Boundary Element Analysis: Theory and Programming

Boundary Element Analysis: Theory and Programming introduces the theory behind the boundary element method and its computer applications. The author uses Cartesian tensor notation throughout the book and includes the steps involved in deriving many of the equations, enabling students to master this powerful and necessary tool for comprehending most of the literature on boundary elements. The book reviews elasticity, plate bending, elastodynamics, and elastoplasticity theories and their boundary element formulations. The author provides computer programs in Fortran 77 for elastostatic, plate bending, and free and forced vibration problems with detailed descriptions of various segments of the code. He adopts a unified approach in developing these programs, so that when students understand of the working of one program, they can easily follow the others. This approach enables students to begin using the boundary element method immediately. The book also presents a brief description of the finite element method with steps to develop efficient computer codes and a number of ways to combine the boundary element and finite boundary element equations to achieve the best results when analyzing a variety of engineering problems. The author's elegant presentation and comprehensive coverage of problems in structural and solid mechanics make Boundary Element Analysis: Theory and Programming an easy-to-use text for both students and professors.

Table of Contents:
MEET THE BOUNDARY ELEMENT METHOD What is the Boundary Element Method? How the Method Works Direct and Indirect Boundary Element Methods Boundary Element Method versus Finite Element Method A Brief History of the Boundary Element Method ELASTOSTATIC PROBLEMS Introduction Brief Review of the Mathematical Theory of Elasticity Two-Dimensional Problems of Elasticity The Reciprocal Theorem and the Somogliana Identity Boundary Integral Equation Numerical Solution of Boundary Integral Equations Boundary Elements and Interpolation of Displacements and Tractions Stresses on the Boundary Body Forces Piecewise Homogeneous Bodies Modelling Traction Discontinuities Solids of Revolution Anistropic Elasticity BOUNDARY ELEMENTS, INTERPOLATION FUNCTIONS, AND SINGULAR INTEGRALS Introduction Two-Dimensional Problems Three-Dimensional Problems Discontinuous Boundary Elements COMPUTER CODES FOR TWO DIMENSIONAL Introduction Fortran Code with Two-Noded Linear Boundary Elements Fortran Code with Three-Noded Isoparametric Quadratic Boundary Elements Sample Problems An Improved Boundary Integral Formulation with Relative Displacements Elastostatics PLATE BENDING PROBLEMS Introduction Review of Thin Plate Flexure Theory The Boundary Integral Equations for Plate Flexure Fundamental Solutions Surface Loads Numerical Implementation COMPUTER CODE FOR PLATE BENDING PROBLEMS Introduction Fortran Code with Two-Noded Linear Boundary Elements Sample Problems ELASTODYNAMIC PROBLEMS Introduction Free Vibration Problems Forces Vibration Problems COMPUTER CODES FOR TWO-DIMENSIONAL ELASTODYNAMIC PROBLEMS Introduction Fortran Code for Free Vibration Problems Fortran Code for Forced Vibration Problems ELASTOPLASTIC PROBLEMS Introduction Some Preliminaries Brief Review of the Theory of Plasticity Governing Equations of Elastoplasticity Boundary Element Formulations Involving Volume Integration Elastoplastic Boundary Element Formulation using Particular Integrals Numerical Implementation Iterative Algorithm COUPLING OF FINITE ELEMENT AND BOUNDARY ELEMENT METHODS Introduction Introduction to Finite Element Method Coupling of Finite Element and Boundary Element Solutions An Example Problem-Analysis of Reinforced Concrete Structural Elements Appendix A: Integral Equations A.1. Definition and Classification of Integral Equations A.2 Cauchy Principle Value of an Integral Appendix B: Numerical Integration B.1 Standard Gauss Quadrature B.2 Logarithmic Gauss Quadrature Appendix C: Fundamental Solution C.1 Three-Dimensional Laplace Equation C.2 Two-Dimensional Laplace Equation