An Integration Method Based on Reusability of Basis Functions in Isogeometric Analysis

In order to overcome the problem which the computational efficiency of isogeometric analysis（IGA） is severely restricted to its integral efficiency, in this paper a quadrature rule based on the classification and reusability of basis functions is proposed. Firstly, the uniform B-spline basis functions were classified according to their properties. Accordingly, the reusable basis functions were defined with the linear transformation of the support regions. Resultantly, under the framework of exact Gaussian quadrature, which is suitable for IGA, the integral efficiency is significantly improved with the same computational accuracy. Numerical examples are provided to demonstrate the validity and efficiency of the proposed method.