Thermal analysis for clamped laminated beams with non-uniform temperature boundary conditions

Abstract

The focus of this study is thermal responses of a clamped composite laminated beam with arbitrary layer numbers under non-uniform temperature boundary conditions. Analytical solutions of temperature, stresses, and displacements are derived based on the theory of thermoelasticity. The temperature distribution in the laminated beam is divided into two parts. The first part is constructed to satisfy the inhomogeneous temperature boundary conditions, while the second part is obtained on the basis of the Fourier law of heat conduction and the temperature environment. On the other hand, the unit pulse function and the Dirac delta function are introduced to translate the clamped support into the simply support with an unknown horizontal stress. According to the continuities at the interface and the state space method, the relationships of displacements and stresses between the top and bottom surfaces of the laminated beam are derived. Finally, the unknown coefficients of displacements and stresses are determined by the mechanical boundary conditions. It can be observed from the numerical results that this method has excellent convergence performance. The accuracy of this method is verified by comparing with the results of the finite element method. Furthermore, the effects of surface temperature, material properties, length-to-thickness ratio and layer numbers on the distributions of temperature, displacements and stresses in the laminated beam are in depth investigated.