Non-Linear Thermal Stability Analysis of SMA Wire-Embedded Hybrid Laminated Composite Timoshenko Beams on Non-Linear Hardening Elastic Foundation

Abstract

In the present study, non-linear thermal post-buckling analysis of hybrid laminated composite Timoshenko beams embedded with the shape memory alloy (SMA) wires resting on a non-linear hardening elastic foundation were studied. Mechanical properties of composite media are considered temperature-dependent. The theory of Timoshenko beams and von Kármán's strain-displacement relations are applied simultaneously in virtual work principles to derive the system of non-linear equilibrium equations. Various types of boundary conditions such as clamped, simply supported, and rolled edges were studied for edge supports. Generalized Differential Quadrature Method (GDQM) was utilized to discrete the equilibrium equations in space domain. Different types of lay-ups, such as symmetric and asymmetric, were considered. Post-buckling paths are depicted for different values of non-linear elastic foundation parameters, volume fractions, pre-strains of the SMA fibers, and boundary conditions. The one-dimensional thermo-mechanical constitutive law suggested by Brinson [1] is applied to model the SMA wires. Numerical results make it possible to recognize that increases in the volume fraction and pre-strain of SMA lead to a dramatic enhancement in thermal buckling and post-buckling capacity of the beam. Pre-buckling, buckling, and post-buckling behavior of the beam are totally different and this is due to variations among critical buckling, austenite start and finish temperatures. Due to the recovery stress of SMA wires, particular consequences are shown.