多弹性体接触问题的数值算法

提出一种新的求解带摩擦的接触问题的数值算法,即拟高斯迭代法。它对法向接触力和切向接触力进行交替迭代,并利用高斯迭代法求解法向接触力,利用分块高斯迭代法求解切向接触力。同其它的数值算法相比,该算法保留了关于接触力的柔度矩阵的稀疏性和对称性,利用矩阵乘向量可以分步进行的技巧,该算法只需存储关于接触力的柔度矩阵的下三角形矩阵的非零元和对角矩阵。根据可能接触边界的分布特点,将区域分解成不同的子区域,引进拉格朗日乘子表示接触力,保证了各子区域的网格剖分和位移求解是完全独立的。基于上述算法和有限元程序自动生成系统开发了相应的求解带摩擦接触问题的软件,数值实验表明,程序是正确的,算法是高效的。

Numerical Algorithm to Solve Elastic Multi-body Contact Problems

A new algorithm to solve frictional contac t problems (Gauss-Seidel like algorithm) is introduced. The Gauss-Seidel method is applied to obtain the normal contact forces and the tangential contact forces and the block Gauss-Seidel method is applied to obtain the tangential contact forces. The double loop goes on until convergence is satisfied. In the new meth od, the flexibility matrix is symmetric and sparse. Only the non-zero elements of the lower triangular matrix and diagonal matrix of the flexibility matrix nee d be stored and a new method to deal with the production of the flexibility matr ix and vector is presented. By use of the domain decomposition method, we can di vide the subdomains by finite element mesh, and use different interpolation func tions and different displacement models in different subdomains. Based on the ab ove algorithm and finite element program generator system (FEGEN), a software to solve frictional contact problems is developed. The numerical results indicate that the software is correct and the algorithm efficient.