Boundary element techniques: Theory and applications in engineering

1 Approximate Methods. - 1.1. Introduction. - 1.2. Basic Definitions. - 1.3. Approximate Solutions. - 1.4. Method of Weighted Residuals. - 1.4.1. The Collocation Method. - 1.4.2. Method of Collocation by Subregions. - 1.5. Method of Galerkin. - 1.6. Weak Formulations. - 1.7. Inverse Problem and Boundary Solutions. - 1.8. Classification of Approximate Methods. - References. - 2 Potential Problems. - 2.1. Introduction. - 2.2. Elements of Potential Theory. - 2.3. Indirect Formulation. - 2.4. Direct Formulation. - 2.5. Boundary Element Method. - 2.6. Two-Dimensional Problems. - 2.6.1. Source Formulation. - 2.7. Poisson Equation. - 2.8. Subregions. - 2.9. Orthotropy and Anisotropy. - 2.10. Infinite Regions. - 2.11. Special Fundamental Solutions. - 2.12. Three-Dimensional Problems. - 2.13. Axisymmetric Problems. - 2.14. Axisymmetric Problems with Arbitrary Boundary Conditions. - 2.15. Nonlinear Materials and Boundary Conditions. - 2.15.1. Nonlinear Boundary Conditions. - References. - 3 Interpolation Functions. - 3.1. Introduction. - 3.2. Linear Elements for Two-Dimensional Problems. - 3.3. Quadratic and Higher-Order Elements. - 3.4. Boundary Elements for Three-Dimensional Problems. - 3.4.1. Quadrilateral Elements. - 3.4.2. Higher-Order Quadrilateral Elements. - 3.4.3. Lagrangian Quadrilateral Elements. - 3.4.4. Triangular Elements. - 3.4.5. Higher-Order Triangular Elements. - 3.5. Three-Dimensional Cell Elements. - 3.5.1. Tetrahedron. - 3.5.2. Cube. - 3.6. Discontinuous Boundary Elements. - 3.7. Order of Interpolation Functions. - References. - 4 Diffusion Problems. - 4.1. Introduction. - 4.2. Laplace Transforms. - 4.3. Coupled Boundary Element - Finite Difference Methods. - 4.4. Time-Dependent Fundamental Solutions. - 4.5. Two-Dimensional Problems. - 4.5.1. Constant Time Interpolation. - 4.5.2. Linear Time Interpolation. - 4.5.3. Quadratic Time Interpolation. - 4.5.4. Space Integration. - 4.6. Time-Marching Schemes. - 4.7. Three-Dimensional Problems. - 4.8. Axisymmetric Problems. - 4.9. Nonlinear Diffusion. - References. - 5 Elastostatics. - 5.1. Introduction to the Theory of Elasticity. - 5.1.1. Initial Stresses or Initial Strains. - 5.2. Fundamental Integral Statement. - 5.2.1. Somigliana Identity. - 5.3. Fundamental Solutions. - 5.4. Stresses at Internal Points. - 5.5. Boundary Integral Equation. - 5.6. Infinite and Semi-Infinite Regions. - 5.7. Numerical Implementation. - 5.8. Boundary Elements. - 5.9. System of Equations. - 5.10. Stresses and Displacements Inside the Body. - 5.11. Stresses on the Boundary. - 5.12. Surface Traction Discontinuities. - 5.13. Two-Dimensional Elasticity. - 5.14. Body Forces. - 5.14.1. Gravitational Loads. - 5.14.2. Centrifugal Load. - 5.14.3. Thermal Loading. - 5.15. Axisymmetric Problems. - 5.15.1. Extension to Nonaxisymmetric Boundary Values. - 5.16. Anisotropy. - References. - 6 Boundary Integral Formulation for Inelastic Problems. - 6.1. Introduction. - 6.2. Inelastic Behavior of Materials. - 6.3. Governing Equations. - 6.4. Boundary Integral Formulation. - 6.5. Internal Stresses. - 6.6. Alternative Boundary Element Formulations. - 6.6.1. Initial Strain. - 6.6.2. Initial Stress. - 6.6.3. Fictitious Tractions and Body Forces. - 6.7. Half-Plane Formulations. - 6.8. Spatial Discretization. - 6.9. Internal Cells. - 6.10. Axisymmetric Case. - References. - 7 Elastoplasticity. - 7.1. Introduction. - 7.2. Some Simple Elastoplastic Relations. - 7.3. Initial Strain: Numerical Solution Technique. - 7.3.1. Examples - Initial Strain Formulation. - 7.4. General Elastoplastic Stress-Strain Relations. - 7.5. Initial Stress: Outline of Solution Techniques. - 7.5.1. Examples: Kelvin Implementation. - 7.5.2. Examples: Half-Plane Implementation. - 7.6. Comparison with Finite Elements. - References. - 8 Other Nonlinear Material Problems. - 8.1. Introduction. - 8.2. Rate-Dependent Constitutive Equations. - 8.3. Solution Technique: Viscoplasticity. - 8.4. Examples: Time-Dependent Problems. - 8.5. No-Tension Materials. - References. - 9 Plate Bending. - 9.1. Introduction. - 9.2. Governing Equations. - 9.3. Integral Equations. - 9.3.1. Other Fundamental Solutions. - 9.4. Applications. - References. - 10 Wave Propagation Problems. - 10.1. Introduction. - 10.2. Three-Dimensional Water Wave Propagation Problems. - 10.3. Vertical Axisymmetric Bodies. - 10.4. Horizontal Cylinders of Arbitrary Section. - 10.5. Vertical Cylinders of Arbitrary Section. - 10.6. Transient Scalar Wave Equation. - 10.7. Three-Dimensional Problems: The Retarded Potential. - 10.8. Two-Dimensional Problems. - References. - 11 Vibrations. - 11.1. Introduction. - 11.2. Governing Equations. - 11.3. Time-Dependent Integral Formulation. - 11.4. Laplace Transform Formulation. - 11.5. Steady-State Elastodynamics. - 11.6. Free Vibrations. - References. - 12 Further Applications in Fluid Mechanics. - 12.1. Introduction. - 12.2. Transient Groundwater Flow. - 12.3. Moving Interface Problems. - 12.4. Axisymmetric Bodies in Cross Flow. - 12.5. Slow Viscous Flow (Stokes Flow). - 12.6. General Viscous Flow. - 12.6.1. Steady Problems. - 12.6.2. Transient Problems. - References. - 13 Coupling of Boundary Elements with Other Methods. - 13.1. Introduction. - 13.2. Coupling of Finite Element and Boundary Element Solutions. - 13.2.1. The Energy Approach. - 13.3. Alternative Approach. - 13.4. Internal Fluid Problems. - 13.4.1. Free-Surface Boundary Condition. - 13.4.2. Extension to Compressible Fluid. - 13.5. Approximate Boundary Elements. - 13.6. Approximate Finite Elements. - References. - 14 Computer Program for Two-Dimensional Elastostatics. - 14.1. Introduction. - 14.2. Main Program and Data Structure. - 14.3. Subroutine INPUT. - 14.4. Subroutine MATRX. - 14.5. Subroutine FUNC. - 14.6. Subroutine SLNPD. - 14.7. Subroutine OUTPT. - 14.8. Subroutine FENC. - 14.9. Examples. - 14.9.1. Square Plate. - 14.9.2. Cylindrical Cavity Problem. - References. - Appendix A Numerical Integration Formulas. - A.1. Introduction. - A.2. Standard Gaussian Quadrature. - A.2.1. One-Dimensional Quadrature. - A.2.2. Two- and Three-Dimensional Quadrature for Rectangles and Rectangular Hexahedra. - A.2.3. Triangular Domain. - A.3. Computation of Singular Integrals. - A.3.1. One-Dimensional Logarithmic Gaussian Quadrature Formulas. - A.3.3. Numerical Evaluation of Cauchy Principal Values. - References. - Appendix B Semi-Infinite Fundamental Solutions. - B.1. Half-Space. - B.2. Half-Plane. - References. - Appendix C Some Particular Expressions for Two-Dimensional Inelastic Problems.