Calculation of composite plates and beams taking into account their structure using complex multigrid finite elements

The basic discrete models of composite beams and plates, taking into account their heterogeneity(micro-heterogeneous) structure are known to have a very high dimensionality. Constructing complex multigrid finite elements(MgFE) of cuboid n - type to calculate the elastic composite plates and beams is given. When constructing complex MgFE of n - type, complex MgFE of (n -1 )-type are used, and complex MgFE of type 1are design ed with double-grid finite elements(DgFE). When building Dg FE, two nested grid nodes, both fine and large, are used. Fine grid is generated by base partition of DgFE taking into account its heterogeneity (microheterogeneous) structure. Large grid is used to reduce the dimension base partition of DgFE. The proposed complex MgFE in composite plates and beams describe a three-dimensional stress state, take into account the heterogeneous (micro-heterogeneous) multigrid structure and form the discrete models of small dimension. Moreover, the complex MgFE of n - type generate the discrete models of plates, beams of smaller dimension than do the complex MgFE of (n -1 )-type. Stresses are determined in any component of composite plates and beams.