The method of forming finite elements

Calculations by Finite Element Method (FEM) of the three-dimensional strained state of large-sized structures (wings and fuselages of aircraft, marine hulls, submarines and rockets) reduce to the construction of discrete models of very high dimension. To reduce the dimensionality of discrete models, three-dimensional multigrid finite elements (MgFE) are used. When constructing a composite MgFE, a nested grid system is used. A fine grid is generated by a basic parti- tioning of the MgFE that arbitrarily closely takes into account its heterogeneous structure and shape (without increasing the dimension of the MgFE). On large grids the functions of movements applied to the decrease of dimension of basic splitting allowing to project MgFE of small dimension are de- termined by FEM. The MgFE displacement functions and stress state described by the equations of the three- dimensional elasticity problem are represented in local Carte- sian coordinate systems. In this case MgFE of cover type has no movements as rigid whole...