Shape control of shape memory alloy composite beams in the post-buckling regime

The aim of the paper is to investigate active shape control of post-buckled elastic beams subjected to in-plane compressive loadings using surface-bonded shape memory alloy (SMA) layer actuators. A robust macroscopic SMA model is used to simulate main features of the SMA layer under dominant axial and transverse shear stresses during non-proportional thermo-mechanical loadings. The SMA model is able to reproduce martensite transformation/orientation, pseudo-elasticity, shape memory effect and in particular reorientation of martensite and ferro-elasticity effects. Non-linear equations of equilibrium for the moderately thick smart beam are derived by means of the principle of minimum total potential energy based on the first-order shear deformation theory and von Kármán geometrical non-linearity. The governing equations of equilibrium are solved using Ritz based finite element method along with an iterative numerical algorithm. Effects of the pre-strain state, thickness and temperature of the SMA layer actuator are examined, and their implications upon the pre/post-buckling behavior of the smart beam under in-plane compressive loadings are highlighted. The obtained results reveal that installing the SMA layer actuator can play a significant beneficial role toward confining deformation of the smart structure in the post-buckling regime. Due to lack of similar results in the specialized literature, the results of this research are expected to contribute to a better understanding of active shape control capability of the SMA composite beams under in-plane mechanical loadings.