new algorithm for near–singular integration of 3D Boundary Element Integrals for thin–walled elements

Abstract

The accuracy of the Boundary Element Method (BEM) is strongly dependent on an accurate evaluation of boundary integrals. For thin-walled structures, collocation points and integration elements are often very close, making the kernel of the integrations nearly singular and requiring the use of special numerical integration techniques. In this paper, an effective algorithm is presented for near–singular integration of boundary element integrals applied to three–dimensional thin-walled structures. A combination of Telles’ transformation of variables technique and an adaptive Gaussian quadrature method for regular integrals is used to improve the integration accuracy and to decrease the computation time. The choice of parameters for the technique depends on the relationship between the distance from collocation point to integration element and a reference element length. The proposed integration algorithm is applied to thin plate uniaxial loading and pressurized thin-walled cylindrical shells. The results obtained are in good agreement with theoretical results and the reduction in integration times is significant.