Generalized equivalent strength conditions in the calculations of composite bodies

Structures with an inhomogeneous regular structure (plates, beams, shells) are widely used in engineering, especially in aviation and rocket and space. In calculations for the strength of elastic composite structures using the finite element method (FEM), it is important to know the error of the solution. To analyze the error of the solution, it is necessary to use a sequence of approximate solutions constructed according to the FEM using the grinding procedure for basic discrete models that take into account the non-homogeneous, micro-homogeneous structure of structures (bodies) within the micro-approach. The implementation of the grinding procedure for basic models requires large computer resources.

In this paper, the method of equivalent strength conditions (MESC) for testing the static strength of elastic bodies with an inhomogeneous regular structure, for which sets of different loads are given, is briefly described. According to the MESC, the calculation of the strength of a composite body for which the loading is set is reduced to the calculation of the strength of an isotropic homogeneous body (having the same loading as a composite body) using equivalent strength conditions. In the numerical implementation of the MESC, adjusted equivalent strength conditions are used, which take into account the error of approximate solutions. Here, the MESC is implemented on the basis of the FEM. If a set of different loads is specified for a composite body, then generalized equivalent strength conditions are applied in this case. The procedure for constructing generalized equivalent strength conditions is shown. The calculation of the strength of composite bodies according to the MESC using multigrid finite elements requires  times less computer memory than a similar calculation using crushed basic models of composite bodies. The given example of calculating the strength of a composite beam, for which a set of loads is set, using the MESC using generalized equivalent strength conditions shows its high efficiency.