无网格伽辽金方法在线弹性断裂力学中的应用研究

通过对移动最小二乘形函数进行局部修正，将混合变换法应用于无网格伽辽金方法，给出分析线弹性断裂力学问题的有效的无网格伽辽金方法。这一方法克服了无网格伽辽金方法中常用的拉格朗日乘子法和罚函数法的缺点，实现了本质边界条件在节点处的精确施加。运用线弹性断裂力学理论，采用基于t-分布的新型权函数和部分扩展基函数，对有限板单边裂纹的应力强度因子和拉剪复合型裂纹的扩展进行分析。由于该方法仅需节点信息，而不需要节点的连接信息，从而避免了有限元方法中的网格重构，大大简化了裂纹扩展的分析过程。数值计算结果表明了方法的有效性。

STUDY ON THE APPLICATION OF ELEMENT FREE GARLERKIN METHODIN LINEAR-ELASTIC FRACTURE MECHANICS

An efficient element free Galerkin method is given for simulation of crack propagation. The modified moving least square(MLS) approximation, for implementing the essential boundary conditions, is given by establishing the relationship between the nodal value and the generalized displacement. The proposed method eliminates the shortcomings of Lagrange multipliers and penalty functions typically used in element free Galerkin method. As a consequence, the essential boundary conditions can be imposed directly at nodes. By using the theory of linear elastic fracture mechanics,a new type of weight function basing on t-distribution and partially enriched basis function, analysis of stress intensity factors and crack propagation is given for finite plates with single edge crack and with a mixed-mode crack in tensile-shear state, respectively. Without the connectivity information of elements, the burdensome remeshing, which is used in finite element method, is avoided in the present meshless method. The analysis of crack propagation is dramaticlly simplified. The examples reveal the effectiveness of the present method.