A Modal Multifield Approach for an Extended Flexible Body Description in Multibody Dynamics

Abstract

This paper presents a new methodology to simulate the behaviour of flexible bodies influenced by multiple physical field quantities in addition to the classical mechanical terms. The theoretical framework is based on the extended Hamilton Principle and an adapted modal multifield approach. Furthermore, the use of finite element analysis for the necessary data preprocessing is explained. Numerical solution strategies for the coupled system of differential equations with different time scale properties are mentioned. The method is applied to simulate a structure with distributed piezo-ceramic devices inducing an additional electrostatic field. Two thermoelastic problems, which have to consider the influence of spatial temperature distribution, also demonstrate the benefits of the presented approach.

Modeling for control of an inflatable space reflector, the nonlinear 1-D case

“…The equations of motion for the model we derive via the generalized Hamilton's principle [8]. This principle states that for a piezoelectric material it must hold that…”

“…The approach we propose differs from [4], [9], because we derive a model which can represent nonlinear deformations of the beam. Additionally we derive the equations of motion by the generalized Hamiltonian's principle, see [8]. We approach the problem with the purpose to extend it to the 2-D case in the future.…”

Optimization of a satellite with composite materials

“…The distribution of the time points has to be sufficiently dense to avoid large constraint violations between two adjacent time points [Hsieh and Arora 1984]. Thus, discretizing time-dependent constraints can significantly increase the number of constraints, and thereby the cost of optimization [Haftka and Gürdal 1992].…”

“…The technical system modeled within this application consists in the unfolding process of a satellite antenna, the Synthetic Aperture Radar (SAR) antenna, which is a part of the European research satellite ERS-1. The model of this antenna has been the object of different studies in several studies in multibody dynamics being first proposed by Hiller [1983] and Anantharaman and Hiller [1991]. Figure 3 is achieved through a relatively complex spatial mechanism.…”

“…For systems in which the bodies are made of standard materials, there is a wide variety of finite elements that may be used, but when bodies are made of composite materials, the model flexibility often necessitates expensive finite element models with an inherent growth in complexity. Models of systems involving multibody dynamics methodologies also require a complete knowledge of the arrangement of the system components, which is achieved by the definition of kinematic joints, the introduction of models for external forces and the incorporation of the equilibrium equations of other disciplines [Heckmann et al 2005;Møller et al 2005;Bottasso et al 2006]. Regardless of each particular type of joint used, the mathematical description of the restrictions involving only rigid bodies are the simplest to obtain.…”