正交各向异性材料断裂分析的插值型无单元伽辽金比例边界法

Analysis of interpolating element-free Galerkin scaled boundary method for fracture problems in orthotropic materials

插值型无单元伽辽金比例边界法是一种在改进的插值型移动最小二乘法框架下,结合了比例边界法和无单元伽辽金法长处的半解析数值方法。这种方法通过引入比例边界坐标系,只需在求解域的环向上进行数值离散,在径向上采用解析的方法进行计算,处理各向同性材料断裂问题时拥有可观的精度与效率。为进一步发挥这种方法的显著优势并提高其适用性,将插值型无单元伽辽金比例边界法运用于正交各向异性材料断裂分析研究中。最后利用两种不同裂纹形式的数值算例证实了本文方法的有效性与准确性。

The interpolating element-free Galerkin scaled boundary method is a semi-analytical numerical method which combines the advantages of the scaled boundary method and the element-free Galerkin method under the framework of improved interpolating moving least-squares method. By introducing the scaled boundary coordinate system, this method only needs to perform numerical discretization on the boundary of the computational domain and solve the problem by using the analytical method in the radial direction, which has considerable accuracy and efficiency in analyzing the fracture problem of isotropic materials. In order to make full use of the virtues of this method and improve its service ability, the interpolating element-free Galerkin scaled boundary method is proposed to study the fracture of orthotropic materials. Finally, two numerical examples of different crack forms are used to certify the effectiveness and precision of the method.