Modeling of the Thermally Stressed State of Functionally Graded Shallow Shells in a Three-Dimensional Formulation

The problems of the thermal stress state of layered functionally graded shallow shells based on a 3D problem statement are considered. Two approaches for solving the problems are presented. The first approach is based on the Reissner variational principle, and a system of integro-differential equilibrium equations and the corresponding boundary conditions are obtained without introducing an approximation. The second approach performs the differential equations of 3D thermoelastic equilibrium and a polynomial approximation of sought-for functions across the structure thickness. Its salient feature is an 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 case of hinge-supported shallow shells with a thermal load distributed according to a trigonometric law, the integro-differential equilibrium equations obtained for the first approach and the differential equations of the second approach allow an analytical implementation. In this statement, the proposed models are implemented analytically for the particular case of hinged support. The same result obtained based on the two methods may indicate reliability.