Thermal post-buckling behavior of sandwich beams with CNT–reinforced composite core and axially restrained ends resting on Winkler/Pasternak/Kerr foundations

Thermal buckling and post-buckling behavior of sandwich beams constituted of carbon nanotube (CNT) reinforced composite core and homogeneous face sheets under uniform temperature rise are investigated in this paper. Unlike previous studies, the combined influences of axial elastic constraints of two ends and interaction from three Winkler/Pasternak/Kerr foundation models on the thermal instability of nanocomposite sandwich beams are considered. The properties of constituent materials are temperature–dependent and the effective properties of nanocomposite are determined by means of an extended rule of mixture. CNTs are reinforced into matrix according to functionally graded distributions. Governing equations are established within the framework of Timoshenko beam theory taking into account von Kármán nonlinearity, initial geometric imperfection, axial constraints of two ends and interaction from elastic foundations. These equations are solved by means of analytical solutions and Galerkin method to obtain a nonlinear load–deflection relation for simply supported beams. Critical thermal loads and post-buckling temperature–deflection paths are determined using an iteration process. Parametric studies find that there exists a very small value of thickness of face sheets for which the buckling resistance and post-buckling loading carrying capabilities of sandwich beams are the strongest. The study also indicates that the support of elastic foundations enhances the critical thermal loads and thermal post-buckling curves. Furthermore, it is worth that initial geometric imperfection has beneficial influences on the loading bearing capacity in the deep region of deflection of the sandwich beams.