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Full Description
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications.
This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover:
Weak forms
Variational forms
Multi-dimensional field problems
Automatic mesh generation
Plate bending and shells
Developments in meshless techniques
Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis.
Contents
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
