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Introduction to the Finite Element Method: Theory, Programming and Applications

Introduction to the Finite Element Method: Theory, Programming and Applications

Erik G. Thompson

ISBN: 978-0-471-26753-9

360 pages

Select type: Hardcover

£79.50

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Description

Written for students with any engineering or applied science background, Erik Thompson's new text presents the theory, applications, and programming skills needed to understand the finite element method and use it to solve problems in engineering analysis and design. Offering concise, highly practical coverage, this introductory text provides complete finite element codes that can be run on the student version of MATLAB or easily converted to other languages.

This text gives students the opportunity to:

Master the basic theory: The text promotes an understanding and appreciation of the theoretical basis of finite element approximations by building on concepts that are intuitive to the students. Throughout, the text uses matrix notation to help students visualize the finite element matrices. Study problems reinforce basic theory.

Experiment with the code: Numerical experiments show how to test programs for possible errors, experiment with boundary conditions, and study accuracy and stability. Code development exercises suggest ways to modify the codes to create additional capabilities. All codes are available on the book's web page along with sample data files for testing them. Each code can be run immediately using only the student version of MATLAB. Because each code is written using explicit programming, they also serve as pseudo-codes that can be used to develop programs in any computer language.

Gain hands-on experience: Projects, representing a wide variety of engineering disciplines, enable students to conduct analyses of fairly complex problems. Many of these projects encourage investigations of new techniques for using the finite element method.

Related Resources

1. Introduction.

2. Calculus of Variations.

3. A Finite Element Program.

4. Linear Second Order Ordinary Differential Equations.

5. A Finite Element Function for Two Dimensions.

6. Poisson’s Equation -- FEM Approximation.

7. Poisson’s Equation -- Applications.

8. Higher-Order Elements.

9. A FEM Program for Two-Dimensional Boundary Value Problems.

10. Analysis of Transient Behavior.

11. Elasticity.

12. Higher-Order Equations.

Appendix A. Equation Solvers and Compact Storage.

Appendix B. The Shape Function Array.

Appendix C. Gaussian Quadrature.

Appendix D. Auxiliary Codes.

  • A balanced approach between theory, programming, and applications. This approach allows student to see the big picture--from the development of theory, to writing a workable program, to solving a practical problem. Many applications of finite element methods are given, so that the instructor will have no problem relating the method to students in different areas of engineering.
  • The text is not directed toward a particular discipline. The approach is general and does not discourage students by constantly describing the theory through examples that are unfamiliar to the student. Instructors can teach from this text regardless of the background of the students in the class.
  • Use of MATLAB. MATLAB script provides an easy, yet versatile, programming language to help students learn the intricacies of finite element programming. Each code is presented in the text side by side with a detailed explanation. Equations on the explanation side of the page show the reader what is taking place in the code.
  • A textbook rather than a reference text. This text is truly a textbook, designed to explain concepts in terms easily understood by students.
  • Use of projects as examples of additional concepts. This text allows students to gain experience by presenting interesting projects with hints and/or suggestions as to how they can best be solved. The variety of projects allows students to choose applications that appear most interesting.
  • Exercises for testing and modifying codes. For each section of the text that presents a new concept, exercises show students how to test the code for accuracy, stability, etc. These exercises often include suggested modifications to the code and auxiliary codes that can be written to increase the versatility of the code presented in the text. In this way, students gain confidence in a code and can create their own personal version of a code.
  • Provocative study questions. This text offers many questions that challenge students to better understand the material and the theory behind the finite element method.