An Approach for the Representation of Piezothermoelastic Bodies in Multibody Dynamics

Abstract

The consideration of the linearised displacement field of elastic bodies has become a state-of-the-art technique in multibody dynamics. For this task the modal approach has been applied with great success. Therefore, it is reasonable to extend the modal approach to a modal multifield approach if it is aimed to describe bodies with multiple distributed properties. That way not only the displacement field may be dicretised by the product of predefined time independent modal functions and time dependent coefficients but also an existing inhomogeneous temperature distribution or the electrical potential of an additional electrostatic field. In order to establish a closed description, the modal multifield approach is inserted into an extended Hamilton Principle and is connected to a thermodynamical potential. Thus, the field equations and the material constitution can be provided. As a result a coupled system of discretised field equations is composed. It may be solved efficiently combining specially adapted classical methods from multibody numerics with modular solution methods such as co-simulation. Beneath the outline of the theoretical framework the presentation gives some moderately complex verification examples. The capabilities of active damping by structure-integrated piezoceramic devices are demonstrated. The presented approach is also applied to the classical problem thermoelasticity. The simulation of a high precision tooling machinery with thermal loads emphasizes the significance of the approach for industrial scale problems.