A comparison in terms of accuracy and efficiency between a MBS dynamic formulation with stress analysis and a non‐linear FEA code

Abstract

SUMMARYTo perform the mechanical design of a machine through computer-aided techniques, at least three main di erent products should be used: a CAD software, to model the parts of the machine; a MBS program, to analyse the kinematics and dynamics of the whole system; and a FEA code, to determine the level of stress and strain su ered by each component. If it is true that CAD software is usually well connected with the two other tools, the same does not happen in what respects to FEA-MBS interfaces. Moreover, since both the large-amplitude motion and the elastic deformation are coupled, they cannot be solved separately, and the usual practice consisting of ÿrst analysing the machine motion assuming rigid bodies, and then calculating stresses under the loads previously generated, is just an approximation. In order to provide mechanical designers with a tool which makes easier and shorter the design-cycle, this paper presents a comparison between the two options that are currently available to address the mentioned problem: a dynamic MBS formulation which simultaneously solves motion and performs stress analysis by considering exible bodies; and a non-linear module of a FEA code, which takes into account large displacements and ÿnite rotations. The comparison is carried out in terms of accuracy and e ciency through four examples. The results lead to the conclusion that, for similar accuracy, the ÿrst method is largely more e cient. Therefore, the interest of developing MBS commercial codes which integrate motion calculation and stress analysis through the mentioned approach is envisioned, as long as they would provide faster solutions.

Dealing with multiple contacts in a human-in-the-loop application

“…The formalism was extensively described in Ref. [12], for this reason only a brief summary is given here.…”

Two implementations of IRK integrators for real‐time multibody dynamics

“…The global method [3] uses natural (global and dependent) co-ordinates to model the multibody system. It consists of an index-3 augmented Lagrangian formulation, whose equations are combined with the difference equations of the numerical integrator, to produce a nonlinear algebraic set of equations wherein the dependent positions are the unknowns.…”

“…The new method, called hybrid, was obtained as combination of a topological semi-recursive formulation based on velocity transformations [2], and a global penalty formulation for closed-loops consideration [3]. The three formulations (we will refer to them as global, topological and hybrid) were compared through the analysis of several multibody systems, and the proposed formulation showed to be more robust and efficient that its predecessors for large problems.…”

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“…Double pendulum under gravity effect. This example, which has been proposed in [Cuadrado et al 2001], shows the performance of the algorithm in the case of rigid body motion with multiple links. The double pendulum chosen for study has two identical links of length 1.5 m, and uniform rectangular crosssection of width 0.018973 m and height 0.0632455 m. The acceleration due to gravity g, the Young's modulus E, the Poisson's ratio, and the density are taken to be 9.81 m/s 2 , 7 × 10 10 N/m 2 , 0.0, and 2000 kg/m 3 , respectively.…”

“…The double pendulum starts from rest in the horizontal position and falls under the action of gravity. The motion is studied in the interval [0, 5] seconds with t = 0.02 s (which is twenty times that used in [Cuadrado et al 2001]). Two H27/I27 elements (one element per link) are used to carry out the simulation.…”