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Table of Contents
1 Cover
4 Preface to the second edition
5 Preface to the first edition Notes
6 Preface
8 1 Introduction to the finite element method 1.1 An introductory problem 1.2 Generalized formulation 1.3 Approximate solutions 1.4 Post‐solution operations 1.5 Estimation of error in energy norm 1.6 The choice of discretization in 1D 1.7 Eigenvalue problems 1.8 Other finite element methods Notes
9 2 Boundary value problems 2.1 Notation 2.2 The scalar elliptic boundary value problem 2.3 Heat conduction 2.4 Equations of linear elasticity – strong form 2.5 Stokes flow 2.6 Generalized formulation of problems of linear elasticity 2.7 Residual stresses 2.8 Chapter summary Notes
10 3 Implementation 3.1 Standard elements in two dimensions 3.2 Standard polynomial spaces 3.3 Shape functions 3.4 Mapping functions in two dimensions 3.5 Finite element spaces in two dimensions 3.6 Essential boundary conditions 3.7 Elements in three dimensions 3.8 Integration and differentiation 3.9 Stiffness matrices and load vectors 3.10 Post‐solution operations 3.11 Computation of the solution and its first derivatives 3.12 Nodal forces 3.13 Chapter summary Notes
11 4 Pre‐ and postprocessing procedures and verification 4.1 Regularity in two and three dimensions 4.2 The Laplace equation in two dimensions 4.3 The Laplace equation in three dimensions 4.4 Planar elasticity 4.5 Robustness 4.6 Solution verification Notes
12 5 Simulation 5.1 Development of a very useful mathematical model 5.2 Finite element modeling and numerical simulation Notes
13 6 Calibration, validation and ranking 6.1 Fatigue data 6.2 The predictors of Peterson and Neuber 6.3 The predictor Gα 6.4 Biaxial test data 6.5 Management of model development Notes
14 7 Beams, plates and shells 7.1 Beams 7.2 Plates 7.3 Shells 7.4 Chapter summary Notes
15 8
