A simultaneous space‐time discretization approach to the inverse dynamics of geometrically exact strings. (7th March 2022)

• Record Type: Journal Article
• Authors: Ströhle, Timo; Betsch, Peter
• Is Part Of: International journal for numerical methods in engineering. Volume 123:Number 11(2022)
• Page Start: 2573
• Page End: 2609
• Publication Date: 2022-03-07
• Subjects: feedforward control -- inverse dynamics -- method of characteristics -- space‐time finite elements -- trajectory tracking; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6951
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: A continuous space‐time Galerkin method is newly proposed for the numerical solution of inverse dynamics problems. The proposed space‐time finite element method is combined with servo‐constraints to partially prescribe the motion of the underlying mechanical system. The new approach to the feedforward control of infinite‐dimensional mechanical systems is motivated by the classical method of characteristics. In particular, it is shown that the simultaneous space‐time discretization is much better suited to solve the inverse dynamics problem than the semi‐discretization approach commonly applied in structural dynamics. Representative numerical examples dealing with elastic strings undergoing large deformations demonstrate the capabilities of the newly devised space‐time finite element method.