Analytical model of the stress–strain state of multilayer composite plates under the influence of different load types with asymmetrical boundary conditions

Abstract

Composite structure design experience has demonstrated that use of the finite element method during the first stage of the design process is unfounded and that analytical methods to determine the stress–strain state are needed for more accurate calculations. Therefore, an analytical model of the stress–strain state of multilayer composite plates under the influence of temperature, technological, and power loads with different boundary conditions around four boundaries of a rectangular plate was developed. This model enables the solution of more than 240 different boundary value problems with a combination of the following boundary conditions: fixed, moving, hinged, and free edge. In the derivation of this mathematical analytic model, the Kirchhoff hypothesis was applied to the entire body of the anisotropic medium for the interconnected deflection and bending in the plate plane. The resulting equation is an octic linear partial differential equation to express the generalized function of movements.