Two-dimensional thermoelastic analysis of beams with variable thickness subjected to thermo-mechanical loads

Two-dimensional thermoelastic analysis for simply supported beams with variable thickness and subjected to thermo-mechanical loads is investigated. An approximate analytical method is proposed. Firstly, the heat conduction equation is analytically solved to obtain the temperature distributions for two kinds of boundary conditions at the beam ends, which are the harmonic series with unknown coefficients. Then the two-dimensional equilibrium differential equations are analytically solved to obtain the displacement component series with unknown coefficients and the stress component series is obtained. The unknown coefficients in the temperature series and the stress component series are approximately determined by using the upper surface and lower surface conditions of the beam. With the proposed procedure, the solutions satisfy the governing differential equations, the loading conditions, and the simply supported end conditions. The proposed solution method shows a good convergence and the results agree well with those obtained from the commercial finite element software ANSYS. Several 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 beam are examined.