The finite element method: linear static and dynamic finite element analysis

Directed toward students without in-depth mathematical training, this text cultivates comprehensive skills in linear static and dynamic finite element methodology. Included are a comprehensive presentation and analysis of algorithms of time-dependent phenomena plus beam, plate, and shell theories derived directly from three-dimensional elasticity theory. Solution guide available upon request.

Reprint. Originally published: Englewood Cliffs, N.J. : Prentice-Hall, 1987. The author has corrected minor errors in the text and deleted the sections of Chapters 10 and 11 that are no longer necessary.

Part 1. Linear Static Analysis -- 1. Fundamental Concepts; A Simple One-Dimensional Boundary-Value Problem -- 1.1. Introductory Remarks and Preliminaries -- 1.2. Strong, or Classical, Form of the Problem -- 1.3. Weak, or Variational, Form of the Problem -- 1.4. Eqivalence of Strong and Weak Forms; Natural Boundary Conditions -- 1.5. Galerkin's Approximation Method -- 1.6. Matrix Equations; Stiffness Matrix K -- 1.7. Examples: 1 and 2 Degrees of Freedom -- 1.8. Piecewise Linear Finite Element Space -- 1.9. Properties of K -- 1.10. Mathematical Analysis -- 1.11. Interlude: Gauss Elimination; Hand-calculation Version -- 1.12. The Element Point of View -- 1.13. Element Stiffness Matrix and Force Vector -- 1.14. Assembly of Global Stiffness Matrix and Force Vector; LM Array -- 1.15. Explicit Computation of Element Stiffness Matrix and Force Vector -- 1.16. Exercise: Bernoulli-Euler Beam Theory and Hermite Cubics -- Appendix 1.I. An Elementary Discussion of Continuity, Differentiability, and Smoothness -- 2. Formulation of Two- and Three-Dimensional Boundary-Value Problems -- 2.1. Introductory Remarks -- 2.2. Preliminaries -- 2.3. Classical Linear Heat Conduction: Strong and Weak Forms;…