一种消除线性独立性问题的单位分解三角形单元

A Partition of Unity Triangle Finite Element Free from the Linear Dependence Problem

为建立高效的消除线性独立性问题的单位分解有限单元公式,采用多项式基函数用来作局部近似。普通的线性三角形形函数作单位分解函数,提出有限元无网格耦合三角形单元。该三角形单元形函数具有Kronecker delta性质,能够直接施加位移边界条件。数值算例表明,该三角形单元能够消除普通单位分解有限元的线性相关问题,并且具有较高的计算精度,结果优于普通线性三角形单元和线性四边形等参元。

In order to construct efficient finite element formulation based on partition of unity free from the line-ar dependence problem, a new triangle element is developed by combining the shape functions of finite element and meshfree methods. The polynomial basis functions are used for the local approximation and the shape functions for classical linear triangle element are used as partition of unity functions. The present element has Kronecker delta property so as to could implement displacement conditions directly. Numerical results show that the present triangle element is free from the linear dependence problem, and possesses higher precision, which is superior to classical linear triangle element and classical isoparametric quadrilateral element.