Synopses & Reviews
Originally developed to address specific areas of structural mechanics and elasticity, the finite element method is applicable to problems throughout applied mathematics, continuum mechanics, engineering, and physics. This text elucidates the method's broader scope, bridging the gap between mathematical foundations and practical applications. Intended for students as well as professionals, it is an excellent companion for independent study, with numerous illustrative examples and problems.
The authors trace the method's development and explain the technique in clearly understandable stages. Topics include solving problems involving partial differential equations, with a thorough finite element analysis of Poisson's equation; a step-by-step assembly of the master matrix; various numerical techniques for solving large systems of equations; and applications to problems in elasticity and the bending of beams and plates. Additional subjects include general interpolation functions, numerical integrations, and higher-order elements; applications to second- and fourth-order partial differential equations; and a variety of issues involving elastic vibrations, heat transfer, and fluid flow. The displacement model is fully developed, in addition to the hybrid model, of which Dr. Tong was an originator. The text concludes with numerous helpful appendixes.
This text introduces mathematical foundations, developing them coherently and rigorously to reveal the method's broad applications. It emphasizes use of the variational approach, providing appendixes on variational calculus and matrix algebra for a self-contained treatment. Detailed examples employ Poisson's equations and the general Sturm-Liouville problem. 1977 edition.
This coherent, rigorous introduction to mathematical foundations reveals the method's broad applications. It emphasizes the variational approach, providing a self-contained treatment with appendixes on variational calculus and matrix algebra. 1977 edition.
Table of Contents
Preface1. The Finite-Element Method2. The Finite-Element Method for Poisson's Equation3. Assembly and Solution for Large Systems4. Implementation of Assembly and Solution Schemes for Large Systems on High-Speed Computers5. Applications to Solid Mechanics6. Interpolation Functions, Numerical Integration, and Higher-Order Elements7. Bending of Beams and Plates8. Hybrid Methods9. Selected Topics and Recent DevelopmentsAppendix A. Notation and Matrix AlgebraAppendix B. Rectangular ElementsAppendix C. Triangular Elements with Straight EdgesAppendix D. Variational MethodsReferencesIndex