Development and implementation of a geometrically nonlinear beam theory model for SMA composite beams with asymmetric behavior

• Published in: Composite structures 2021-03, Vol.259, p.113417, Article 113417
• Main Authors: Samadi-Aghdam, Kosar, Fahimi, Pouya, Baniassadi, Majid, Baghani, Mostafa
• Format: Article
• Language: English
• Subjects: Asymmetric behavior; Brinson model; FEM; Multi-layered SMA
• ISSN: 0263-8223; 1879-1085
• DOI: 10.1016/j.compstruct.2020.113417

This work aims at developing a finite element solution with consideration of the geometric nonlinearity for analyzing the bending behavior of a Shape Memory Alloy multi-layered beam. In this solution, a numerical method based on the Newton–Raphson method is implemented in order to satisfy equilibrium equations. The validation of the model is carried out by means of comparing the simulation results of beam with the semi-analytical solution. The validation outcomes are described for both symmetric and asymmetric models, and it is observed that both methods are in good agreement. The results of simulation of composite SMA beam are reported by both considering and neglecting the geometric nonlinearity and asymmetric behavior. Load-deflection, stress–strain as well as variation of the maximum slope are some of the diagrams that are investigated in this study. In one example, the error between the models which include and neglect the geometric nonlinearity is 107% and also in another case study, the error between asymmetric and symmetric models is 14.9%. The results reveal that considering the geometric nonlinearity and asymmetric behavior have important effects on simulation outcomes. This model is suitable for the design of structures including multilayer SMA composite which undergoes large displacements and moderate rotations.