In the years since the fourth edition of this seminal work was published, active research has developed the Finite Element Method into the pre-eminent tool for the modelling of physical systems. Written by the pre-eminent professors in their fields, this new edition of the Finite Element Method maintains the comprehensive style of the earlier editions and authoritatively incorporates the latest developments of this dynamic field. Expanded to three volumes the book now covers the basis of the method and its application to advanced solid mechanics and also advanced fluid dynamics. Aimed at undergraduate and postgraduate students, and essential as a reference tool for professional engineers, it provides a complete introduction to the method. Volume 1 of The Finite Element Method provides a complete introduction to the method, and is essential reading for undergraduates, postgraduates and professional engineers. Volume 2 concentrates on non-linear solid and structural mechanics and is ideal for postgraduate students and professional engineers working in this discipline. Volume 3 covers the whole range of fluid dynamics and is ideal reading for postgraduate level students and professional engineers working in this discipline.

Table of Contents:
VOLUME 1: Some preliminaries: The standard discrete system * A direct approach to problems in elasticity * Generalisation 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 familiarities of C0 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 problems, 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 * The time dimension semi-discretisation of field and dynamic problems and analytical solution procedures * The time dimension discrete approximation in time * Coupled systems * Computer procedures for finite element analysis * Appendices. VOLUME 2: Plate and shell bending approximation: thin (Kirchoff) plates and C1 continuity requirements * 'Thick' Reissner-Mindlin plates - irreducible and mixed formulations * Shells as an assembly of flat elements * Axisymmetric shells * VOLUME 3: Introduction and the equations of fluid dynamics * Convection dominated problems - finite element * A general algorithm for compressible and incompressible flows - the characteristic based split (CBS) algorithm * Incompressible laminar flow - Newtonian and non-Newtonian fluids * Free surface, buoyancy and turbulent incompressible flows * Compressible high-speed gas flow * Shallow water problems * Waves * Computer implementation of the CBS algorithm