The Finite Element Method: Its Basis and Fundamentals (Hardcover, 7 ed)

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