Lagrange multiplier method implementations for two-dimensional contact problems

The two-dimensional elastic contact problem is considered. Finite element method with bilinear shape functions are used. The Lagrange multiplier method for contact conditions implementation is used in three ways: node-to-surface method, mortar method and advanced mortar method. The tests showed that the mortar method and the advanced mortar method are more accurate, than the node-to-surface method. The advanced mortar method is able to smooth the stress field fluctuations, but only in limited number of problems.