Corrugated structures reinforced by shape memory alloy sheets: Analytical modeling and finite element modeling

In this study, an analytical solution is presented for a trapezoidal corrugated beam, which is reinforced by shape memory alloy sheets on both sides. Formulas are presented for shape memory alloys in states of compression and tension. According to the modified Brinson model, shape memory alloys have different thermomechanical behavior in compression and tension, and also these alloys would behave differently in different temperatures. The developed formulation is based on Euler-Bernoulli theory. Deflection of the smart structure and the effect of asymmetric response in shape memory alloys are studied. Results found from the semi-analytic modeling are compared to and validated through a finite element modeling, and there is more than 90% agreement between two solutions. With regard to the results, the neutral axis of the smart structure changes in each section. The maximum deflection ratio of asymmetric mode to symmetric one mode is 1.7. Additionally, the effect of design parameters on deflection is studied in detail.