The Finite Element Method: Its Basis and Fundamentals

O. C. Zienkiewicz was one of the early pioneers of the finite element method and is internationally recognized as a leading figure in its development and wide-ranging application. He was awarded numerous honorary degrees, medals and awards over his career, including the Royal Medal of the Royal Society and Commander of the British Empire (CBE). He was a founding author of The Finite Element Method books and developed them through six editions over 40 years up to his death in 2009. Previous positions held by O.C. Zienkiewicz include UNESCO Professor of Numerical Methods in Engineering at the International Centre for Numerical Methods in Engineering, Barcelona, Director of the Institute for Numerical Methods in Engineering at the University of Wales, Swansea, U.K. R.L Taylor is a Professor of the Graduate School at the Department of Civil and Environmental Engineering, University of California, Berkeley, USA. Awarded the Daniel C. Drucker Medal by the American Society of Mechanical Engineering in 2005, the Gauss-Newton Award and Congress Medal by the International Association for Computational Mechanics in 2002, and the Von Neumann Medal by the US Association for Computational Mechanics in 1999.

Some Preliminaries: The Standard Discrete System; A Direct Physical Approach to Problems in Elasticity; Generalization of the Finite Element Concepts; Galerkin-Weighted Residual and Variational Approaches; 'Standard’ and ‘hierarchical’ Element Shape Functions: Some General Families of Continuity; Mapped Elements and Numerical Integration – ‘Infinite’ and ‘Singularity’ Elements; Two Dimensional Problems in Plane Stress, Plane Strain and Axisymmetric Elasticity; Steady-State Field Problems; Three-Dimensional Elasticity and Field Problems; Mesh Generation; The Patch Test; Mixed Formulation and Constraints – Complete Field Methods; Incompressible Materials; Mixed Formulation and Constraints; Errors, Recovery Processes and Error Estimates; Adaptive Finite Element Refinement; Point-Based Approximations – 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; Matrix Algebra; Tensor-Indicial Notation in the Approximation of Elasticity Problems; Basic Equations of Displacement Analysis; Some Integration Formulae for a Triangle; Some Integration Formulae for a Tetrahedron; Some Vector Algebra; Integration by Parts in Two and Three Dimensions (Green’s Theorem); Solutions Exact at Nodes; Matrix Diagonalization or Lumping