Closed-form solution for thermal, mechanical, and thermo-mechanical buckling and post-buckling of SMA composite plates

In this paper, an analytical study on thermal, mechanical, and thermomechanical buckling and post-buckling of symmetric laminated composite plates reinforced with shape memory alloy (SMA) fibers are presented. The closed-form solution used in this study is developed based on the FSDT incorporated with the Von-Karman non-linear strains. The effect of SMA fibers is captured by adding a tensile recovery, stress term that determined using 1-D simplified Brinson's model, in the constitutive equations of the SMA composite plate. Galerkin technique is implemented for solving the nonlinear partial differential equations of motion to obtain buckling load and post-buckling path. The influence of several parameters such as SMA activation temperature, SMA fiber volume fraction, SMA pre-strain, biaxial ratio, etc., are studied in this work. Due to the generation of recovery force, significant improvement in buckling load is attained by increasing each of the SMA fiber volume fraction, activation temperature or SMA pre-strain.