A regularized boundary element method for orthotropic elastic problems

This presentation is mainly devoted to the research on the regularization of indirect boundary integral equations (IBIEs) for orthotropic elastic problems, and establishes the new theory and method of the regularized BEM. Some integral identities depicting the characteristics of the fundamental solution of the considered problems and a novel decomposition technique to the fundamental solution are proposed. Based on this, together with a limit theorem for the transformation from domain integral equations into boundary integral equations (BIEs), the regularized BIEs with indirect unknowns, which don't involve the direct calculation of CPV and HFP integrals, are presented for orthotropic elastic problems. The presented method can solve the considered problems directly instead of transforming them into isotropic ones, and for this reason, no inverse transform is required. In addition, this method avoids calculating multiple integral as the Galerkin method. Furthermore, the proposed stress BIEs are suited for the computation of displacement gradients on the boundary, and not only limited to tractions. Also, they are independent of the displacement gradient BIEs and, as such, can be collocated at the same locations as the displacement gradient BIEs. This provides additional and concurrently useable equations for various purposes. A systematic approach for implementing numerical solutions is produced by adopting the discontinuous quadratic elements to approximate the boundary quantities and the quadratic elements to depict the boundary geometry. Especially, for the boundary value problems with elliptic boundary, an exact element is developed to model its boundary with almost no error. The convergence and accuracy of the proposed algorithm are investigated and compared for several numerical examples, demonstrating that a better precision and high computational efficiency can be achieved.