Dynamic modeling and analysis of pseudo-elastic flexure hinges

The main goal of this paper is to establish a dynamic model for pseudo-elastic flexure hinges that are made of shape memory alloys. Based on the co-rotational framework, the nonlinear dynamic formulation of the pseudo-elastic flexure hinges is presented, which considers the continuous variation of the cross section, the material nonlinearity and the geometrical nonlinearity. In order to simplify the calculation process and guarantee the convergence, a piecewise linear model based on Brinson's constitutive law is developed to establish the constitutive relation of shape memory alloys. Newton-Raphson method combined with the Newmark time integration method is employed to solve the highly nonlinear motion equations. Finally, the dynamic behavior of an elliptical flexure hinge subjected to an impulse load is analyzed. Numerical results compared with finite element analysis by ABAQUS show that the proposed approach can predict the dynamic response of the flexure hinges precisely and the hysteretic energy-dissipation phenomenon is also observed.