The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references. @DOI: 10.1115/1.1590354#

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Computational strategies for flexible multibody systems

To facilitate the use of data that describe finite element or continuum models for the simulation of flexible members in multibody codes, standard input data (SID) is defined. The SID are based on a modal representation of small body deformations. Therefore, integrals appearing in the multibody system equations can be pre-calculated by pre-processors and stored in the SID file before simulation. The SID structure is organized using an object-oriented class description.

Standardization of Flexible Body Modeling in Multibody System Codes, Part I: Definition of Standard Input Data*

Geometric, rotational or dynamic stiffening is a well and long known phenomenon in the analysis of flexible bodies. In multibody dynamics the effect has attracted attention only recently. The objective of this paper is to contribute to the understanding of the modeling of geometric stiffening in multibody system simulation. Today's methods for modeling the effect assume that the (applied) stresses in a flexible system body are zero in its reference configuration, in which it performs large overall motions. The corresponding inertial loads are shown to be balanced by constraint stresses. This can be seen easily when formulating the system equations of motion for nonzero reference stresses. As a result one obtains an efficient alternative to compute the geometric stiffening terms. The method increases the generaltity of flexible body models for multibody system simulation.

Representation of geometric stiffening in multibody system simulation

This paper presents a general way of including stress stiffening effects in the dynamic simulation of flexible multibody systems that undergo large overall motion accompanied by small elastic deformation. Stress stiffening terms are derived from the internal virtual work that includes nonlinear terms of the strain-displacement relationship and reference stresses induced by existing loads before deformation. The resultant stress stiffness matrix for a flexible body is obtained through quasi-static structural analyses by applying D'Alembert inertia, joint reaction, and other applied loads. The DAIembert inertia loads arising from gross motion of the body reference frame are expressed as a combination of space-dependent terms and 12 sets of time-dependent terms. An iterative method is proposed to solve the resultant system equations of motion. Examples are presented to illustrate the method and procedures proposed.

A General Approach to Stress Stiffening Effects on Flexible Multibody Dynamic Systems

An easy applicable procedure for the approximate analysis of a flexible body in a multibody system (MBS) is presented. It is based on the major assumptions that the elastic deformations in the MBS are small and that their effect upon the large motion of the MBS is negligible. It can be carried out using a standard code for the analysis of rigid multibody systems and a nonlinear general purpose finite element program which has to be extended, so that the inertia forces and the constraint forces acting on the examined body can be applied. Deformations and stresses are calculated for some examples, also including the effects of dynamic coupling and dynamic stiffening as well as contact problems.

Approximate Analysis of Flexible Parts in Multibody Systems Using the Finite Element Method

For dynamics of flexible multibody systems the deformation of the bodies is described by global assumed modes. The development of geometric stiffness terms due to steady state loads is presented. In particular, the stress stiffening matrix with respect to nominal stresses is derived by superposition of unit stress stiffening matrices and scaling them by actual nominal loads. The method is applied to a flexible pendulum and a helicopter rotor blade. The results are compared with those obtained by a finite elements analysis.

O. Wallrapp

Papers

Superposition Method for Stress Stiffening in Flexible Multibody Dynamics.