Embedded Shape Memory Alloy Wire Composite Beam Thermal Buckling Analysis

Employing theoretical analysis and incorporating with numerical computation, geometrically nonlinear buckling of shape memory alloy reinforced composite beam subjected to a uniform temperature rising is studied. And how to use shape recovery stress of restrained SMA wires to increase the critical temperature and reduce the post-buckling deflection of the beam is examined.Firstly, the basic mechanical behaviors of SMA, such as the shape memory effect, the pseudo-elastic effect, the Young's modulus changing with temperature and et al., are analyzed. Secondly, the one-dimensional SMA constitutive relations are discussed. Stress-strain relations at specific temperature, strain-temperature characteristic relation of free strain recovery and stress-temperature relation of restrained recovery are studied separately for Brinson's constitutive law. The corresponding characteristic curves are plotted. Thirdly, based on the Brinson constitutive relation for SMA and the micro-mechanical law of composite materials, the one-dimensional constitutive model describing the SMA-matrix material system is formulated. Finally on the basis of the geometrically nonlinear theory for axially extensible beams, governing equations for static deformations of shape memory alloy reinforced composite beams subjected to thermal as well as mechanical loadings are formulated. Then by using the shooting method, the strong nonlinear boundary value problem of ordinary differential equations is solved. Thermal post-buckling response of the composite beams with fixed-fixed end, pinned-pinned end and pinned-fixed ends subjected to a uniform temperature rising are obtained. Thermal post-buckling equilibrium paths and configurations are plotted. The result show that by utilizing shape recovery stress the critical temperature is obviously increased, and critical temperature increase monotonically with the increment of the value of the volume fraction of SMA. For the given temperature, the SMA fibers can reduce thermal post-buckling deflections.