用B-可微方程组求解接触问题的一种推广

A generalization of B-differentiable equations method for sdving contact problem

对于接触问题,当接触点对较多时,方程组的求解效率降低很多,而且对于某些多体接触问题,由于刚体位移的存在,柔度阵不易计算.为此,本文利用接触条件的B-可微方程组形式,提出了一种不需形成柔度阵的求解方法.求解时对于不同的接触状态,根据B-可微方程组进行变量替换,再求解整体平衡方程,然后把替换的变量进行恢复.数值算例表明,对于弹塑性接触问题,可大大提高收敛性和计算效率,对于某些不易计算柔度阵的多体接触问题,也可进行求解.

This paper shows that for the contact problem with less contact pairs, the computational efficiency decreases greatly when the number of contact pairs increases. Moreover, for some multi-body contact problems, the contact flexibility matrix cannot be obtained due to the occurrence of rigid body translation. To meet these problems, an application of B -differentiable Equation method for the contact problem is presented and the contact flexibility matrix is no longer needed. In the iteration procedure, the procedure called substitution of contact variables is first implemented according to the contact status and the contact conditions in the form of a B -differentiable equation. And the equilibrium equation of the system is then solved. At last, the procedure called restoration of contact variables is implemented to obtain the value of the substituted variables. Numerical results show that the property of convergence and efficiency are improved for the elasto-plastic contact problem and some multi-body contact problems can also be solved.