不连续问题的无网格分域算法

A domain decomposition algorithm in meshless method for discontinuous problem

提出一种无网格方法中采用分域的思想处理材料和位移不连续问题的方法。该方法将求解域沿不连续面进行分域,通过使用两种转换矩阵使子域交界面上的位移连续性得到满足;采用分块矩阵法计算转换后的刚度矩阵,所得刚度矩阵仍具有稀疏、带状性。可采用与有限元耦合的方式施加本质边界条件。编制了该算法的计算程序,通过对材料不连续悬臂梁弯曲问题的分析和单边裂纹板裂纹张开位移的计算,验证了该算法的正确性和有效性。

A domain decomposition algorithm for material and displacement discontinuity problems in meshless method is presented.The domain is decomposed into sub-domains along the discontinuous interface.The continuity of the displacements on the interface is satisfied through the introduction of two transformation matrixes.The partitioned-matrix method is proposed to calculate the transferred stiffness matrix,which is sparse and bandy.By means of coupling meshless method and finite element method,the essential boundary condition can be imposed directly.The computer program based on the presented method is developed and two numerical examples,a beam consisted with two kinds of materials and an edge-cracked plate under uniform tension,are employed to demonstrate the correctness and efficiency of the method.