随机分布圆孔板有效弹性模量快速多极虚边界元法模拟

将快速多极算法和广义极小残值法(GMRES)结合于虚边界元法的方程求解,形成了快速多极虚边界元法的求解思想.本方法采用了"源点"多极展开和"场点"局部展开的组合处理方案,使得原问题方程组求解的计算耗时量和储存量均降至与所求问题的计算自由度数成线性比例.文中分析了含随机分布多圆孔板的有效弹性模量,并与其它数值方法的结果进行了比较,同时数值验证了本方法的可行性、计算精度及计算效率.

Simulation of Effective Elastic Moduli of Plate with Randomly Distributed Holes Based on Fast Multipole Virtual Boundary Element Method

The main idea of fast multipole virtual boundary element method (VBEM) presented in the paper is that generalized minimal residual algorithm (GMRES) and fast multipole method (FMM) are integrated with the solution of VBEM equations.In virtue of the combined scheme of multipole expansion at the collocation point and local expansion at the integration point,the complexities of operation and memory about solution of the equations are made to be linearly proportional to the freedoms of the problem.As an application of the method,the effective elastic moduli of a plate containing randomly distributed circular holes are analyzed and the results are compared with one of other numerical methods.And the feasibility,accuracy and efficiency of this method are fully demonstrated.