Boundary node method based on parametric space for 2D elasticity

This paper presents a new implementation of the boundary node method (BNM) for 2D elasticity based on the parametric space. The BNM couples the boundary integral equations (BIE) with the moving least square (MLS) approximation, which retains the dimensionality advantage and the meshless attribute. However, the BNM is performed on an approximate geometry by MLS fitting and geometry errors are inevitable. In this paper, the BNM is implemented directly on the boundary representation (B-rep) data structure used in most CAD packages for geometry modeling, which named the boundary line method (BLM). The integration quantities, such as the coordinates of Gauss points, the outward normal and Jacobian are calculated directly from the lines represented in a parametric form which are the same as the real boundary, and thus no errors will be introduced. A new integration scheme has been developed to deal with weakly singular integrals easily. Numerical results presented in this paper show excellent accuracy and high convergence rate.