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In Fall 2000, I asked students in my class in Applied
Elasticity to write a typed 400-word essay on what you learned in the
elasticity class as if you were writing it to a fellow graduate student who
is about to take the class. The essay
needed to be in newspaper style (see any
VW wrote: The engineer placed in charge of the design and construction of the $100 billion terrorist project funded by Doctor Evil, was but an unknowing fool. This engineered based his entire design on the compressive strength of a prismatic member holding the two huge magnets apart, which would be used to destroy the world. This engineer depended on his basic mechanics material knowledge to design the critical member. Not fully understanding the physics of the problem the engineer determined that a concrete member would be used and that no reinforcement was needed since the member was only loaded axially. The concrete member was capable of sustaining huge compressive loads, however the engineer did not know that the member could fail in a more susceptible shear plane. The super spy genius Austin Powers, having taken Applied Elasticity, knew that the entire plan resting on the ability of the member was doomed to fail. The material properties of the members allowed for only small shear capacities and on thus the concrete member was going to fail and the world would be saved. In a world of codes and simplified equations, the physics and math of the problem is seldom used. Most of the time designs are drawn to meet standards. However, in many circumstances the physics behind the problem is far more complicated than what most people take it to be. By understanding what is really going on inside the member and realizing that just because forces are acting in a set direction the member will have stress that are not acting in the same direction as the forces, it is possible to understand the frailty of the simplified equations. A common example would be that of a wedge piece used to support a shelf. The belief that this member will be in compression is not very accurate. By looking at the boundary conditions of the member and the loads applied it is possible to see that the compressive load might not really be controlling the situation. Thus from the merry homemaker fixing a shelf to the super spy saving the world the knowledge of what really is happen from the physic of the problem to the boundary conditions applied, it is possible to determine how a member is going to fail and design the member so that it will not fail in service. ZZZ wrote: Heyyyyyy what is applied elasticity??? Failure is key word in designing of a physical structure. Whenever a designer comes across the word failure his instinct knocks the door of applied elasticity. A course in applied in applied elasticity develops the legitimacy of applying the fundamental concepts in practical applications. Elasticity is all about three things: equilibrium, stress-strain relationship and strain displacement relationship. It's about why a body is prone to failure. Important things dealt in the class were: Analysis of stress, stress-strain relationship, two dimensional problems, mechanical behavior of materials and deflection in beams and most importantly how you interrelate physics and math involved. By going through the course you will realize that understanding the concepts is more important than to just know the formulae. It will insist you to think in pragmatic way and apply the fundamentals of elasticity to practical problems. Comparing these solutions with those obtained by using elementary strength of materials was given due importance. Rather than looking an object in aesthetic view I started looking from design point of view. I experienced how exciting it was to map the fundamentals on to the real world applications such as in construction of bridges, buildings and in aeronautics. Knowing and understanding the boundary conditions was a crucial factor in solving problems. Thinking independent of coordinate system and flexibility in using coordinate system were dealt with utmost precision. Even though the class is for three
hours you don't feel like it to be. Dr. Kaw has
always been a constant stimulant to me in being more inquisitive towards the
subject. Finally last but not the least I learnt not only to diagnose the failure of a body but
also the political system in CK wrote: In the Mechanics of
Materials, the course we study does not allow us to be perspective about the
subject. The exploration of stress analysis focuses
on techniques for analysis in realistic settings.The
thirst for realistic knowledge remains unquenched. Mechanics
of Materials needs extension to understand the realistic concepts. Applied Elasticity fills the gap between the Mechanics
of Materials and the realistic concepts. Applied Elasticity which
involves concepts and mathematical theory of Elasticity focuses on the
nature of approaches and their applications in engineering and points out the
mode of thinking in analyzing problems as well as the proper way to solve
them. Discusses such problems of Elasticity as
plane, spatial, plates and shells. It gives an exact
solution form simple to complex plus numerous figures. Applied Elasticity expands
coverage of Mechanics of Materials theory; three dimensional stress and
strain transformations, strain energy in structural members, analysis of thin
and thick walled cylinders, application of strain energy methods to beams may
be successfully applied to realistic problems. The
above may look more but it is the Applied Elasticity which
does these all only on three fundamental equations... 1)Stress-Strain relationships 2)Strain-Displacement relationships 3)Equilibrium conditions. Applied Elasticity has the basic
course structure which can clear all our questions including basics which are
not cleared in the under-graduate study. Applied
Elasticity is the course not only for Mechanical Engineers but also Civil
Engineers. Civil Engineers can get more knowledge in
the issues of bridges, pipes etc... Applied Elasticity with Maple ( a
mathematical software) is an excellent combination. Maple
which analysis graphs of the problems of Applied Elasticity is fantastic. The appreciation of Applied Elasticity can be done when the problems are analyzed in Maple. My opinion after completion of this course is that my view
pertinent to problems involving stressess and
strains has totally changed. I am not having
disregard for Mechanics of Materials but the extend of solving practical
problems remains an unsatisfactory attitude towards the subject. A Engineer always wants to see the problem physically. I feel Applied Elasticity does want an Engineer wants
whoever may be. I feel Dr. Autar K Kaw who is the
professor who dealt with this course has done justice to his grad students. His sense of humor in the class adds new enthusiasm to
attend the class. I sincerely express my
thankfulness to Dr. Autar K Kaw who guided successfully guided us in the
completion of this course.
SS wrote: Fortune is something, which cannot be predicted nor calculated. But speaking technically it is not true. An answer for this is a course in Applied Elasticity. Theory of Elasticity is a tool to predict the failure point in a structure by analyzing strain and stress concentrations. The alacrity of this point lies in the fact that all major applications deals with theory of elasticity. It eventually proves out to be a key point of social security and a fortune setter for massive constructions. Applied elasticity deals with the general equations to be satisfied by a body in equilibrium under any extended force system. It examines the load-carrying capacity of a body from three standpoints Strength, Stiffness (deformation characteristics),and Stability by using the fundamental principles. The course fills the gap between the mechanics of materials and the mathematical theory of elasticity focusing on the nature of the approaches and their applications in engineering and points out the mode of thinking in analyzing problems as well as the proper way to solve them. The approaches in widespread use for determining the influence of applied loads on elastic bodies are the mechanics of materials and the theory of elasticity. Both rely on the conditions of equilibrium and make use of a relationship between stress and strain. The essential difference between these methods lies in the extent to which the strain is described and in the types of simplification. The theory of elasticity is preferred where critical design constraints such as minimum weight, minimum cost, or high reliability dictate more exact treatment or where prior experience is limited and intuition does not serve adequately to supply the needed simplifications with any degree of assurance. It yields solutions more closely approximating the actual distribution of strain, stress and displacement thus providing a check on the limitations of mechanics of materials solution. To summarize the course in applied elasticity as Dr. Kaw explains, Applied Elasticity plays three important roles to ascertain the distribution of stress, strain and displacement within a elastic body using the fundamental principles of equilibrium, stress-strain and strain-displacement relationships. Firstly, it provides exact solutions where the configurations of loading and boundary are relatively simple. Secondly, it provides a check upon the limitations of the strength of materials approach. Thirdly, it serves as the basis of approximate solutions employing numerical solutions. RR wrote: What did I learn after my summer break? The days of Summer were coming to an end and, with great anticipation, I was awaiting the upcoming Fall semester. It had been a very long break for me, almost three years. I'm what the university would call a "Non-traditional" student, I prefer to refer myself as a "long term" student. So, you see, from my vantage point I have tunnel vision. I've been the educational equivalent of the Orient Express and my final destination is still out if sight. This time the express brought me, at the end
to the Summer of 2000, to the Fall semester and directly to a new locale: Advanced Mechanics
of Materials. The professor
affectionately calls it Applied Elasticity. The
convenient train schedule is what really brought me
to the class, one night a week from However, nothing could have prepared me for what I was about to encounter. Early in the journey I was forced to reckon with the immortal demons of calculus. Vaguely familiar terms from a realm that time forgot were unearthed in the process. Scouring my mind for the quintessence of an era past was like combing a mine field of archaic terminology and recalling the incendiary incidents and battle scars from yesteryear. Couple this with the explosive surprise of wonderment and amazement that comes with each new discovery and rediscovery made during this excursion on the educational highway, was redeeming and thoroughly enjoyable. Old concepts, tried and true, were revisited with a vigor and an intensity that made it appear new and exciting. Seemingly simple concepts were disassembled, analyzed and re-assembled to expose the inner workings of the multitude of simplifications that litter the engineering landscape. What was taken for granted in the past has now been painstakingly revisited and answered beyond any reasonable doubt. Emphasis on the understanding of the underlying theory is undeniably fundamental in this class; an understanding of the basics is crucial. It is rigorous and demanding, commanding all the respect it fully deserves. Although, traditional homework for grade consideration was not mandatory, a compulsion for completion is requisite for a successful conclusion of the class. Emphasis on computer skills and exposure to Maple, the software of choice, is an integral part of the learning experience. The roadmap for the semester included day trips to the analysis of stress and strain. A few outings to two and three dimensional elasticity, as well as, stress-strain equations were expected. An obligatory trip to the criteria for mechanical failure followed by an excursion to axisymmetrically loaded members left us all just waiting for the conclusion: Energy Methods To summarize, Applied Elasticity, has given me the tools to look critically at finite element programs. From input, to output and all the boundary conditions that define the problem. Likewise it has re-emphasized the critical link between science and engineering. Some may say that Engineering is an Art, I would add that it has a solid foundation in science. All that's left to do is to pack my bags and reboard for the next leg of my fantastic voyage. JO wrote: Applied Elasticity
course, offered at the The methods employed in solving of structural problems through the mathematical theory of elasticity are quite different from the approaches used in the basic mechanics of materials. Mechanics of materials focuses on approximate solutions of practical problems and the governing equations are derived based on physical observations and reasoning, combined with partial applications of the procedures of solid-body mechanics. To the contrary, analysis based on the theory of elasticity uses mathematical analysis to determine exact stress and strain distribution in the body loaded with external forces. Although both methods relay on the conditions of equilibrium and relationship between stress and strain associated with elastic materials, the essential difference between these methods lies in the extent to which the strain is described and in the employed specifications. For example, mechanics of materials approach yields the average stress at the specific section under a given loading based on the assumed deformation mode or distribution of strain in the body as whole. In contrast, the elasticity method does not relay on a prescribed deformation mode and bases its analysis on the general equations to be satisfied by the body in equilibrium under any external force system. Three-dimensional problems in elasticity are often very complex, but during the Applied Elasticity course I have learned the right ways to approach them. In many engineering problems it can be justified to simplify assumptions with respect to the state of strain and stress, and to reduce a three-dimensional problem to the two-dimensional one. As a result of this procedure, the complexity of analysis can be significantly reduced without sacrificing accuracy of the analysis. Additionally, for cases when reduction to two-dimensional problem is not recommended, solutions can be obtained by useful, indirect methods of solution offering less formidable task to the engineer. Because of its unique approach to the analysis, the theory of elasticity yields solutions more closely approximating the actual distribution of stress, strain and displacement, providing valuable check on the limitations of the mechanics of materials solutions. Also, it provides useful tool for analysis of structures when the critical design constrains require more exact treatment. For example, when minimum weight or minimum cost are priorities in design solutions, analysis based on theory of elasticity should be seriously considered as the best method to be employed. In conclusion, I believe that familiarity with applied elasticity and the methods of analysis it offers should be seriously considered by every structural engineer. JM wrote: On this essay I'm going to talk about my advance elasticity class. We used the book advanced strength and applied elasticity by Urgural and Fenster, PTR, third edition. The pre-requisite for this class is the course mechanics of materials. Advance elasticity consists mainly of using the strengths of materials to apply it on engineer problems. The chapters covered in this class were as follow: Chapter 1, analysis of stress. Chapter 2, Strain and Stress- strain relations. Chapter 3, two-dimensional problems in elasticity. Chapter 4, criteria for material failure. Chapter 8, axisymmetrically loaded member. Chapter 10, energy methods. I think one of the most important concepts I learned in this class was, the fifteen equations of elasticity that come from these three categories: Equilibrium, Stresses and Shear, and Strain-displacement. From these three categories three equations come from Equilibrium, six equations come from Stresses and shears, and six equations come from Strain-displacement. With these fifteen equations we can solve any engineer problem that deals with forces applied to any type of bodies. I think this class was very interesting and informative. I found interesting that we were able to use the program MAPLE to solve the problems given in class. Before taking this class I really did not have knowledge of the program MAPLE. Thanks to this class I learned how to use the program and how to apply it to solve engineers problems. This program is very useful because it helps you to save time solving equations that would take you longer to do with out this important tool. One reason that I did not like this class was the factor that the class was given once a week for three hours. I think the department should change it from once a week to twice a week. Some of the other things that would benefit this class would be to review the trigonometric functions and also Mohr's circle. The grading system of this class was very fair. We had four exams all equally distributed through out the semester. I liked this grading system because I study for each test approximately the same amount of information instead of just having two big tests - midterm and final- to study with more information to cover. I think that for the next class it can be better to have homework graded. I think it motivates students to study more if they are graded for the homework. MH wrote: It started for me as a young boy, always fantasizing about building things. You could say I always wanted to be an Engineer. I am not sure if I chose the right career, but it's a bit late now. I have always liked building things, even the games I played as a little kid revolved around construction. I would imitate my dad working around the house, playing with the left over pieces of wood, block and nails. I
emphasized this desire of wanting to be an Engineer
as I got older. Of course, during
these times, even playing with playdough or such
things, you have no engineering background, but you still apply it with mere
common sense. I
had no understanding of stress or strain the way I do now, but common sense
helped. I got
my wish after finishing high school. I
went to college and, you guessed it, the Now I am on my way to doing what I always wanted. After the first year and getting to study the basic engineering sciences, everything started to make more sense. Once I studied mechanics of materials (which I think is the most important engineering science), I understood why structural elements behave the way they do and why they fail; understanding the yielding concepts. As most students rush through the four years to graduate, they really do not think beyond what is merely scratching the surface. I graduated, worked for some time, then went on to pursue my dreams of higher studies. I got my fill of design courses, but discovered that I needed to place more emphasis on the basic ideas. You remember those second year courses, the ones that shape up your understanding of the basic concepts of the mechanics of materials? A course was suggested to me by one of my professors, which was the "Theory of Elasticity". I can not thank him enough for his suggestion. After finishing this course, I realized a lot of things I'd never thought about in my undergraduate courses. This course emphasized my entire understanding of the mechanics of material science. It brought it all together, the physical aspect with the mathematical aspect. I no longer apply some formulas blindly. It made me think more deeply and more logically about materials, their properties and the emphasis of the concepts of stress and strain in a way I can truly appreciate. I learned many new concepts and theories that will help to make me a better Engineer. Whether you are a working Engineer or a research student, you will appreciate what you will learn in this class. If any Mechanical or Structural Engineer does not take this course, they will be missing a lot. BF wrote: As the end of the semester approaches and everything is becoming due, I can't help to reflect upon such an eventful semester. What has just happened? After my reflection period is over, I plunge back into my studies to see what is next on the agenda. Ah, the Applied Elasticity assignment is due. After discovering my assignment for this course involved an even further and deeper reflection of the semester, I began collecting my thoughts as any good writer does. Several things come to mind, but then I remember what the assignment is. What have I learned in Applied Elasticity? Well, the easiest way to complete this assignment is to give up and say that I have learned nothing. I think I should be honest with you, I did learn something. To prove it, I am not going to use the book to look up equations, or glance over my notes to refresh my memory of the topics of this course. The first thing I have learned from this course is not to just memorize things for a test. Applying concepts to a practical application involves drilling the concepts into your mind so that you know them by heart. Unfortunately, I have not accomplished that this semester. I have also learned that a spirited professor can set the stage for the excitement level of the class. When Dr. Kaw comes into the room, you feel a unique charge, and you know that class will be enjoyable today. Moreover, here are several practical things I have learned from the course material. First of all, at any given point of a body there are 6 stresses, 6 strains, and 3 displacements that can be experience by that point. This next part is for all the engineers. That means we need 15 equations! There are three types of equations, stress- strain relationships, strain- displacement, and equilibrium equations. We also analyzed plane stress, which was a good part of the course because you can make a lot of assumptions. I think the most practical of them all is the compound cylinder problem due to its direct effect for human safety. This course did a good job of opening my eyes to a different way of looking at stress in a body, and how important it is to realize that a failure can occur at any point, and safety is the number one priority. I think my most valuable experience in this course is when I think about how important the semi-colon is in Maple. SS wrote:
To begin, let me advance the idea that graduate school is where you finally So,
what new "tools" did this course in Applied Elasticity add to my
tool box? I added a deeper understanding of what various failure
criteria actually I developed an appreciation for the concept of
interference fit. This is These
and many other small tools are now safely stored away in my toolbox of FG wrote: In response to your letter as to what you should expect in the "Applied Elasticity" class. The first lesson you will learn as did I is that if you were to study for five days for the first test, you will be doing way too much. This class concept is based on theory. So by understanding the general material you should be able to do well on the tests what I am saying is don't over do it, think simple not complex. Also it would be recommended that you study your basic trig. Functions. As this has nothing to do with what was taught in class, you will see it on a test. The overall objective of the class is to prepare you to be able to apply the basics of Applied Elasticity to engineering problems. You will need to be able to compare elementary strength or materials, so you are able to solve common engineering problems. As simple as it seems the answers that you solve for in class are at best estimations of what is found to be the real answer in the real world, the reason being that there are factors that are not taken into account. This class is only to understand the fundamentals of Applied Elasticity, if you choose to further your studies you must realize that these are only the basics. The coarse should only be used to understand the properties of Applied Elasticity. The second thing that you should understand are the Stress- Strain, Strain-Displacement and Equilibrium relationship, these are the basics of Applied Elasticity. To these three parts there are fifteen components, three differential equations for equilibrium, six simultaneous linear equations for Stress-Strain, and six partial differential equations for Strain-Displacement. With these realize that the only thing that will change among them will be the boundary conditions. The third thing is that you need to be good at deriving equations. Since Dr. Kaw is very big on this subject, he usually in class gives you enough to get started then you need to work the rest of the solution yourself, by deriving equations to arrive at the proper solution. A few other things that you should brush up on that would prepare you for the class besides your trig functions are Mohr's circle, which is very important to solve problems, and the different coordinate systems. It would be to your benefit to go to every class and do all the assigned problems as well as the recommended problems. These tips should prepare you for the class if you pay attention to detail, since you will have marks taken off of your grade for simple sign convention, this is not the only detail to be concerned with but is very important to getting the correct solution. KSS wrote: As a first year graduate student, I was very nervous to take this course since it obviously states ‘Advanced' in its title. However, through the course, I found myself enjoying this class very much. I am very happy to have an opportunity to share my experiences and thoughts about this class. In terms of Dr. Kaw's course description, it is a class to apply fundamentals of elasticity to broad engineering fields. In addition to theories and concepts, the class also covers problem solving using computer programs. I benefited a lot from this class since it helped me enhance my levels of understanding on basic concepts of strain and stress, and be able to apply knowledge to other disciplines. Actually, I have learned more than I expected to learn, and the knowledge that I learned in this class will be a good guideline in my future work. I am very much impressed by the quality of the class. Even though the class covers a variety of materials, it always provides well-organized information, which is easy to understand. The text book in the class ‘Advanced Strength and Applied Elasticity' helped me build up the knowledge base on the issues, and the mathematical computer Program ‘Maple' made my life much easier. I really like Dr. Kaw's teaching style. He always explains class materials very clearly and helps understanding. He also provided a lot of useful information related to the class, such as practical examples in real world and sources from internet. Most of all, his good sense of humor makes the class more interesting and enjoyable. One of unique characteristics of this class is that Dr. Kaw teaches focal points in his class rather than providing huge body of information. His class is usually brief and clear, and it leads students to go further based on the lecture. I think his purpose is to establish basic structure of the knowledge in the lecture, and to make student develop more knowledge upon it by investing their time and efforts. Dr. Kaw doesn't give you a fish, but he teaches how to catch a fish. The learning from his class, such as how important logical thinking is, and how to apply basic knowledge to other disciplines, was also very valuable. It showed me how to successfully survive in engineering graduate school. Most importantly, the class taught me how to be an independent student who can make a good use of the class and get more out of the class. I feel fortunate to learn this valuable lesson in the first year of my graduate program. I am sure that the knowledge and lesson from this class will make me a successful engineering graduate student.
TM wrote: The other day, when a classmate asked me what this class was like, I was forced to stop and think. Just what did we learn in this class? One could read the syllabus for a catalog of topics covered, but most of these were covered to some extent by undergraduate coursework. The concepts of elasticity and its 15 equations and 15 unknowns proved to be interesting. In retrospect, it would have been nice to actually solve a system of 15 equations and 15 unknowns, but that would have taken us further into the realm of tedious mathematics than time would allow. Unfortunately, many of the various simplifications required assuming a solution, and then using that assumption to obtain results that, in the end, were used to verify the assumption. No big surprises there! From a practical standpoint, the study of stress concentrations around holes would be useful. The study of compound cylinders, while not directly applicable to my work, could be useful for the case of shrink fitting a hub to a shaft. The determination of principal stresses and the understanding of stress transformations will be useful in helping to understand the extraordinary engineering problems. The axisymetric approach to stress analysis will be especially useful to someone who, like myself, will have to design a pressure vessel, or two, sometime before retirement. After registering for any class and purchasing my books, I always browse through them with anticipation and, often, apprehension. This class was no different. The seemingly endless use of partial differential equations and linear algebra made me wish that I were better prepared to attempt this task. The use of MAPLE helped to relieve this sense of dread that had been cast upon me. As a structural engineer, I looked forward with great anticipation to the study of such relevant areas as: torsion of open cross-section members, beams on elastic foundations, buckling stability, and plastic behavior of materials. Unfortunately, none of these subjects were covered in the class. Nevertheless, the class was clearly not a waste of time for many of the reasons outlined above. Although the class may not have provided much in the way of immediately useful, practical solutions to real world problems, it has been my experience that everything you learn becomes useful at some point in time. In many cases, just a broader understanding of fundamental principals, and the ability to properly apply these principles, is the most valuable outcome one can derive from a class such as this. AT wrote: State of the art and practical in perspective, this classic exploration of stress analysis focuses on techniques for analysis in the realistic setting. This prospective analysis of stress emphasize on the three important aspects, it provides exact solution where the configuration of loading and boundary are relatively simple; it provides a check upon the limitations of the strength of materials approach; it serves as basis of approximate solution employing numerical analysis. The physical significance of the solution and practical application are delta with at most gravity. An effort has been made in the course work to present a balance between the theories necessary to gain insight in the mechanics. Mechanics of materials often offer no more than crude approximation to the real problems because of simplification related to the geometry and condition of loading and numerical solutions, which are very useful in presenting stress analysis in amore realistic fashion. Thus an attempt has been made in APPLIED ELASTICITY to emphasize those aspects of theory and application, which expose a student to inherent concepts for the professional practice and design analysis. It provides a uniquely balanced coverage of practical applications pertaining to design. The key topics covered in this course are ANALYSIS OF STRESS, STRESS AND STRESS –STRAIN RELATIONS, TWO DIMENSIONAL PROBLEMS IN ELASTICITY, MECHANICAL BEHAVIOUR OF MATERIALS, AXISYMMETRICALLY LOADED MEMBERS, ENERGY METHODS AND DEFLECTION IN BEAMS. It placed emphasis on application to aeronautical, civil and mechanical engineering applications. This course not only forms a firm basics for mechanical engineers but also for the civil engineers who come across the practical use of applied elasticity in there profession. In my opinion the course certainly gives a proper orientation and insight regarding practical approach in stress analysis .It would definitely assist students in making a prospective practical endeavours. It's my personnel experience that on the completion of this course my way of looking at things has changed a lot. Whenever I came across a physical structure instead of concentrating on its visual properties , I started to see the graphical view of the direction of different stresses and stress concentrations. I think this would be an appropriate example for justifying the point that "course in applied elasticity would not only gives more perspective view but also an intricate sense of humor". It's my deepest pleasure to express my gratitude towards Dr.KAW, who guided me meticulously in completing my course. |