Some Advances in Mathematical Programming Method for Numerical Simulation of Contact Problems

This paper reviews some advances and applications in mathematical programming method for numerical modeling of elastic-plastic contact problems. Emphases are on the parametric variational principle and quadratic programming method used for analysis of elastic-plastic contact problems with isotropic/orthotropic friction law. The contact problem with friction between two elastic-plastic Cosserat bodies is treated in the same way as that in the conventional plastic analysis. There is no available rule for choosing a reasonable value of the penalty factors for simulation of the contact problems of Cosserat materials, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. Two numerical examples are presented to show the efficiency of the model and algorithm presented.

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