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Elastic Motion

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Computational Flexible Multibody Dynamics

Part of the book series: Differential-Algebraic Equations Forum ((DAEF))

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Abstract

In this chapter, we turn our attention to the more general class of flexible multibody systems that include rigid as well as elastic bodies. While an elastic body is described by a partial differential equation, the rigid body motion, on the other hand, satisfies an ordinary differential equation or, in the presence of Euler parameters or joints, a differential-algebraic equation. Thus, the overall mathematical model consists of a coupled system with a subtle structure. We apply a step-by-step procedure in order to derive the underlying models. This chapter is mainly devoted to the motion of a single elastic body under the assumption of linear elasticity. Large rotations and translations will be treated by the method of floating reference frames in the subsequent Chap. 4. Hamilton’s principle of stationary action is the starting point to generate the equations of motion. Constraints are appended by means of Lagrange multipliers and lead to the notion of a time-dependent saddle point formulation that can be viewed as the continuous analogue of the constrained system for rigid bodies.

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Authors and Affiliations

  1. Felix-Klein-Zentrum für Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Bernd Simeon

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  1. Bernd Simeon
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Simeon, B. (2013). Elastic Motion. In: Computational Flexible Multibody Dynamics. Differential-Algebraic Equations Forum. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35158-7_3

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