Zienkiewicz O.C., Taylor L.R. The Finite Element Method. Volume 1. The Basis

5th Edition. — Butterworth-Heinemann, 2000. — 707 p.It is just over thirty years since The Finite Element Method in Structural and Continuum Mechanics was first published. This book, which was the first dealing with the finite element method, provided the base from which many further developments occurred. The expanding research and field of application of finite elements led to the second edition in 1971, the third in 1977 and the fourth in 1989 and 1991 The size of each of these volumes expanded geometrically (from 272 pages in 1967 to the fourth edition of 1455 pages in two volumes). This was necessary to do justice to a rapidly expanding field of professional application and research. Even so, much filtering of the contents was necessary to keep these editions within reasonable bounds.
It seems that a new edition is necessary every decade as the subject is expanding and many important developments are continuously occurring. The present fifth edition is indeed motivated by several important developments which have occurred in the 90s. These include such subjects as adaptive error control, meshless and point based methods, new approaches to fluid dynamics, etc. However, we feel it is important not to increase further the overall size of the book and we therefore have eliminated some redundant material.Some preliminaries: the standard discrete system.
A direct approach to problems in elasticity.
Generalization of the finite element concepts. Galerkin-weighted residual and variational approaches.
Plane stress and plane strain.
Axisymmetric stress analysis.
Three-dimensional stress analysis.
Steady-state field problems - heat conduction, electric and magnetic potential, fluid flow, etc.
Standard' and 'hierarchical' element shape functions: some general families of Co continuity.
Mapped elements and numerical integration - 'infinite' and 'singularity' elements.
The patch test, reduced integration, and non-conforming elements.
Mixed formulation and constraints- complete field methods.
Incompressible materials, mixed methods and other procedures of solution.
Mixed formulation and constraints - incomplete (hybrid) field methods, boundary/Trefftz methods.
Errors, recovery processes and error estimates.
Adaptive finite element refinement.
Point-based approximations; element-free Galerkin - and other meshless methods.
The time dimension - semi-discretization of field and dynamic problems and analytical solution procedures.
The time dimension - discrete approximation in time.
Coupled systems.
Computer procedures for finite element analysis.Appendix A: Matrix algebra.
Appendix B: Tensor-indicial notation in the approximation of elasticity problems.
Appendix C: Basic equations of displacement analysis.
Appendix D: Some integration formulae for a triangle.
Appendix E: Some integration formulae for a tetrahedron.
Appendix F: Some vector algebra.
Appendix G: Integration by parts in two and three dimensions (Green's theorem).
Appendix H: Solutions exact at nodes.
Appendix I: Matrix diagonalization or lumping.
Author index.
Subject index.