A nonlinear two-node superelement with deformable-interface surfaces for use in flexible multibody systems

Abstract

A nonlinear two-node superelement is proposed for efficient modelling of arbitrary-shaped flexible members with two interfaces in a flexible multibody model. The formulation is based on a small rotation and displacement hypothesis in a local co-rotational frame. Component mode substructuring methods can then be used to determine the dynamical properties of the superelement from a linear finite element model. The key contribution of this paper is the inclusion of the so-called deformable-interface modes to model the deformability of the interface surfaces. This allows for a compliant connection to other superelements. With this capability, a component can be modelled with a number of superelements, and its dynamical properties can be accurately analysed even for large deflections provided that the deformations remain small with respect to the co-rotational frame. Three examples demonstrate the applicability of the method. In the first example, large deflections of a relative short sheet flexure are analysed. Next, the formulation is used to obtain a dynamically reduced model of a complex-shaped component. In the third example, the time-response of a compliant mechanism is considered that is composed of the components of the first two examples. For all three examples, eigenfrequency results are in good agreement with results obtained using a classical nonlinear finite element method.