Example of selecting an optimal finite element mesh for calculating machinebuilding structures

When solving various problems in the field of mechanical engineering, an engineer has to face problems that cannot be solved by exact methods due to significant mathematical difficulties. Equations or systems of equations, as a rule differential equation, which describe the problem have no exact solution. When solving such problems in deformable solid mechanics, approximate methods of calculation are widely used, one of which is the finite element method (FEM). When solving the same problem of deformable solid mechanics by the finite element method (FEM), using different finite element meshes (FEM) and types of finite elements, the solution results may differ sharply from each other, and in some cases these differences may reach 50%. The question arises - what finite element size should be adopted for further investigations so that the calculation results correspond to reality? The answer to this question is given by the solution of a test verification problem, the results of which should be used to select the dimensions and determine the type of finite element suitable for further calculation.