April 04, 2008
Author: Robert D. Cook
University of Wisconsin - MadisonPreface
(Note: the preface is written by Robert D. Cook known as “I”)
This book is intended for beginning courses in finite elements (FE) that are oriented toward users of the method. The course envisioned emphasized the behavior of FE and include computational work in which problems are solved by means of commercial software and the computed results are critically examined. The instructor may often site with students at the computer to offer advice and to monitor their skill in modeling and assessment of result. The course would use computational problems as vehicles to teach proper use of FE, rather than use FE as a way to solve certain problems. The book presents a modest amount of theory, discusses the nature of FE solutions, offer modeling advice, suggests computational problems, and emphasizes the need for checking the computed results. Problem areas treated are common in mechanical engineering and related disciplines. Suggested computational problems include topics often treated in a second course in stress analysis, such as spinning disks and elastic foundations. The computational problems usually have simple geometry, so that FE may be emphasized rather than details of data preparation. Some instructors especially those who teach more advanced students, may wish to devise problems of a more “real world” nature, despite their greater complexity.
Several commercial FE programs are available for use on microcomputers and workstations. This book is not tailored to any particular FE program and therefore does not discuss the formalisms of input data preparation. Suitable software will have most of the following features: capability in static stress analysis, structural dynamics, vibration, and heat transfer; a good library of elements; some node and element generation capability; help screens; plotting and animation of displaced shapes; contour plotting of computed stresses without nodal averaging. The software must be easy to use, at the expense of versatility if necessary, so that time will not be wasted in learning procedures peculiar to a certain code bu having little to do with insight in to FE method.
Many powerful analytical tools are readily available in the form of computer software. Engineers do not have time to study the theory of all these tools, and undergraduates usually study theory with little enthusiasm. For undergraduate and graduate students alike, it appears that study of only the theory of FE confers no ability in the use of FE. Theory cannot be ignored, however; an engineer mus understand the nature of the analytical method as well as the physical nature of the phenomenon to be studied because computer implementation makes it all too easy to choose inappropriate options or push an analytical method beyond its limits of applicability. Fortunately, the user of FE software need not understand all its details. Mainly, the FE user should grasp the physical problem, understand how FE’s behave, know the limitation of the theory on which they are based, and be able and willing to check results for correctness. The checking phase relies more on physical understanding of the problem than on knowledge of FE.
The presentation in this book presumes a knowledge of elementary matrix algebra and the level of physical understanding that a good student should have after completing a first course in mechanics of materials. This is adequate preparation for a one-semester course in the practice of FE, during which students will inevitably be exposed to concepts of stress analysis not treated in an elementary mechanics of materials course. The understanding they gain by working with these problems will be primarily physical but will be helpful if theory is to be studied subsequently. In my opinion students in a beginning course learn theory only if forced to do so, and then with little understanding of it. Only later, when the nature of a problem area has become familiar, can theory be understood and its practical value appreciated. These remarks are not intended to imply that the book is unsuitable for students who have advanced knowledge of stress analysis theory. In my experience, a student at any level may be deficient in physical understanding, and graduate students make many of the modeling mistakes also made by undergraduates.
The beginning course I teach is taken by seniors. We currently discuss most of chapter 1 through 7 and the first four articles of Chapter 9. Isoperimetrical elements and Sections 5.5 and 6.6 are omitted. For this course I find that previous exposure to the theories of elasticity, plates, shells, and vibrations is not necessary because the essential physical behavior of such problems is easily grasped: flat plates and stretch or bend; curved plates (shells) can simultaneously stretch and bend; examples of vibration are common-place (e.g., a bell). If courses in these areas were prerequisites, a few would enroll in the FE course. Students would then have education in neither FE nor problems to which FE analysis is applied. Yet after graduation they will use FE whether of not they are prepared to do so.
In addition to serving as the primary text in a first FE course, the book should be useful as an adjunct text in a second FE course that considers theory in more detail, and in other courses such as vibrations where the solution of practical problems is considered important. It in this context that the latter part of Chapter 9 (Vibration and Dynamics) and Chapter 10 (Nonlinearity in Stress Analysis) seem most appropriate. Practicing engineers as well as students may find that the book contains useful suggestions for modeling and solution strategy.
Several reviewers of the manuscript made many good suggestions. Their contributions are gratefully acknowledged. Thanks are also due to Pat Grinyer, who made it unnecessary for me to update my technical typing skills.
Robert D. Cook
Madison Wisconsin July 1994
To be continued…
