Three dimensional thermoelastic stress analysis of anisotropic solids by the boundary element method

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The main objective of this research is to develop efficient techniques using the Boundary Element Method (BEM) for three-dimensional (3D) stress analysis of anisotropic solids under thermo-mechanical loads. These materials which have properties that vary with orientation are increasing being used in engineering and scientific applications. Although the BEM is very well established as an efficient tool for treating isotropic elastic solids, the same cannot be said for the case of 3D anisotropy. This is due to the mathematical complexity of the Green's functions that were used in the boundary integral equation (BIE). There is also paucity of publications indeed dealing with 3D BEM anisotropic thermal stress analysis. In the basic form of the BIE, thermal effects manifest themselves with the Green's functions in an additional volume integral which has to be transformed into surface ones to restore the distinctive feature of the BEM as a boundary solution technique. To this end, simplifying approximations have been adopted in the schemes reported in the few available publications; cases where cracks or internal corners are present need to be treated differently. As an advance in the development of the BEM in this area, the applicant and his co-workers have recently implemented an approach based on an exact, explicit, algebraic form of the Green's functions. They can be implemented and computed in a relatively efficient manner compared to previous formulations. The proposed research aims to extend it to handle thermal effects. Because of the algebraic form, the associated volume integral containing these Green's functions and the temperature terms can, in principle, be transformed exactly into surface ones. The BEM formulation for thermoelasticity can thus be applied to both crack and non-crack problems with the same algorithm without further approximations. Once this has been accomplished, the two-parameter approach for fracture mechanics analysis of cracked anisotropic solids under thermal loads will be implemented. Some important non-crack and crack problems of practical interest will be investigated.