Comparison of Planar Structural Elements for Multibody Systems with Large Deformations

Abstract

In the field of multibody dynamics, structural components, such as beams or plates, have been discretized in different ways, according to special requirements of certain problem configurations. In literature, models, which follow the same mechanical theories but a different numerical discretization technique, such as the absolute nodal coordinate formulation (ANCF) and the floating frame of reference formulation (FFRF), have been calculated for comparison. In existing examples, the solutions of these calculations do not always coincide very accurately. Therefore, in the present contribution, which is an extension of a former work of the authors, standard static and dynamic problems in the large deformation regime are treated. Special emphasis is laid on converged solutions, using an analytical reference value in the static case. For dynamic examples a reference value based on the strain energy is provided, in order to simplify the comparison of the different formulations and to provide a reference value, similar to the static case, for future studies. For both formulations planar finite elements based on the Bernoulli–Euler theory are utilized. In case of the ANCF the finite element consists of two position and two slope coordinates in each node only. In the FFRF beam finite element, as usual, two sets of coordinates are used to describe the actual configuration. The first set of coordinates defines the location and orientation of the body reference frame. The second set of coordinates describes small superimposed transverse and axial deflections relative to the body frame. The transverse deflections are approximated by means of two static modes for the rotation at the boundary and a user-defined number of eigenmodes of the clamped-clamped beam. The axial deflection is represented by a linear approach. In numerical studies, the accuracy of the two formulations is compared for two example problems, a cantilever beam with a singular force at the free end and a slider-crank mechanism. It turns out that both formulations have comparable performance and that the results coincide in the converged case.