Flexure Hinge Mechanisms Modeled by Nonlinear Euler‐Bernoulli‐Beams

Abstract

AbstractA flexure hinge is an innovative engineering solution for providing relative motion between two adjacent stiff members by the elastic deformation of an arbitrary shaped flexible connector. In the literature, modeling of compliant mechanisms incorporating flexure hinges is mainly focused on linear methods. However, geometrically nonlinear effects cannot be ignored generally. This study presents a nonlinear modeling technique for flexure hinges based on the Euler‐Bernoulli beam theory, in contrast to the predominant linear modeling approaches. Higher order beam elements of variable cross‐section are employed to model the flexure hinge region. A Newton‐Raphson scheme is applied to solve the resulting nonlinear system equations. The proposed approach reduces the overall degrees of freedom and is computationally efficient compared to commonly applied 3D finite element methods. A compliant displacement amplification mechanism is studied by means of the proposed method, where an excellent agreement with results of a reference solution is achieved. The modeling approach is suitable for the structural optimization of compliant mechanisms towards a less intuitive design process. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)