Finite Element Analysis

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.

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