Analytical Solution of the Problem on the Thermally Stressed State of Composite Plates with Rigid and Sliding Contacts Between Layers Based on the 3D Elasticity Theory

Two approaches to studying the thermally stressed state of layered composite plates in the 3D formulation have been developed. In the first approach, using the Reissner variational principle, a system of integrodifferential equilibrium equations and the corresponding boundary conditions are obtained without introducing an approximation. In the second approach, to construct differential equations of 3D thermoelastic equilibrium, a polynomial approximation of sought-for functions across the structure thickness is used. Its salient feature is assignment of the functions to the outer surfaces of layers, which allows splitting the layers into sublayers with a corresponding increase in the accuracy of calculation results. For the particular case of hinge-supported plates with a thermal load distributed according to a trigonometric law, the system of integrodifferential equilibrium equations obtained for the first approach and the differential equations of the second approach allow an analytical implementation. Then, equations of the first approach are transformed into a system of ordinary differential equations for the distribution of required functions across the plate thickness, with an analytical search for the roots of characteristic equations and the corresponding eigenvectors. In the second approach, the system of differential equations is converted to a system of algebraic equations. The assignment of sought-for functions to the outer surfaces of layers allows one to split the layers into sublayers and thus to reduce the approximation error. The same result obtained by the two methods may point to its reliability.