Analysis of flexible structures with occasionally rigid parts under transient loading

Abstract

In the computation of solid structures under long duration transient loading it is often advisable to treat parts of the structure at least for some time of the analysis as rigid bodies. Such a procedure increases first the efficiency of the analysis considerably and second the numerical condition of the system of equations benefits substantially within the numerical solution process. In particular structural modeling capabilities concerning boundary conditions and load transfer are considerably extended compared to a straightforward modeling with rigid bodies. The parts assumed rigid with small strains and sharing almost only a rigid body motion can be found in systems with high difference in stiffness as well as in systems with modestly loaded parts.A methodology based on the Energy Momentum Method is developed for creating occasionally rigid bodies within the computation. A criterion based on strain rates is used to decide for the modification from flexible to rigid. For optimal reduction of the number of degrees of freedom the rigid bodies are formulated using a transformation to minimal coordinates, also called master slave concept. The numerical examples involving long duration motion and large rotations demonstrate the possibilities of the developed procedure.

Dynamic modeling of flexible multibody system using a meshing method

“…However, this method still separates the motion of the system into rigid displacements and the elastic deformations, the two types of motion and the coupling of them increase the complexity of the system. Go¨ttlicher and Schweizerhof 28 developed another method which could convert some parts of the system from flexible into rigid and reduce the DOFs of the system. Oghbaei and Anderson 29 presented a new time-finite-element implicit integration scheme for multibody system dynamics simulation to simplify the equations of the system.…”

A rigid body and a master-master contact formulation for multibody railway applications.

“…definitely worth commenting here, as already pointed out by several authors (e.g. : [2] and [3]), is the fact that when the analysis of stresses, strains and wave propagation is not critical for a component, the use of rigid bodies becomes very attractive. Since the movement of the whole body can be described by a maximum of 6 degrees of freedom in a rigid approach, significant computational time can be saved.…”

“…These constraint equations are not enough to ensure a rigid body correct kinematics for the chosen set of material points. We still have to impose that all of them must present the same rotation 3 . Taking the pilot point as a reference, one may state a second constraint equation, which must be obeyed: The term δ 1k is given by: The term 2k is given by:…”