论文部分内容阅读
针对摩擦接触问题,给出一种新型的无网格数值方法。该方法基于单位分解思想,在标准无网格Galerkin法的位移模式中嵌入不连续函数和裂尖奇异函数,分别反映接触面的不连续性和接触面端点的奇异性;结合接触摩擦定律,继而构造出求解摩擦接触问题的无网格线性互补模型。在该方法中,接触面方程使用接触点对离散,全局离散系统方程则转化为标准的线性互补问题,可以很方便地使用Lemke算法求解。算例分析证明,本文方法的正确性和有效性。
Aiming at the problem of frictional contact, a new meshless numerical method is given. Based on the idea of unit decomposition, this method embeds discontinuous functions and crack-tip singularities in the displacement model of the standard meshless Galerkin method, which respectively reflects the discontinuities of the contact surfaces and the singularities of the contact surfaces. Based on the contact friction law and then A meshless linear complementary model for solving the frictional contact problem is constructed. In this method, the contact surface equation is discretized by using contact points, and the global discrete system equation is transformed into a standard linear complementarity problem, which can be easily solved by the Lemke algorithm. The case study proves that the method in this paper is correct and effective.