A First Course in the Finite Element Method

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A FIRST COURSE IN THE FINITE ELEMENT METHOD provides a simple, basic approach to the course material that can be understood by both undergraduate and graduate students without the usual prerequisites (i.e. structural analysis). The book is written primarily as a basic learning tool for the undergraduate student in civil and mechanical engineering whose main interest is in stress analysis and heat transfer. The text is geared toward those who want to apply the finite element method as a tool to solve practical physical problems. Key Features Now includes examples from other fields in order to demonstrate that FEM can be used to solve problems from a variety of engineering and mathematical physics areas. Chapter objective sections have been added to each chapter as a strategy to increase understanding and retention of the material. Short answer type problems have been added to the end of each chapter to invoke the use of the creative thought process in understanding the principles of the Finite Element Method. End of chapter summaries and key equations sections have been added to each chapter for easy review. Additional plate bending real-world examples and problems have been included in order to enhance student understanding. Increased amount of illustrations of 3D applications and solutions in stress and heat transfer analysis. Written as a basic learning tool for students in civil and mechanical engineering, the text does not presume an extensive background in structural analysis. Topics progress from basic to advanced, making the text suitable for a one or two-course sequence. Mathematics is presented in a simple and straightforward manner making this text accessible and easily understood. Each chapter is structured in a similar format. General principles are presented for each topic, followed by traditional applications of these principles, which are in turn followed by computer applications where relevant. The principle of minimum potential energy and Galerkin's residual method are introduced at various stages as required to develop the equations needed for analysis. Appendices include basic matrix algebra (used throughout the text), solutions methods for simultaneous equations, equations from elasticity theory, equivalent nodal forces, the principle of virtual work, and properties of structural steel and aluminum sha Many worked examples appear throughout the text. These examples are solved "longhand" to illustrate how essential concepts are applied. Includes a 4-color insert that provides a clear visual application of FEM. Table of Contents 1. Introduction 2. Introduction To The Stiffness (Displacement) Method 3. Development Of Truss Equations 4. Development Of Beam Equations 5. Frame And Grid Equations 6. Development Of The Plane Stress And Strain Stiffness Equations 7. Practical Considerations In Modeling: Interpreting Results And Exampels Of Plane Stress/Strain Analysis 8. Development Of The Linear-Strain Traingle Equations 9. Axisymmetric Elements 10. Isoparametric Formulation 11. Three-Dimensional Stress Analysis 12. Plate Bending Element 13. Heat Transfer And Mass Transport 14. Fluid Flow In Porous Media And Through Hydraulic Networks; And Electrical Networks And Electrostatics 15. Thermal Stress 16. Structural Dynamics And Time-Dependent Heat Transfer Appendix A: Matrix Algebra Appendix B: Methods For Solution Of Simultaneous Linear Equations Appendix C: Equations For Elasticity Theory Appendix D: Equivalent Nodal Forces Appendix E: Principle Of Virtual Work Appendix F: Properties Of Structural Steel And Aluminum Shapes Answers To Selected Problems Index