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 timeresponse 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.

A multinode superelement in the generalized strain formulation

“…The full expression is derived in Appendix A.3. This result is similar to the result obtained in the superelement of [13].…”

“…By using these models, arbitrarily shaped bodies can be defined by a single element with few degrees of freedom. In several formulations, such an arbitrary shaped element is called a superelement [10][11][12][13].…”

“…A two-node superelement is derived in the generalized strain formulation [12,13]. However, many frame parts are connected to more than two other components such that these frame parts cannot be modeled using the two-node superelement.…”

“…For many default elements deformation modes are defined, like trusses, beams [4,38], hinges [38], and wheels [39]. Also a two-node superelement [12,13] was formulated, based on the deformation modes of beam elements. However, a superelement with more than two interface nodes has not been derived.…”

Coupled simulation of elastohydrodynamics and multi-flexible body dynamics in piston-lubrication system

“…Among the various techniques, eigen solutions, constraint modes, the Krylov subspace scheme, and singular value decomposition (SVD) are the mainly used basis vectors. [33][34][35][36][37][38][39][40][41] Since these basis vectors have their own advantages and disadvantages, users have to thoughtfully select an optimal basis vector, or have to combine them to accurately approximate the flexible model.…”