A beam element with arbitrary active cross sections for multibody simulation of large-deflection flexure mechanisms

Damping parasitic vibrations in flexure mechanisms can be achieved by integrating piezoelectric material in the flexures. Efficient models of such active flexures can aid in the design and optimization of such mechanisms to meet ever-increasing performance targets. In this paper, we present a novel beam element that is able to accurately and efficiently capture the large-deflection behavior of active flexures. The element combines a cross-sectional analysis based on the variational asymptotic method with the generalized strain beam formulation used in the multibody software SPACAR. The cross-sectional analysis converts an arbitrary active-section geometry to an asymptotically accurate equivalent beam model. This model is then used in the formulation of the geometrically nonlinear beam element. The element is validated against existing approaches and a challenging case study is presented, which shows that the element can be used to simulate complex active flexure mechanisms undergoing large deflection. The element is able to achieve results with a fraction of the computational effort required by a 3D finite-element package, with only a minor decrease in accuracy.