Basic Principles and Applications

ISBN-13: 9783642822179 / Angielski / Miękka / 2011 / 258 str.

C. A. Brebbia

Opis

As the Boundary Element Method develops into a tool of engineering analysis more effort is dedicated to studying new applications and solving different problems. This book contains chapters on the basic principles of the technique, time dependent problems, fluid mechanics, hydraulics, geomechanics and plate bending. The number of non-linear and time dependent problems which have become amenable to solution using boundary elements have induced many researchers to investigate in depth the basis of the method. Chapter 0 of this book presents an ap proach based on weighted residual and error approximations, which permits easy construction of the governing boundary integral equations. Chapter I reviews the theoretical aspects of integral equation formulations with emphasis in their mathematical aspects. The analysis of time dependent problems is presented in Chap. 2 which describes the time and space dependent integral formulation of heat conduction problems and then proposes a numerical procedure and time marching algorithm. Chapter 3 reviews the application of boundary elements for fracture mechanics analysis in the presence of thermal stresses. The chapter presents numerical results and the considerations on numerical accuracy are of interest to analysts as well as practising engineers."

Spis treści

0 Boundary Integral Formulations.- 0.1 Fundamentals of Functional Analysis.- 0.2 Generalized Green’s Formula.- 0.3 Variational Formulation.- 0.4 Weighted Residual Scheme.- 0.5 Boundary Integral Formulation of Poisson’s Equation.- 0.6 Boundary Integral Formulation of Navier Equations.- 0.7 Final Remarks.- 1 A Review of the Theory.- 1.1 Historical Introduction.- 1.2 Potential Theory: Green’s Formula.- 1.3 Boundary Integral Equations.- 1.4 Vector Potential Theory: Somigliana’s Formula.- 1.5 Indirect Vector Formulations.- 1.6 Two-Dimensional Potential Theory.- References.- 2 Applications in Transient Heat Conduction.- 2.1 Introduction.- 2.2 Integral Formulation of Heat Conduction Problems.- 2.3 Numerical Solution of the Integral Equations.- 2.4 Time-Marching Procedures.- 2.5 Examples and Conclusions.- References.- Notation.- 3 Fracture Mechanics Application in Thermoelastic States.- 3.1 Introduction.- 3.2 Integral Equation Formulation.- 3.3 Computational Scheme.- 3.3.1 Transient Heat Conduction Problems.- 3.3.2 Thermoelastic Problems.- 3.4 Numerical Results and Discussion.- 3.4.1 Transient Heat Conduction.- 3.4.2 Stress Intensity Factor Computation.- 3.5 Some Considerations on Numerical Accuracy.- 3.6 Concluding Remarks.- References.- 4 Applications of Boundary Element Methods to Fluid Mechanics.- 4.1 Introduction.- 4.2 History.- 4.3 Aerodynamics and Hydrodynamics.- 4.4 Porous Media Flow.- 4.5 Free Boundary Problems.- 4.6 Unsteady Free Boundaries — Water Waves.- 4.7 Linear Waves.- 4.8 Stoke’s Flow.- 4.9 Porous-Elasticity.- 4.10 Concluding Remarks.- References.- 5 Water Waves Analysis.- 5.1 Introduction.- 5.2 Basic Theory.- 5.3 Boundary Element Formulation.- 5.4 Special Structural Types.- 5.5 Equations of Motion for the Structure.- 5.6 Numerical Examples.- 5.7 Conclusions.- References.- 6 Interelement Continuity in the Boundary Element Method.- 6.1 Introduction.- 6.2 Continuous Elements.- 6.3 Planar Discontinuous Elements.- 6.4 Discontinuous Elements for Three Dimensional Analysis.- 6.5 Closure.- References.- 7 Applications in Geomechanics.- 7.1 Introduction.- 7.2 Basic Formulation.- 7.3 No-Tension and Discontinuity Problems.- 7.4 Viscoplasticity.- 7.5 Conclusions.- Appendix: Fundamental Solutions and Other Tensor Forms.- References.- 8 Applications in Mining.- 8.1 Introduction.- 8.2 Review of the Development and Application of Boundary Element Formulations in Mining.- 8.3 Displacement Discontinuity Formulation.- 8.4 The Boundary Element Formulation.- 8.5 Elasto-plastic Material Behaviour.- 8.6 Combination of BEM with Other Techniques.- 8.7 Summary and Future Outlook.- Appendix A: Equation Solvers.- Appendix B: Fundamental Solutions.- References.- 9 Finite Deflections of Plates.- 9.1 Introduction.- 9.2 Geometrically Nonlinear Governing Equations.- 9.3 Integral Equation Formulation for von Karman-type Equations.- 9.4 The Approximate Berger Equation.- 9.5 Integral Formulation for the Berger Equation.- 9.6 Numerical Examples.- 9.7 Nonlinear Shallow Shell and Sandwich Plate/Shell Problems.- 9.8 Concluding Remarks.- References.- Appendices.- 10 Trefftz Method.- 10.1 Introduction.- 10.2 Scope.- 10.3 Green’s Formulas.- 10.4 Illustration of Green’s Formulas.- 10.5 Green’s Formulas in Discontinuous Fields.- 10.6 T-Complete Systems.- 10.7 Hilbert-Space Formulation.- 10.8 Representation of Solutions.- References.