the 12 kN concentrated force into an equivalent pressure applied to the edge. Plane Stress / Plane Strain 2-27 Figure P2-1 -2 Find the maximum stress for the plate from 2-1 if the hole is located halfway between the centerline and top edge as shown. You will now need to model half of the plate instead of just one quarter and properly restrain vertical rigid body motion. One way to do this is to fix one keypoint along the centerline from UY displacement. Figure P2-2 2-28 ANSYS Tutorial 2-3 An aluminum square 10 inches on a side has a 5-inch diameter hole at the center. The object is in a state of plane strain with an internal pressure of 1500 psi. Determine the magnitude and location of the maximum principal stress, the maximum rincipal strain, and the maximum von Mises stress. Note that no thickness need be supplied for plane strain analysis. Figure P2-3 2-4 Repeat 2-3 for a steel plate one inch thick in a state of plane stress. 2-5 See if yo u can reduce the maximum stress for the plate of problem 2-1 by adding holes as shown below. Select a hole size and location that you think will smooth out the ‘stress flow’ caused by the load transmission through the plate. Figure P2-5 2-6 Repeat 2-1 but the object is now a plate with notches or with a step in the geometry. (See the next figure. ) Select your own dimensions, materials, and loads.Use published stress concentration factor data to compare to your results. The published results are for plates that are relatively long so that there is a uniform state of axial stress at either end relatively far from notch or hole. Create your geometry accordingly. Plane Stress / Plane Strain 2-29 Figure P2-6 2-7 Solve the seatbelt component problem of Tutorial 2B again using six node triangular elements instead of the quadrilaterals. Experiment with mesh refinement. Turn on Smart Sizing using size controls to examine the effect on the solution. See if you can compute a maxi mum von Mises stress of around 140 kpsi. -8 Determine the stresses and deflections in an object ‘at hand’ (such as a seatbelt tongue or retaining wall) whose geometry and loading make it suitable for plane stress or plane strain analysis. Do all the necessary modeling of geometry (use a CAD system if you wish), materials and loadings. 2-9 A cantilever beam with a unit width rectangular cross section is loaded with a uniform pressure along its upper surface. Model the beam as a problem in plane stress. Compute the end deflection and the maximum stress at the cantilever support. Compare your results to those you would find using elementary beam theory.Figure P2-8 Restrain UX along the cantilever support line, but restrain UY at only one keypoint along this line. Otherwise, the strain in the Y direction due to the Poisson effect is prevented here, and the root stresses are different from elementary beam theory because of the singularity created. (Try fixing all node points in UX and UY and see what happens. ) Select your own dimensions, materials, and pressure. Try a beam that’s long and slender and one that’s short and thick. The effect of shear loading becomes more important in the deflection analysis as the slenderness decreases.