Dynamic Analysis of Compliant Mechanisms Using Absolute Nodal Coordinate Formulation and Geometrically Exact Beam Theory

Abstract

Compliant mechanism mainly relies on large deformations of compliant rods to transmit motions, forces and energy. The geometric nonlinearity of the compliant rods is one of the most serious challenges when accurate modeling and dynamic simulation are performed. The absolute nodal coordinate formulation (ANCF) and geometrically exact beam theory (GEBT) are employed to investigate the nonlinear modeling and analysis of compliant mechanisms in this paper. By taking account of deformation characteristics of the compliant rod at the external connection, a new ANCF beam element with one nodal deformation constraint is proposed. Based on the locking alleviation technique, strain split method, the effect of the locking phenomenon of the ANCF beam element on the dynamic simulation of compliant mechanism is investigated. In comparison, the Euler-Bernoulli beam element, which is a kind of locking free GEBT element, is also used for the dynamic analysis of the compliant mechanism. Finally, the numerical example of a partial compliant four-bar mechanism is presented to illustrate the accuracy and effectiveness of ANCF and GEBT beam elements for the dynamic problems of compliant mechanisms.