三维摩擦接触问题不动点算法

Fixed Point Method on Three Dimensional Frictional Contact Problem

三维摩擦接触问题具有多重非线性性质,使求解变得比较困难,为了解决此问题,建立了三维摩擦接触问题的模型,介绍了一种非光滑混合不动点算法。该算法克服了在接触面上由于可能的滑动状态有无穷多个而难以确定的难点,算法未引入人工变量,计算量较小,计算结果精确满足接触状态条件,收敛性得到保证。根据此算法编制程序,将叠合悬臂梁算例数值计算结果与商用有限元软件进行比较,也表明了不动点算法的有效性。

The multiple nonlinear properties of three dimensional frictional contact problems make its calculation difficult. Model of contact problems and a fixed point method were introduced to solve the problems. This method overcomed the difficulty of determining the slipping angle at contact problems, which was caused by the uncertain directions of the relative slipping. No additional variable is imported. The numerical results accord with the contact states exactly and the convergence is guaranteed. This method was applied to compute the cantilever beam. The comparison of fixed point method and finite element software suggests that this method is highly efficient.