Method of multigrid finite elements of the composite rotational and bi-curved shell calculations

To calculate the stress-strain state of elastic three-dimensional rotational and bi-curved shells of inhomogeneous structure, irregular shape and static loading, multigrid finite element method (MFEM) represented on the basis of finite element method (FEM) algorithms using three-dimensional (homogeneous) composite curvilinear multigrid finite elements (MFE) was proposed. At creation of MFE (without increase in their dimension) it is possible to use as much as small (basic) splittings covers allowing to consider as much as precisely in MFE difficult non-uniform structure and to describe the ten-sion the equations of a three-dimensional task of the theory of elasticity. As at creation of n-net final element (FE) n of en-closed grids is used. Small grid is generated by MFE basic splitting others n- 1 large grids are used to decrease MFE dimension. In MFEM uniform and non-uniform MFE and sys-tems of enclosed grids that expands the area of its application are used. In FEM uniform one-net FE are applied. As at crea-tion of n-net FE not one, but n of enclosed grids are used, MFEM is generalization of MFE, i.e. MFE is a special case of MFEM. The method of forming FE for the design of three-dimensional MFE of difficult form in local Cartesian systems of coordinates is offered. The method is based on the area of three-dimensional MFE turns out by turn of flat one-net (forming) FE of difficult form round some axis on a small corner or parallel movement forming FE along the set straight line. At creation of MFE Lagrangian polynomials are used. Such approach allows to project three-dimensional MFE for calculation of composite covers of rotation (double curvature) and designs, one characteristic size of which is much more others. The covers of double curvature are repre-sented by the set of covers of rotation. Offered MFE are effec-tive in calculation of round composite plates, disks, rings and shaft. Three-dimensional MFE which can effectively be ap-plied at calculation of wings, fuselages of planes and frames of the ships, rockets and flying structures of bridges are con-sidered. MFE generate discrete models of small dimension and the decision with small error.