Isogeometric Analysis Based on Boundary Element Method

Abstract

The isogeometric analysis is implemented for boundary element method (BEM) for the first time, and two-dimensional potential and elastostatic problems with arbitrary shape and topology are formulated in detail. In conventional isogeometric analysis based on finite element method (FEM) and non-uniform rational B-splines (NURBS), several NURBS patches are needed to deal with the geometry in various topological shapes because the analysis domain, which is the parametric domain of NURBS, is composed of only rectangular grids. Since these NURBS patches should be connected together with seamless interfaces, additional efforts are required for analysis with complex shapes. To overcome this difficulty, the isogeometric analysis concept is applied to BEM. With the proposed method, a problem domain can be analyzed by closed NURBS curve(s), which constitutes the boundary of the domain, instead of NURBS surface for two-dimensional boundary value problems without geometric error. In this research, B-splines, which are the special case of NURBS with uniform control weights, are adopted both for modeling of boundary curve(s) and for physical variables to solve the boundary integral equation (BIE) derived from Green’s second identity which transforms domain integrals into surface ones. The physical field is approximated by a linear combination of B-spline basis functions and their associated control variables defined at the control points. In BEM, source point and field point should be defined for fundamental solutions to set a BIE. That is to say, for each source point, a boundary integration is performed over field points as variables. In this manner, a system of linear equations is constructed. Unlike the classical isoparametric BEM where boundary nodes are selected as source points, a new selection scheme of source points should be suggested in the proposed method because the control points are not interpolated by boundary curve(s). This scheme must satisfy th...