THERMOELASTIC DEFORMATION OF LAMINATED SHELLS OF A COMPLEX SHAPE - Smetankina, N. V. (Computer Science and Applied Mathematics, 2017)
A topical problem in modern engineering is reliable determination of temperature fields and stresses in structural elements. A review of models and methods of solving heat conduction and thermoelasticity problems has shown that uniform structures are the most investigated ones. If a temperature field changes slowly with time, one can ignore the inertia terms in the equations of motion and the coupling term in the heat conduction equation, and treat the thermoelasticity problem as a quasistatic one. A constant-thickness non-closed cylindrical laminated shell is considered. It comprises isotropic layers with constant thickness and various physical and mechanical properties. The number of layers and their layout is arbitrary. In the coordinate surface, it occupies the complex domain limited by a boundary . Convective heat exchange occurs on the shell surfaces. The shell is affected by interlayer heat sources. The nonstationary heat conduction equation and the boundary conditions for the laminated shell are derived from the heat balance variational equation. The temperature fields are determined while solving the nonstationary heat conduction problem for laminated shells when the latter are heated with interlayer film heat sources. The shell behavior is described within the framework of the refined first-order theory. It accounts for lateral shear strain and thickness reduction in each shell layer. The polygonal line hypothesis holds for the pack, and interlayer contact excludes their delamination and mutual slippage. The shell equilibrium equations and the boundary conditions are derived from the Lagrange variational equation. According to the extension method, the complex-shape shell virtually extends to an auxiliary laminated cylindrical non-closed simply supported shell of rectangular planform shape with the same composition of layers. An auxiliary shell is one whose contour shape and boundary conditions yield a simple analytical solution. In this case, the auxiliary shell is a simply supported non-closed cylindrical laminated with rectangular plan-view shape, allowing to find the problem solution as trigonometric series. To satisfy actual boundary conditions, additional distributed compensating loads, the intensity of which are to be found, are applied to the auxiliary shell over the boundary . Based on the condition of satisfying boundary conditions on the boundary , we form a system of integral equations for determining the intensities of compensating loads. Displacements and loads are expanded in the auxiliary shell domain in trigonometric series for functions satisfying simply supported conditions. The compensating loads are expanded into a series along the boundary . Hence, the system of integral equations is transformed to a system of algebraic equations with respect to the expansion coefficients of the compensating loads. The method feasibility has tested on five- and seven-layer shells. Results of calculation of stresses in layers are compared with the data obtained by an integral-difference method. The method suggested can be used for designing heating systems and determining temperature stresses in the laminated glazing of different transport vehicles.