Zienkiewicz O.C., Taylor L.R. The Finite Element Method. Volume 2: Solid Mechanics

5th Edition. — Butterworth-Heinemann, 2000. — 479 p.The first volume of this edition covered basic aspects of finite element approximation in the context of linear problems. Typical examples of two- and three-dimensional elasticity, heat conduction and electromagnetic problems in a steady state and transient state were dealt with and a finite element computer program structure was introduced. However, many aspects of formulation had to be relegated to the second and third volumes in which we hope the reader will find the answer to more advanced problems, most of which are of continuing practical and research interest.
In this volume we consider more advanced problems in solid mechanics while in Volume 3 we consider applications in fluid dynamics. It is our intent that Volume 2 can be used by investigators familiar with the finite element method in general terms and will introduce them here to the subject of specialized topics in solid mechanics. This volume can thus in many ways stand alone. Many of the general finite element procedures available in Volume 1 may not be familiar to a reader introduced to the finite element method through different texts. We therefore recommend that the present volume be used in conjunction with Volume 1 to which we make frequent reference.
General problems in solid mechanics and non-linearity.
Solution of non-linear algebraic equations.
Inelastic materials.
Plate bending approximation: thin (Kirchhoff) plates and C1 continuity requirements.
'Thick' Reissner-Mindlin plates - irreducible and mixed formulations.
Shells as an assembly of flat elements.
Axisymmetric shells.
Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions.
Semi-analytical finite element processes - use of orthogonal functions and 'finite strip' methods.
Geometrically non-linear problems - finite deformation.
Non-linear structural problems - large displacement and instability.
Pseudo-rigid and rigid-flexible bodies.
Computer procedures for finite element analysis.
Appendix A: Invariants of second-order tensors.
Author index.
Subject index.