| The ideas presented in this thesis are directed towards widening the scope and improving computational efficiency of the boundary element and the related displacement discontinuity methods applied to linear elasticity.; In the first part of the thesis, a comprehensive and unified method to obtain Green's functions is developed using the method of images. The application of the method of images has one additional complexity. The boundary value problem is governed by the biharmonic equation, which is a higher order equation than the Laplace equation that governs simple heat conduction. In the Galerkin vector formulation, the Green's functions are vector valued, in contrast to the scalar valued Green's functions used with the Laplace equation. Green's functions are developed for perfectly and bonded bi-materials and that with sliding interface.; In the second part of the thesis, an efficient integration methodology is developed for the evaluation of singular and near singular integrals. Singular integrals arising in the boundary element methods are often counter intuitive and their computation is slow and inaccurate using the classical quadrature methods. The singular integrals arise in the cases where the integration is done in the calculation of self influence.; In the third part of the thesis, a computational framework, the node-centric method, which uses the new integration methodology, is introduced. |
