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Introduction to Finite Element Analysis: Formulation, Verification and Validation
1 Introduction 1
1.1 Numerical Simulation 2
1.2 Why is numerical accuracy important? 11
2 An Outline of the Finite Element Method 17
3 Formulation of Mathematical Models 79
4 Generalized Formulations 109
5 Finite Element Spaces 145
6 Regularity and Rats of Convergence 167
7 Computation and Verification of Data 215
8 What should be Computed and Why? 237
9 Beams, Plates and Shells 261
10 Nonlinear Models 297
A Definitions 315
B Numerical Quadrature 321
C Properties of the Stress Tensor 325
D Computation of Stress Intensity Factors 331
E Saint-Venant’s principle 337
F Solutions for Selected Exercises 345
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