Modeling and analysis of a superelastic elliptic flexure hinge using co-rotational beam elements

Compared with the conventional flexure hinges, the motion range of superelastic flexure hinges can be significantly increased, due to the material's superelasticity effect. In this paper, the deformation of superelastic elliptic flexure hinges is investigated by using finite element method (FEM). The superelastic behavior of the material is described by a bilinear one-dimensional constitutive model based on the experimental data. A Bernoulli beam element considering the variation of cross section, and the geometry and material nonlinearities is presented by using co-rotational approach. Equilibrium equations of the structure are constructed by beam elements and solved by the Newton-Raphson iterative method. Numerical results show that the proposed method agrees well with the results calculated by ANSYS, and also reduces the element number and the computation cost greatly. The maximum rotation angles and rotation errors of flexure hinges are also investigated by the co-rotational beam element with the variety of notch length and minimum thickness.