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. In the study the method of the forming final elements (FE) for creation of elastic three- dimensional composite (uniform) MgFE of two types is of- fered. Curvilinear type 1 MgFE are obtained by turning a giv-en plane forming FE around a given axis at a given angle, type 2 MgFE - by parallel moving forming FE in a given direc- tion for a given distance. This approach allows projecting the design of MgFE which size is significantly larger (smaller) than others’. MgFE of the 1st and 2nd type are applied at calculation of composite covers of rotation, rings, round plates, disks, shaft, cylindrical covers with a variable radius of curvature, plates and beams of difficult form. The 1st and 2nd type MgFE are proposed for calculating three-dimensional stress state of the main power elements of the wings and fuselage of aircraft, ship hulls, submarines and missiles, cor- rugated plates and shells. The procedure of constructing the first and second type MgFE used to calculate the three- dimensional stress state of the primary structural members of the wings and aircraft fuselages, marine hulls, submarines and missiles (stringers, frames, spars, bulkheads, floor, deck and shells of various shapes) is considered. Proposed MgFE generate small dimensional discrete models. Upper errors of approximate soiutions are proposed.
elasticity, composites, multigrid final ele- ments, beams, plates rings, shafts, covers of rotation and cylindrical covers
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