Deformation of a three-layer plate with a compressible filler in the temperature field

The elastic axisymmetric bending of a circular three-layer plate in a nonstationary temperature field is herein investigated. An approximate solution to the problem of thermal conductivity is used, obtained by averaging the thermo-physical characteristics of the materials of the layers over the thickness of the plate. It is accepted that the deformation of the plate obeys the polyline hypothesis. Kirchhoff's hypotheses are valid for thin load-bearing layers that take on the main load. A relatively thick lightweight filler is compressible in thickness, and the Timoshenko hypothesis is fulfilled in it. To derive a system of equilibrium equations, the principle of possible Lagrange displacements is applied. A general analytical solution of the corresponding boundary value problem is obtained. The change of displacements in the plate at different temperatures is numerically investigated.