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Three-Dimensional Thermoelastic Analysis of Rectangular Plates with Variable Thickness Subjected to Thermomechanical Loads

Three-dimensional thermoelastic analysis of simply supported rectangular plates with variable thickness and subjected to thermomechanical loads is investigated. An approximate analytical solution method is proposed. The temperature field and the displacements are represented by a double harmonic series, respectively. First, the heat conduction equation is solved analytically to obtain the nonlinear temperature series with unknown coefficients. Then the three-dimensional equilibrium differential equations are analytically solved to obtain the displacement component series with unknown coefficients. Thus the stress component series can be determined. The unknown coefficients in the temperature series and stress component series are approximately determined by using the upper surface and lower surface conditions of the plate. With the proposed procedure, the solutions satisfy the governing differential equations, the loading conditions, and the simply supported boundary conditions. The proposed solution method shows a good convergence and the results agree well with those obtained from a commercial finite element software, ANSYS. Two examples are used to demonstrate the effectiveness of the proposed solution method. The simultaneous effects of temperature change and applied mechanical load on the behavior of the plate are examined.