Stress Analysis by Boundary Element Methods

Abstract

1. Solution of Partial Differential Equations by the Boundary Integral Equation Method (BIEM). Ordinary differential equations. Partial differential equations. 2. Elastostatics. Governing equations and fundamental solutions. The Somigliana identity. Boundary integral equations (BIE). Integral representation of stresses. Boundary integro-differential equations (BIDE). Stresses on the boundary. BIE and BIDE for an anisotropic medium. Axisymmetric problems. Semi-infinite problems. Numerical implementation. Numerical examples. 3. Elastodynamics. Equations of motion. Fundamental solutions. Integral representations of displacements and stresses. Boundary integral and integro-differential equations. Numerical solution. Alternative formulation of boundary element method. Numerical examples. 4. Thermoelasticity. Governing equations. Fundamental solutions. Integral representations of displacements and temperature. Integral representations of temperature gradients and stresses. Boundary integral and integro-differential equations. Numerical implementation. Alternative BEM formulation. Application to fracture mechanics. Numerical examples. 5. Micropolar Thermoelasticity. Equations of motion. Fundamental solutions in three dimensions. Fundamental solutions for plane problems. Fundamental solutions for antiplane problems. Integral representations. BIE and BIDE. Applications to fracture mechanics. 6. Elastoplasticity. Governing equations. Boundary integral formulations. Elastoplastic stress-strain relations. Incremental computations for elastoplasticity. 7. Viscoelasticity. Rheological models and the correspondence principle. Boundary integral formulation. Schapery's inversion algorithm. Application to fracture mechanics. 8. Thin Elastic Plates in Bending. Governing equations in classical plate theory. Integral formulation. Numerical solution. Large deflections. Berger equation. Plates on elastic foundations. 9. Stress Analysis by Hybrid Methods. Computation of stresses at internal points from stresses on boundary. Combination of BIE with holographic interferometry measurements. Hybrid method in fracture mechanics. Appendices. References. Subject Index.