Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

Abstract

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.

Bifurcation Analysis of a Nose Landing Gear System

“…The total number of generalized coordinates is 66, but, since the presence of 60 constraints, the degree of freedoms are six. In order to couple AUTO to LMS Virtual.Lab Motion the all states of the model are re-built at each step of the continuation based on the connectivity between the different bodies in the system 19 . In the developed code for coupling AUTO to LMS Virtual.Lab Motion, the six states considered for the continuation, as illustrated in Figure 1b, are:…”