First Course in the Finite Element Method

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A First Course in the Finite Element Analysis provides a simple, basic approach to the finite element method that can be understood by both undergraduate and graduate students. It does not have the usual prerequisites (such as structural analysis) required by most available texts in this area. 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. This revised fourth edition includes the addition of a large number of new problems (including SI problems), an appendix for mechanical and thermal properties, and more civil applications. Key Features Over 150 new problems added, many of which are application and design based. Appendix for Properties of Structural Steel and Aluminum Shapes. Appendix for mechanical and thermal properties. Added sections on I-beam definition and standard dimensions. More civil applications anda mix of SI and English units for problems. Timoshenko beam matrix stiffness compared with conventional Euler-Bernoulli stiffness matrix. Illustrations of how different element types can be combined in one infinite model. The book proceeds from basic to advanced topics and is suitable for a one or two-course sequence. 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 shapes.Many worked examples appear throughout the text. These examples are solved "longhand" to illustrate how essential concepts are applied. Table Of Contents Introduction Introduction to the Stiffness (Displacement) Method Development of Truss Equations Development of Beam Equations Frame and Grid Equations Development of the Plane Stress and Plane Strain Stiffness Equations Practical Considerations in Modeling; Interpreting Results and Examples of Plane Stress/Strain Analysis Development of the Linear-Strain Triangle Equations Axisymmetric Elements Isoparametric Formulation Three-Dimensional Stress Analysis Plate Bending Element Heat Transfer and Mass Transport Fluid Flow Thermal Stress Structural Dynamics and Time-Dependent Heat Transfer AppendixesAnswer to Selected Problems. Index.