摘要
利用变分不等式和基于信息熵的凝聚函数把有摩擦接触问题模型化为一个标准的凸二次规划问题，极大地简化了这一复杂的问题，同时引入摩擦方向约束并构造了以无摩擦解为初值的迭代算法，在较大摩擦系数时计算也能保证收敛，算例表明算法高效可靠．
The model of elastic frictionless contact problems, after finite element discretization, is a formulation of quadratic programming(QP), but the model of frictional contact problems will be more complicated. In tradition, the iterative methods with incremental loading are often adopted, the convergence is guaranteed only on the condition that the step length of the incremental load is sufficiently small. Recently, the linear or nonlinear complementary methods in mathematical programming are utilized as an alternative. Although many algorithms for complementarity problems have been developed in the past years, the convergence of most of these methods requires the monotonicity of the complementarity problems, and the monotonicity cannot be guaranteed by the complementary formulations resulting from the frictional contact, especially in the cases with larger coefficient of friction. In this paper a smooth model and iteration algorithm for solving frictional contact problems is presented. The model is obtained by regularizing the tangential frictional works using entropy based aggregation function. A similar smooth function is constructed to approximate the discrete value --1, 0 and 1, i.e. the inverse slipping, sticking and forward slipping of the potential contact node pairs on the contact surfaces. Several advantages or distinguished features are embodied in the algorithm. At first, the solution of the structure with frictionless contact is used to act as an initial value, and the frictional directions on potential contact surfaces in the current iteration are determined using the ones of the previous iteration. Then, in each iteration step only a very simple standard convex quadratic programming problem is to be solved, and the convergence can be guaranteed in each sub-step, it is one of the most important steps for the convergence for the whole iteration procedure. In addition, the algorithm uses only one loading step. Finally, some typical examples verify the feasibility and efficiency of the method.
出处
《力学学报》
EI
CSCD
北大核心
2001年第3期340-348,共9页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(59775065).
