Introduction to Finite Element Analysis Formulation Verification and Validation Wiley Series in Computational Mechanics 1st Edition by Barna Szabo, Ivo Babuska ISBN 0470977280 9780470977286
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ISBN 10: 0470977280
ISBN 13: 9780470977286
Author: Barna Szabo, Ivo Babuska
The revised and updated second edition of Finite Element Analysis: Method, Verification, and Validation offers a comprehensive review of the theoretical foundations of the finite element method and highlights the fundamentals of solution verification, validation, and uncertainty quantification. Written by noted experts on the topic, the book covers the theoretical fundamentals as well as the algorithmic structure of the finite element method. The text contains numerous examples and helpful exercises that clearly illustrate the techniques and procedures needed for accurate estimation of the quantities of interest. In addition, the authors describe the technical requirements for the formulation and application of design rules.
Designed as an accessible resource, the book has a companion website that contains a solutions manual, PowerPoint slides for instructors, and a link to finite element software. This important text:
- Offers a comprehensive review of the theoretical foundations of the finite element method
- Puts the focus on the fundamentals of solution verification, validation, and uncertainty quantification
- Presents the techniques and procedures of quality assurance in numerical solutions of mathematical problems
- Contains numerous examples and exercises
Written for students in mechanical and civil engineering, analysts seeking professional certification, and applied mathematicians, Finite Element Analysis: Method, Verification, and Validation, Second Edition includes the tools, concepts, techniques, and procedures that help with an understanding of finite element analysis.
Introduction to Finite Element Analysis Formulation Verification and Validation Wiley Series in Computational Mechanics 1st Table of contents:
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
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
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
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
5 Simulation
5.1 Development of a very useful mathematical model
5.2 Finite element modeling and numerical simulation
Notes
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
7 Beams, plates and shells
7.1 Beams
7.2 Plates
7.3 Shells
7.4 Chapter summary
Notes
8 Aspects of multiscale models
8.1 Unidirectional fiber‐reinforced laminae
8.2 Discussion
Notes
9 Non‐linear models
9.1 Heat conduction
9.2 Solid mechanics
9.3 Chapter summary
Notes
Appendix A: Appendix ADefinitionsDefinitions
A.1 Normed linear spaces, linear functionals and bilinear forms
A.2 Convergence in the space
A.3 The Schwarz inequality for integrals
Notes
Appendix B: Appendix BProof of h‐convergenceProof of h‐convergence
Appendix C: Appendix CConvergence in 3D: Empirical resultsConvergence in 3D: Empirical results
Appendix D: Appendix DLegendre polynomialsLegendre polynomials
D.1 Shape functions based on Legendre polynomials
Appendix E: Appendix ENumerical quadratureNumerical quadrature
E.1 Gaussian quadrature
E.2 Gauss‐Lobatto quadrature
Note
Appendix F: Appendix FPolynomial mapping functionsPolynomial mapping functions
F.1 Interpolation on surfaces
Appendix G: Appendix GCorner singularities in two‐dimensional elasticityCorner singularities in two‐dimensional elasticity
G.1 The Airy stress function
G.2 Stress‐free edges
Notes
Appendix H: Appendix HComputation of stress intensity factorsComputation of stress intensity factors
H.1 Singularities at crack tips
H.2 The contour integral method
H.3 The energy release rate
Note
Appendix I: Appendix IFundamentals of data analysisFundamentals of data analysis
I.1 Statistical foundations
I.2 Test data
I.3 Statistical models
I.4 Ranking
I.5 Confidence intervals
Notes
Appendix J: Appendix JEstimation of fastener forces in structural connectionsEstimation of fastener forces in structural connections
Appendix K: Appendix KUseful algorithms in solid mechanicsUseful algorithms in solid mechanics
K.1 The traction vector
K.2 Transformation of vectors
K.3 Transformation of stresses
K.4 Principal stresses
K.5 The von Mises stress
K.6 Statically equivalent forces and moments
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