非光滑方程组方法在求解非匹配网格接触问题中的应用

Applications of non-smooth equations methods for the contact problems with non-matching meshes

将非光滑方程组方法与Mortar StS接触模型(Mortar Segment-to-Segment)相结合,来求解接触面网格非匹配时的弹性接触问题。其中,非光滑方程组方法是求解弹性摩擦接触问题的有效方法,具有精确满足接触条件、迭代算法收敛性有理论保证的优点,但目前仅用于求解网格匹配的接触问题。Mortar StS接触模型可以较为方便地处理网格非匹配接触问题,其特点是不引入过多约束,满足接触分片检验条件,但目前大都采用"试验-误差"迭代方法求解控制方程,对于复杂接触问题,其收敛性不易保证。因此,将二者结合来处理网格非匹配接触问题,既可以提高求解精度,又能使得算法的收敛性得到理论保证。数值算例对接触分片检验和算法的计算精度进行了验证。

In this paper, the non-smooth equation methods combined with Mortar Segment-to-Segment methods（Simply denoted as Mortar StS model） ,is proposed to solve the elastic contact problem in which the discretization of two contact surfaces are not matched with each other. The non-smooth methods, which satisfying the contact conditions accurately and have proven convergence property, are only used for solve the contact problems with matching meshes. In the Mortar StS model,it is suitable to deal with the non-matching contact problem. The over-constraints can be avoided and the contact patch test can be satisfied. However, usually the trial-and-error iteration method,in which it is difficult to guarantee the convergence of solution for complex contact problem,is employed with Mortar StS model. Therefore,the combination of two methods will improve the accuracy and guarantee the convergence of solution for the contact problem with non-matching meshes. The numerical examples demonstrate the contact patch test results and the accuracy of the combined method.