Finite-Difference equations for 2D elasticity problems on a non-uniform grid

In this article proposes a new method for constructing finite-difference equations on a non-uniform grids for two-dimensional boundary value problems of elasticity. Usually non-uniform meshes useful for boundary value problems of elastic and plastic, considered in domains with some complex boundaries. Usually, when using non-uniform grids, a decrease in the order of approximation of finite-difference equations is observed. To avoid this, an efficient algorithm for dividing a two-dimensional area into a non-uniform grid has been developed, which eliminates the effect of reducing the order of approximation of difference equations. To solve discrete equations based on non-uniform grids, an efficient iterative process is proposed. As an example, a two-dimensional static problem of the theory of elasticity for an isotropic material is solved numerically. The obtained numerical results are compared with the exact solution and their reliability is proved. Based on the numerical results, 3D graphs are built.

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