基于等几何分析基函数重用的积分方法

摘要

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 reus-ability 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 sup-port regions. Resultantly, under the framework of exact Gaussian quadrature, which is suitable for IGA, the inte-gral efficiency is significantly improved with the same computational accuracy. Numerical examples are provided to demonstrate the validity and efficiency of the proposed method.%针对等几何分析方法计算过程中的积分效率严重制约计算效率的问题，提出一种基于基函数分类重用的积分方法。首先通过均匀 B 样条基函数的性质将基函数分类，然后通过支撑域的线性变换实现了基函数的重用，最后采用适合等几何分析的精确高斯积分方法，在保证计算精度的同时显著提高积分效率。数值算例结果表明，该积分方法是可行的和有效的。