Finite Element Analysis. Barna Szabó

      

      Table of Contents

      1  Cover

      2  Title Page

      3  Copyright

      4  Preface to the second edition

      5  Preface to the first edition Notes

      6  Preface

      7  About the companion website

      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 Aspects of multiscale models 8.1 Unidirectional fiber‐reinforced laminae 8.2 Discussion Notes