The essentials of finite element modeling and adaptive refinement for beginning analysts to advanced researchers in solid mechanics /
Tallennettuna:
| Päätekijä: | |
|---|---|
| Aineistotyyppi: | Elektroninen E-kirja |
| Kieli: | englanti |
| Julkaistu: |
[New York, N.Y.] (222 East 46th Street, New York, NY 10017) :
Momentum Press,
2012.
|
| Aiheet: | |
| Linkit: | An electronic book accessible through the World Wide Web; click to view |
| Tagit: |
Ei tageja, Lisää ensimmäinen tagi!
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Sisällysluettelo:
- Preface
- 1. Introduction
- 1.1 Problem definition
- 1.2 Overall objectives
- 1.3 Specific tasks
- 1.4 The central role of the interpolation functions
- 1.5 A closer look at the interpolation functions
- 1.6 Physically interpretable interpolation functions in action
- 1.7 The overall significance of the physically interpretable notation
- 1.8 Examples of model refinement and the need for adaptive refinement
- 1.9 Examples of adaptive refinement and error analysis
- 1.10 Summary
- 1.11 References
- 2. An overview of finite element modeling characteristics
- 2.1 Introduction
- 2.2 Characteristics of exact finite element results
- 2.3 More demanding loading conditions
- 2.4 Discretization errors in an initial model
- 2.5 Error reduction and uniform refinement
- 2.6 Error reduction and adaptive refinement
- 2.7 The effect of element modeling capability on discretization errors
- 2.8 Summary and future applications
- 2.9 References
- 2A. Elements of two-dimensional modeling
- 2A1. Introduction
- 2A2. Submodeling refinement strategy
- 2A3. Initial model
- 2A4. Adaptive refinement results
- 2A5. Summary
- 2A6. References
- 2B. Exact solutions for two longitudinal bar problems
- 2B1. Introduction
- 2B2. General solution of the governing differential equation
- 2B3. Application of a free boundary condition
- 2B4. Second application of separation of variables
- 2B5. Solution for a constant distributed load
- 2B6. Solution for a linearly varying distributed load
- 2B7. Summary
- 3. Identification of finite element strain modeling capabilities
- 3.1 Introduction
- 3.2 Identification of the strain modeling capabilities of a three-node bar element
- 3.3 An introduction to physically interpretable interpolation polynomials
- 3.4 Identification of the physically interpretable coefficients
- 3.5 The decomposition of element displacements into strain components
- 3.6 A common basis for the finite element and finite difference methods
- 3.7 Modeling capabilities of the four-node bar element
- 3.8 Identification and evaluation of element behavior
- 3.9 Evaluation of a two-dimensional strain model
- 3.10 Analysis by inspection in two dimensions
- 3.11 Summary and conclusion
- 3.12 Reference
- 4. The source and quantification of discretization errors
- 4.1 Introduction
- 4.2 Background concepts, the residual approach to error analysis
- 4.3 Quantifying the failure to satisfy point-wise equilibrium
- 4.4 Every finite element solution is an exact solution to some problem
- 4.5 Summary and conclusion
- 4.6 Reference
- 5. Modeling inefficiency in irregular isoparametric elements
- 5.1 Introduction
- 5.2 An overview of isoparametric element strain modeling characteristics
- 5.3 Essential elements of the isoparametric method
- 5.4 The source of strain modeling errors in isoparametric elements
- 5.5 Strain modeling characteristics of isoparametric elements
- 5.6 Modeling errors in irregular isoparametric elements
- 5.7 Results for a series of uniform refinements
- 5.8 Summary and conclusion
- 5.9 References
- 6. Introduction to adaptive refinement
- 6.1 Introduction
- 6.2 Physically interpretable error estimators
- 6.3 A model refinement strategy
- 6.4 A demonstration of uniform refinement
- 6.5 A demonstration of adaptive refinement
- 6.6 An application of an absolute error estimator
- 6.7 Summary
- 6.8 References
- 7. Strain energy-based error estimators, the Z/Z error estimator
- 7.1 Introduction
- 7.2 The basis of the Z/Z error estimator, a smoothed strain representation
- 7.3 The Z/Z elemental strain energy error estimator
- 7.4 The Z/Z error estimator
- 7.5 A modified locally normalized Z/Z error estimator
- 7.6 A demonstration of the Z/Z error estimator
- 7.7 A demonstration of adaptive refinement
- 7.8 Summary and conclusion
- 7.9 References
- 7A. Gauss points, super convergent strains, and Chebyshev polynomials
- 7A1. Introduction
- 7A2. Modeling behavior of three-node elements
- 7A3. Gauss points and Chebyshev polynomials
- 7A4. References
- 7B. An unsuccessful example of adaptive refinement
- 7B1. Introduction
- 7B2. Example 1
- 7B3. Example 2
- 7B4. Summary
- 8. A high resolution point-wise residual error estimator
- 8.1 Introduction
- 8.2 An overview of the point-wise residual error estimator
- 8.3 The theoretical basis for the point-wise residual error estimator
- 8.4 Computation of the point-wise residual error estimator
- 8.5 Formulation of the finite difference operators
- 8.6 The formulation of the point-wise residual error estimator
- 8.7 A demonstration of the point-wise finite difference error estimator
- 8.8 A demonstration of adaptive refinement
- 8.9 A temptation to avoid and a reason for using child meshes
- 8.10 Summary and conclusion
- 8.11 Reference
- 9. Modeling characteristics and efficiencies of higher order elements
- 9.1 Introduction
- 9.2 Adaptive refinement examples (4.0% termination criterion)
- 9.3 Adaptive refinement examples (0.4% termination criterion)
- 9.4 In-situ identification of the five-node element modeling behavior
- 9.5 Strain contributions of the basis set components
- 9.6 Comparative modeling behavior of four-node elements
- 9.7 Summary, conclusion, and recommendations for future work
- 10. Formulation of a 10-node quadratic strain element
- 10.1 Introduction
- 10.2 Identification of the linearly independent strain gradient quantities
- 10.3 Identification of the elemental strain modeling characteristics
- 10.4 Formulation of the strain energy expression
- 10.5 Identification and evaluation of the required integrals
- 10.6 Expansion of the strain energy kernel
- 10.7 Formulation of the stiffness matrix
- 10.8 Summary and conclusion
- 10A. A numerical example for a 10-node stiffness matrix
- 10A1. Introduction
- 10A2. Element geometry and nodal numbering
- 10A3. Formulation of the transformation to nodal displacement coordinates
- 10A4. Formulation and evaluation of the strain energy expression
- 10A5. Formulation of the stiffness matrix
- 10A6. Summary and conclusion
- 10B. Matlab formulation of the 10-node element stiffness matrix
- 10B1. Introduction
- 10B2. Driver program for forming the stiffness matrix for a 10-node element
- 10B3. Form phi and phi inverse for 10-node element
- 10B4. Form integrals in stiffness matrix using Green's theorem
- 10B5. Form strain energy kernel for 10-node element
- 10B6. Plot geometry and nodes for 10-node element
- 10B7. Function to transform Matlab matrices to form for use in Word
- 11. Performance-based refinement guides
- 11.1 Introduction
- 11.2 Theoretical overview for finite difference smoothing
- 11.3 Development of the refinement guide
- 11.4 Problem description
- 11.5 Examples of adaptive refinement
- 11.6 An efficient refinement guide based on nodal averaging
- 11.7 Further comparisons of the refinement guides
- 11.8 Summary and conclusion
- 11.9 References
- 12. Summary and research recommendations
- 12.1 Introduction
- 12.2 An overview of advances in adaptive refinement
- 12.3 Displacement interpolation functions revisited: a reinterpretation
- 12.4 Advances in the finite element method
- 12.5 Advances in the finite difference method
- 12.6 Recommendations for future work and research opportunities
- 12.7 Reference
- Index.