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Introduction to Finite Element Analysis : Formulation, Verification and Validation.
When using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided?Whenever numerical simulation is employed in connection with engineering decisi...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
John Wiley & Sons,
2011.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Series; Title Page; Copyright; Dedication; About the Authors; Series Preface; Preface; 1: Introduction; 1.1 Numerical simulation; 1.2 Why is numerical accuracy important?; 1.3 Chapter summary; 2: An Outline of the Finite Element Method; 2.1 Mathematical models in one dimension; 2.2 Approximate solution; 2.3 Generalized formulation in one dimension; 2.4 Finite Element Approximations; 2.5 FEM in one dimension; 2.6 Properties of the generalized formulation; 2.7 Error estimation based on extrapolation; 2.8 Extraction methods; 2.9 Laboratory exercises; 2.10 Chapter summary.
- 3: Formulation of Mathematical Models3.1 Notation; 3.2 Heat conduction; 3.3 The scalar elliptic boundary value problem; 3.4 Linear elasticity; 3.5 Incompressible elastic materials; 3.6 Stokes' flow; 3.7 The hierarchic view of mathematical models; 3.8 Chapter summary; 4: Generalized Formulations; 4.1 The scalar elliptic problem; 4.2 The principle of virtual work; 4.3 Elastostatic problems; 4.4 Elastodynamic models; 4.5 Incompressible materials; 4.6 Chapter summary; 5: Finite Element Spaces; 5.1 Standard Elements in Two Dimensions; 5.2 Standard Polynomial Spaces; 5.3 Shape Functions.
- 5.4 Mapping Functions in Two Dimensions5.5 Elements in Three Dimensions; 5.6 Integration and Differentiation; 5.7 Stiffness Matrices and Load Vectors; 5.8 Chapter Summary; 6: Regularity and Rates of Convergence; 6.1 Regularity; 6.2 Classification; 6.3 The Neighborhood of Singular Points; 6.4 Rates of Convergence; 6.5 Chapter Summary; 7: Computation and Verification of Data; 7.1 Computation of the Solution and Its First Derivatives; 7.2 Nodal Forces; 7.3 Verification of Computed Data; 7.4 Flux and Stress Intensity Factors; 7.5 Chapter Summary; 8: What should be Computed and Why?
- 8.1 Basic Assumptions8.2 Conceptualization: Drivers of Damage Accumulation; 8.3 Classical Models of Metal Fatigue; 8.4 Linear Elastic Fracture Mechanics; 8.5 On the Existence of a Critical Distance; 8.6 Driving Forces for Damage Accumulation; 8.7 Cycle Counting; 8.8 Validation; 8.9 Chapter Summary; 9: Beams, Plates and Shells; 9.1 Beams; 9.2 Plates; 9.3 Shells; 9.4 The Oak Ridge Experiments; 9.5 Chapter Summary; 10: Nonlinear Models; 10.1 Heat Conduction; 10.2 Solid Mechanics; 10.3 Chapter Summary; Appendix A: Definitions; A.1 Norms and Seminorms; A.2 Normed Linear Spaces.
- A.3 Linear FunctionalsA. 4 Bilinear Forms; A.5 Convergence; A.6 Legendre Polynomials; A.7 Analytic Functions; A.8 The Schwarz Inequality for Integrals; Appendix B: Numerical Quadrature; B.1 Gaussian Quadrature; B.2 Gauss-Lobatto Quadrature; Appendix C: Properties of the Stress Tensor; C.1 The Traction Vector; C.2 Principal Stresses; C.3 Transformation of Vectors; C.4 Transformation of Stresses; Appendix D: Computation of Stress Intensity Factors; D.1 The Contour Integral Method; D.2 The Energy Release Rate; Appendix E: Saint-Venant's Principle; E.1 Green's Function for the Laplace Equation.