Book:S.L. Crouch/Boundary Element Methods in Solid Mechanics

Subject Matter

 * Applied Mathematics

Contents

 * Preface
 * List of tables


 * 1 Introduction


 * 2 Review of linear elasticity
 * 2.1 Introduction
 * 2.2 Stress
 * 2.3 Strain
 * 2.4 Generalized Hooke's Law
 * 2.5 Index notation
 * 2.6 Plane stress and plane strain
 * 2.7 Formulation of elasticity problems
 * 2.8 Co-ordinate transformations


 * 3 Introduction to boundary element methods
 * 3.1 Normal load on a half-plane (Flamant's problem)
 * 3.2 Distributed loading
 * 3.3 An indentation problem
 * 3.4 Numerical procedure
 * 3.5 Solution of rigid die problem
 * 3.6 Non-uniform element spacing
 * 3.7 Incorporation of symmetry condition
 * 3.8 Recapitulation
 * 3.9 Integral formulation


 * 4 The fictitious stress method
 * 4.1 Introduction
 * 4.2 Kelvin's problem for plane strain
 * 4.3 Constant tractions over a line segment
 * 4.4 Numerical procedure
 * 4.5 Co-ordinate transformations
 * 4.6 Influence coefficients
 * 4.7 Interior / exterior problems
 * 4.8 Symmetry conditions
 * 4.9 Examples
 * 4.10 Program structure


 * 5 The displacement continuity method
 * 5.1 Introduction
 * 5.2 Displacement discontinuity in an infinite solid
 * 5.3 Pressurized crack problem
 * 5.4 Numerical procedure
 * 5.5 Co-ordinate transformations
 * 5.6 Influence coefficients
 * 5.7 Interior / exterior
 * 5.8 Symmetry conditions
 * 5.9 Examples
 * 5.10 Computation of tangential stress along a boundary


 * 6 The direct boundary integral method
 * 6.1 Introduction
 * 6.2 The reciprocal theorem and its consequences
 * 6.3 Selection of the test solutions
 * 6.4 Influence conditions
 * 6.5 Formulation of the system of equations
 * 6.6 Example
 * 6.7 Somigliana's formlas
 * 6.8 Co-ordinate transformations
 * 6.9 Another formulation of the method


 * 7 Improvements and extensions
 * 7.1 Introduction
 * 7.2 A higher-order formulation of the direct boundary integral method
 * 7.3 Crack tip elements
 * 7.4 Program modules for a half-plane
 * 7.5 Inhomogeneous bodies
 * 7.6 Program modules for bonded half-planes
 * 7.7 Anisotropic elasticity


 * 8 Applications in rock mechanics and geological engineering
 * 8.1 Numerical modeling in rock mechanics
 * 8.2 Stresses and displacements around underground excavations in jointed rock
 * 8.3 Excavations in stratified rock
 * 8.4 Joints with cohesion and friction
 * 8.5 Excavations in seam-type ore deposits
 * 8.6 Simulation of mining in faulted rock
 * 8.7 Tabular ore bodies; three-dimensional effects


 * Appendix A Computer program for the two-dimensional fictitious stress method (TWOFS)


 * Appendix B Computer program for the two-dimensional displacement discontinuity method (TWODD)


 * Appendix C Computer program for the two-dimensional direct boundary integral method (TWOBI)


 * References


 * Index


 * List of Tables
 * 4.1 Stresses along $x$ axis of disk (TWOFS)
 * 4.2 Radial and tangential displacements at boundary of hole (TWOFS)


 * 5.1 Stresses along $x$ axis of disk (TWODD)
 * 5.2 Radial and tangential displacements at boundary of hole (TWODD)
 * 5.3 Displacements along right half of upper crack (see Fig. 5.11)


 * 6.1 Radial and tangential displacements at boundary of hole (TWOBI)


 * 7.1 Displacement discontinuity $\hat u_y \left({a}\right)$ at the center $x = a$ of an element at a crack tip