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" Boundary Element Techniques in Computer-Aided Engineering "
edited by C.A. Brebbia.
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BL
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773641
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b593635
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| Main Entry
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edited by C.A. Brebbia.
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Boundary Element Techniques in Computer-Aided Engineering\ edited by C.A. Brebbia.
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| Publication Statement
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Dordrecht : Springer Netherlands, 1984
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| Series Statement
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NATO ASI series., Series E,, Applied sciences ;, 84.
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(452 pages)
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| ISBN
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9400961928
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: 9400961944
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: 9789400961920
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: 9789400961944
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| Contents
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1. Weighted Residual Formulation of Approximate Methods --; 1.1. Introduction --; 1.2. Basic Definition --; 1.3. Approximate Solutions --; 1.4. Method of Weighted Residuals --; 1.5. Weak Formulations --; 1.6. The Inverse Problem --; 1.7. Conclusions --; References --; 2. Boundary Element Methods --; 2.1. Fundamentals of Functional Analysis --; 2.2. Generalized Green's Formula --; 2.3. Variational Formulation --; 2.4. Weighted Residual Scheme --; 2.5. Boundary Element Formulation of Poisson's Equation --; 2.6. Fundamental Solutions --; 2.7. Boundary Discretisation and Systems Equations --; 2.8. Computation of Integrals --; 2D case --; 3. Boundary Integral Equations --; 3.1. Simple-layer Formulations --; 3.2. Double-layer Formulations --; 3.3. Direct Formulations --; 3.4. Indirect Vector Formulations --; 3.5. Direct Formulations --; References --; 4. Scalar and Vector Potential Theory --; 4.1. The Simple-layer Potential --; 4.2. The Double-layer Potential --; 4.3. Green's Formula --; 4.4. Identification of Scalar and Vector Symbolism --; 4.5. Somigliana's Identity --; 4.6. Rigid-body Displacement Field --; References --; 5. Potential Problems in Two Dimensions --; 5.1. Introduction --; 5.2. Flow past an Obstacle --; 5.3. Discretisation --; 5.4. Green's Boundary Formula --; 5.5. Applications --; 5.6. Boundary Singularities --; 5.7. Composite Domains --; 5.8. Conclusion --; References --; 6. Three-dimensional Axisymmetrical Potential Problems --; 6.1. Introduction --; 6.2. The Newtonian Potential --; 6.3. Discretisation --; 6.4. General Domain --; 6.5. Axisymmetric Problems --; 6.6. Conclusion --; References --; 7. Heat Transfer Applications --; 7.1. Introduction --; 7.2. Integral Equations associated with Steady Heat Conduction Problems --; 7.3. Numerical Solution of the Integral Equations --; 7.4. Poisson's Equation --; 7.5. Non-homogeneous Bodies; Method of Subregions --; 7.6. Anisotropic Bodies --; References --; 8. Numerical Integration and other Computational Techniques --; 8.1. Introduction --; 8.2. Isoparametric Elements --; 8.3. Numerical Integration --; References --; 9. Starting to work with Boundary Elements --; 9.1. Introduction --; 9.2. The Boundary Element Method --; 9.3. Advantages and Disadvantages of the BEM compared to FEM --; 9.4. Introduction to BEASY --; 9.5. Examples --; 9.6. Conclusions --; References --; 10. Experiences in Boundary Element Applications --; 10.1. Introduction --; 10.2. Pre- and Post Processing --; 10.3. C.A.D. Coupling --; 10.4. Installation on Different Computers --; 10.5. Recommendations for BEM use --; 11. Electrostatics Problems --; 11.1. Introduction --; 11.2. Theoretical Basis --; 11.3. Boundary Elements --; 11.4. Applications --; 11.5. Conclusions --; References --; 12. A Boundary Element Solution of the Wave Equation --; 12.1. Introduction --; 12.2. Theoretical Development --; 12.3. Boundary Conditions --; 12.4. Numerical Implementation --; 12.5. Velocities and Pressures --; 12.6. Identification of Areas in Shadow --; 12.7. Test Example --; 12.8. Conclusions --; References --; 13. Elasticity Problems --; 13.1. Introduction --; 13.2. Governing Equations --; 13.3. Boundary Integral Formulation --; 13.4. Two Dimensional Elasticity Problems --; 13.5. Three Dimensional Elasticity Problems --; 13.6. Axisymmetric Elasticity Problems --; References --; 14. Elasticity Problems with Body Forces --; 14.1. Introduction --; 14.2. Transformation to Boundary Integrals --; 14.3. 2D Body Forces --; 14.4. 3D Body Forces --; 14.5. Axisymmetric Body Forces --; References --; 15. Time Dependent Problems --; 15.1. Introduction --; 15.2. Time Dependent Diffusion --; 15.3. The Scalar Wave Equation --; 15.4. Transient Elastodynamics --; 15.5. Mass Matrix Representation --; 15.6. Conclusions --; References --; 16. Time Dependent Potential Problems --; 16.1. Introduction --; 16.2. Integral Formulation of Heat Conduction Problems --; 16.3. Numerical Solution of the Integral Equations --; 16.4. Conclusions --; References --; 17. Plate Bending Problems --; 17.1. Preliminaries --; 17.2. Reciprocal Work Relation --; 17.3. Boundary Integral Representations --; 17.4. Concluding Remarks --; References --; 18. A Choice of Fundamental Solutions --; 18.1. Introductory Remarks --; 18.2. A simple example: 2D Heat Conduction --; 18.3. A more significant example: Plane Elastostatics --; 18.4. Concluding Remarks --; References --; 19. Formulation for Cracks in Plate Bending --; 19.1. Fundamental Solutions for Cracks --; 19.2. Augmented Boundary Integral Equations --; 19.3. Concluding Remarks --; References --; 20. Fracture Mechanics Stress Analysis, I. --; 20.1. Introduction --; 20.2. Stress Intensity Factors --; 20.3. Integral Equation Methods for Crack Tip Stress Analysis --; References --; 21. Fracture Mechanics Stress Analysis, II --; 21.1. Introduction --; 21.2. Invariant Integral based on the Energy Momentum Tensor --; 21.3 Invariant Integrals deduced from Betti's Reciprocal Theorem --; 21.4. Some Numerical Results for a Nocht Problem --; 21.5. A Problem of Debond Stress Analysis --; References --; 22. BEM in Geomechanics --; 22.1. Introduction --; 22.2. Notation and some Basic Ideas --; 22.3. BEM applied to the Interaction between Structures and the Supporting Ground --; 22.4. Inhomogeneity, Zoning and Layering --; 22.5. Elastoplasticity --; 22.6. Concluding Remarks --; References --; 23. An Asymptotic Error Analysis and Underlying Mathematical Principles for Boundary Element Methods --; 23.1. Projection Methods and Garding's Inequality --; 23.2. Examples of Strongly Elliptic Boundary Integral Equations --; 23.3. Asymptotic Convergence of Galerkin type Boundary Element Methods --; 23.4. Asymptotic Convergence of Collocation Methods --; References.
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Computer engineering.
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| Subject
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Computer science -- Mathematics.
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Mathematics.
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| Added Entry
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C A Brebbia
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| Parallel Title
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Proceedings of the NATO Advanced Study Institute on Boundary Elements in CAD, Southampton, England, September 19-30, 1983
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