Analytical solutions for laminated beams subjected to non-uniform temperature boundary conditions

An exact analytical method is proposed based on two-dimensional thermoelasticity theory to predict the temperature, stresses and displacements of the simply supported laminated beam subjected to non-uniform temperature boundary conditions. Firstly, the unknown distribution of temperature, stresses and displacements in the laminated beam under the non-uniform temperature boundary conditions are divided into two parts by introducing a temperature function. The general solutions of temperature, stresses and displacements are obtained with the Fourier series expansion from the boundary conditions of the laminated beam. Then, the relationships of the temperature, heat flux, displacements and stresses between the top and bottom layers are derived on the basis of the continuities at the interface by the state space method. Finally, the exact solutions of temperature, displacements and stresses can be obtained from the temperature and stress conditions on the surface of the laminated beam. Excellent performance of convergence of the present method is observed from the numerical results. The accuracy of this approach is verified by comparing the present results with those using the finite element method. Moreover, the influence of surface temperature, material properties, length-to-thickness ratio and layer numbers on the distributions of temperature, displacements and stresses are discussed in detail.

Automated summary

An exact analytical method based on thermoelasticity theory is proposed to predict the temperature, stresses and displacements of simply supported laminated beams under non-uniform temperature boundary conditions. The method utilizes Fourier series expansion and state space method to derive the relationships between temperature, heat flux, displacements and stresses, with excellent convergence performance observed in numerical results. The accuracy of the approach is verified by comparison with results from the finite element method, with detailed discussions on the influences of surface temperature, material properties, length-to-thickness ratio, and layer numbers on temperature, displacements and stresses distributions.