Elasticity solution of laminated beams with temperature-dependent material properties under a combination of uniform thermo-load and mechanical loads

An exact solution for simply-supported laminated beams with material properties variable with temperature under a combination of uniform thermo-load and mechanical loads was investigated, based on the two-dimensional (2-D) thermo-elasticity theory. Firstly, the beam was divided into a series of layers with uniform material properties along the interfaces of the beam. The uniform thermo-load acted on each layer was transformed into a combination of the normal surface forces acted at the two ends and the transverse thermo-load. Secondly, the state space method was employed to obtain the general solutions of displacements and stresses in an arbitrary layer. Thirdly, based on the interfacial continuity conditions between adjacent layers, the relations of displacement and stress components between the top and bottom layers of the beam were recursively derived by use of the transfer-matrix method. The unknowns in the solutions can be solved by the mechanical loads acted on the top and bottom surfaces. The convergence of the present solutions was checked. The comparative study of the present solutions with the Timoshenko's solutions and the finite element (FE) solutions was carried out. The effects of material properties variable with temperature on the thermo-elastic behavior of laminated beams were discussed in detail.