Obtaining The Finite Difference Approximation of The Lame System By Using Barycentric Coordinates

The elasto-plastic contact problem with an unknown contact domain (UCD) has attracted mathematicians, mechanics and engineers for decades. So, the problem of determining the stresses in the UCD is very important nowadays in terms of engineering and applied mathematics. To improve the finite element model, the remeshing algorithm is used for the considered indentation problem. The algorithm allows the determination of the UCD at each step of the indentation with high accuracy. This paper presents the analysis and numerical solution of the boundary value problem for the Lame system, and the modeling of the contact problem for rigid materials. By using barycentric coordinates, the finite difference approximation of the mathematical model of the deformation problem with undetermined bounded is obtained and the relations between the finite elements and finite differences are investigated.