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This book provides an introduction to finite element analysis as a tool for the solution of practical engineering problems; teach the principles of finite element analysis including the mathematical fundamentals as required; to how to construct an appropriate finite element model of a physical system, to interpret the results of the analysis.

Finite Element Analysis

Table of Content











Introduction





Book Aims and Objectives





History and Perspective





The Finite Element Mesh: Terminology











Matrix Stiffness Methods





The Simple Bar Element





Assembly of Bar Elements - The Global Stiffness Matrix





Loads and Boundary Conditions





A Solution Strategy





Numerical Examples





Error Analysis and Ill-Conditioning





Singular Equations: Rigid Body Modes and Mechanisms





Symmetry, Anti-symmetry and Asymmetry





Thermal Loads











The Finite Element Formulation - One-Dimensional Problems





The Fundamental Equations





The Shape Function





The Finite Element Equations





The Element Stiffness Matrix for a 2 Node Bar with Linear Shape Functions











The Finite Element Formulation - Two-Dimensional Problems





The Fundamental Equations





The Finite Element Formulation for a Continuum





A Triangular Element





A Quadrilateral Element





Numerical Study - Pin-Jointed Frame with a Shear Web





Restrictions on Element Formulation - Completeness and Compatibility











Computational Implementation of the Finite Element Method





Solution Methodologies - Frontal v Banded Solvers





Storage of the Stiffness Matrix





Numerical Integration - Gaussian Quadrature











Beams, Plates, Shells and Solids





Solid Elements





A Beam Element





Plates and Shells











Parametric Element Formulation





Isoparametric bar element





Isoparametric Four-Node Quadrilateral Element





Isoparametric Eight-Node Quadrilateral Element