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A simultaneous space‐time discretization approach to the inverse dynamics of geometrically exact strings
Author(s) -
Ströhle Timo,
Betsch Peter
Publication year - 2022
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6951
Subject(s) - discretization , finite element method , galerkin method , inverse dynamics , mathematics , inverse problem , inverse , space (punctuation) , dynamics (music) , mathematical analysis , computer science , classical mechanics , geometry , physics , acoustics , thermodynamics , operating system , kinematics
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.