Analytical study of thermal buckling and post-buckling behavior of composite beams reinforced with SMA by Reddy Bickford theory

Shape memory alloys are used in composite structures due to their shape memory effect and phase transformation. The recovery force of the shape memory alloy improves the post-buckling behavior of the structure. In this study, the thermal buckling and post-buckling of Shape Memory Alloy (SMA) hybrid composite laminated beam subjected to uniform temperature distribution is investigated. To this purpose, considering Von-Karman non-linear strain terms for large deformation, the non-linear equations of SMA reinforced beam based on Reddy Bickford theory have been derived. Besides, the recovery stress of the restrained SMA wires during martensitic transformation was calculated based on the one-dimensional constitutive law of the Brinson’s model. A numerical solution using Galerkin’s method has been presented for solving the nonlinear partial differential equations to obtain the critical buckling temperature and transverse deformation of the beam in the post-buckling region in both symmetric and anti-symmetric layups. The effect of SMA volume fraction, pre-strain, the boundary condition of the beam, stacking sequence, and its geometric properties have been studied. The results show that even by adding a small amount of SMA to the composite, the critical buckling temperature increases significantly, and the beam deflection decreases. Besides, using this theory has an evident effect on the anti-symmetric layup, especially for the thick beams.