| Summary: | The article discusses an algorithm development to solve an elastic contact problem. Solving such problems is often associated with necessity to use mismatched grids. Their joining can be carried out both by the iterative procedures that form the so-called Schwarz alternating methods, and by the Lagrange multipliers method or the penalty method. The article proposes the algorithm that uses a mortar-method for matching the finite elements on the contact line. All these methods of joining the grids provide ensuring continuity of displacements and stresses near the contact line. However, one of the main mortar-method advantages is that it is possible to have an independent choice of different types of finite elements and functions of forms both on both boundaries of two bodies on the contact line, and when integrating along it. The application of this method in conjunction with the classical formulation of the finite element method based on the minimization of the Lagrange functional, leads to a system of linear algebraic equations with a saddle point. The article discusses in detail its numerical solution based on the modified method of symmetric successive upper relaxation.Three test contact problems demonstrate the results of the algorithm constructed. They analyse the stress-strain state of differently loaded contacting two-dimensional plates. The examples considered show that near the contact line a continuity of distribution of displacements and stresses is retained. A versatility of the developed algorithm leaves the possibility to use different types of finite elements and form functions to conduct further analysis of the mortar-method effectiveness.
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