Exact solution for nonlinear thermal stability of hybrid laminated composite Timoshenko beams reinforced with SMA fibers

Post-buckling behavior of Shape Memory Alloy (SMA) hybrid composite laminated beams under uniform heating is investigated in this paper. Properties of the constituents are temperature-dependent. The von-Karman type of geometrical non-linearity suitable for small strains and moderate rotations is taken into account. Displacement field through the beam obeys the kinematics of first order shear deformation theory of Timoshenko. To model the SMA fibers, the one-dimensional thermomechanical constitutive law proposed earlier by Brinson (1993) [1], is implemented. These basic assumptions are incorporated with the static version of virtual displacements to extract the nonlinear governing equations of the beam. The resulting system of nonlinear equations are uncoupled and solved analytically. Closed-form expressions are presented to trace the deflection-temperature as well as bending moment-temperature and end-shortening force-temperature in heating process. After validating the proposed approach, various parametric studies are performed to study the influence of lay-up, SMA volume fraction, SMA prestrain, boundary condition, and thickness of the layer in which SMA fibers are embedded. Fascinating results are extracted due to the recovery stress of SMA fibers.