断裂力学的半解析相似边界元法

本文首先对弹性力学的相似边界元法进行了研究，推导了相应的计算公式。与传统的边界元法相比，相似边界元法由于只需在少数单元上进行数值积分，大大减少了计算量。在此基础上，对断裂力学问题，利用裂纹尖端位移场的解析表达式将裂纹尖端节点未知量转化为几个待定常数，提出了半解析相似边界元法，可大大减少最终形成的线性代数方程组的系数矩阵的阶数，进一步减小计算量。最后给出了算例，说明了本文方法的有效性。

Semi-Analytical Similar Boundary Element Method for Fracture Mechanics

Similar boundary element method (SBEM) for elasticity problems is discussed, and the corresponding formulae are obtained. Comparing with the conventional boundary element method, similar boundary element method can decrease the computing time to a great extent. On the basis of similar boundary element method for fracture problems, the analytical solution at the tip of crack is used to change the variables on the nodes near the tip as some undetermined constants, and the semi analytical similar boundary element method (SSBEM) is presented. The order of the coefficient matrix in the last linear algebraic equations is decreased, and the computing speed is increased. At last a numerical example is given, and the efficiency of the method is shown.