LAUSR

Abstract For boundary element analysis of the orthotropic potential problems in thin structures, the higher order elements are expected to discretize the boundary. However, the use of the higher order elements leads to more complex forms of the integrands in boundary integral equations. The resulting nearly singular integrals on the higher order elements are difficult to be evaluated when the source point is very close to the integral element. In this paper, a semi-analytic algorithm is presented to evaluate the nearly singular integrals on the quadratic elements in two dimensional (2-D) orthotropic potential problems. By constructing the approximate singular integral kernels, the nearly singular integrals through subtraction technique are transformed into the sum of regular parts and singular parts. Then, the former are calculated by the conventional Gaussian quadrature and the latter are calculated by the analytical integral formulas. Numerical examples demonstrate that the present semi-analytic algorithm is efficient and accurate to calculate the nearly singular integrals on the quadratic elements. Especially, the BEM with the present semi-analytic algorithm is successfully applied to analyzing 2-D orthotropic potential problems in very thin structures.