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

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## S.L. Crouch and A.M. Starfield:

## S.L. Crouch and A.M. Starfield: *Boundary Element Methods in Solid Mechanics*

Published $\text {1983}$, **Unwin/Hyman**

- ISBN 0-04-445913-0.

### 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