Doundary Element Method For Semi-Infinite Domain And Layered Media And Its Programming

An infinite element approach for three-dimensional boundary element analysis of half-space problems is presented. And an efficient linear three-dimensional multi-region boundary element method algorithm which can deal with arbitrarily many regions is presented. The illustrative results demonstrate the good efficiency and accuracy of these suggested methods. The following achievements have been gained:Accurate and efficient integration of the displacement and traction integrals over the surface of the problem domain is vitally important. Because the kernel functions must be evaluated many millions of times, significant improvements in run times can be realized by coding the arithmetic efficiently. So the adaptive integration that delivers high accuracy at minimum computational cost is adopted.To treat half-space problems rationally, the infinite boundary element is incorporated into the conventional boundary element analysis. In the analysis of linear half-space problems, boundary element need only be specified on the surface of the semi-infinite domain. Decay function is adopted to represent the asymptotic behavior of displacements in the far-field. On the basis of anti-symmetry of traction kernel, the integral over the infinite surfaces are transformed into line integrals which form a closed contour and are evaluated analytically. Using this formulation, the numerical integrations over the entire region is obviated.Taking into account the interface equilibrium and compatibility conditions. the systems equations of multi-region boundary element method are developed. Since displacements are uniquely defined but the tractions are multi-valued at corners, to treat corners rationally, it is necessary to introduce additional nodes and then develop auxiliary equations which are derived from the symmetry...