A new isogeometric boundary element method to analyze two-dimensional potential and elasticity problems

To reduce the impact of inhomogeneous boundary conditions on computational accuracy and the impact of redundant geometry refinement on computational efficiency in traditional isogeometric boundary element methods (IGABEM), a new IGABEM that introduces geometry-independent field approximation (GIFT) is proposed and applied to 2D potential and elasticity problems. Unlike in IGABEM, element nodes are located on the boundary, which facilitates the precise application of boundary conditions on nodes to improve computational accuracy. The constructed element features multiple inner nodes, allowing for the use of fewer elements in solving problems, which is beneficial for reducing redundancy and improving the computational efficiency of IGABEM. First, the geometrically precise BEM element is constructed using non-uniform rational B-splines (NURBS) to describe the geometry, while the field is approximated using B-spline interpolation and a transformation matrix. Second, the calculation formats of problems are derived by using parameter mapping. Third, the calculation of variables at boundary points is performed on the element through the relationship between variables. The subsequent processing is like the BEM. Finally, several numerical examples are discussed. It can be concluded from examples that the proposed method can obtain a high-precision solution and reduce computation costs.