Thermal Force Loading of a Physically Nonlinear Three-Layer Circular Plate

Abstract

The article considers the effect of a heat flux of constant intensity on a circular, three-layer, nonsymmetrically thick plate subjected to the action of an axisymmetric local loading. The temperature field in the plate was calculated by the formula obtained in solving the problem of thermal conductivity by averaging thermophysical parameters over the thickness of the packet. The materials of the layers deform physically nonlinearly. For describing the kinematics of the packet, the hypotheses of a broken normal are adopted. In thin carrying layers, the Kirchhoff hypotheses are valid. In the normally uncompressed relatively thick filler, the hypothesis on rectilinearity and incompressibility of the deformed normal holds. The work of the filler in the tangential direction is taken into account. The formulation of the corresponding boundary-value problem is given. Equilibrium equations are obtained by the variational Lagrange method. Boundary conditions on the plate contour are formulated. The solution of the boundary-value problem is reduced to finding three unknown functions: of deflection, shear, and of radial displacement. For these functions, an inhomogeneous system of ordinary nonlinear differential equations is written out. A method of rigid Il′yushin solutions is applied for its solution. Iteration analytical solutions are obtained in Bessel functions at circular and annular loadings. Their parametric analyses are made at different local loadings and for the hinged support of the plate contour. The influence of temperature and nonlinearity of the materials of the layers on the displacements in the plate is investigated numerically.