Nonlinear analysis of shape memory alloy curved beams under a central concentrated load

This work aims to cope with the nonlinear analysis of curved beams made of shape memory alloy (SMA) under a central concentrated load. The assumptions of Euler-Bernoulli beam theory are considered, and the Von Karman strain field is employed to account for large deflections. Thus, the beam undergoes large displacements with small strain and moderate rotations (intermediate nonlinear theory) under general boundary conditions which may be nonlinear. The formulation of the problem is displacement-based, regarding the axial (tangential) and transverse (normal) displacements, while the two governing equations are coupled and nonlinear. In order to introduce the SMA constitutive law, a fiber approach is used at specific control cross-sections along the beam. The numerical solution of the longitudinal problem is achieved using the analog equation method (AEM) and a boundary element method (BEM)-based technique. The iterative procedure is based on Newton-Raphson scheme that uses a displacement control algorithm to trace the full nonlinear equilibrium path and overcome the possible limit points. Two representative examples are studied, and the results are compared to those taken either from the literature or by models developed with commercial software packages, validating the reliability and effectiveness of the proposed method.