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Geometric non‐linear substructuring for dynamics of flexible mechanical systems
Author(s) -
Wu ShihChin,
Haug Edward J.
Publication year - 1988
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.1620261006
Subject(s) - substructure , linear elasticity , equations of motion , multibody system , vibration , mathematics , rigid body , geometry , structural engineering , mathematical analysis , classical mechanics , finite element method , physics , engineering , quantum mechanics
A substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric non‐linear effects. Large relative displacement is permitted between points within bodies that undergo small strain elastic deformation. Components are divided into substructures, on each of which the theory of linear elasticity relative to a body reference frame is adequate to describe deformation and its coupling with system motion. Normal vibration and static correction deformation modes are used to account for elastic deformation within each substructure. Compatibility conditions are derived and imposed as constraint equations at boundary points between substructures. System equations of motion that include geometric non‐linear effects of large rotation, in terms of generalized co‐ordinates of a reference frame for each substructure and a set of deformation modes that are defined within the substructure, are assembled. The method is implemented in an industry standard flexible multibody dynamics code, with minimal modification. Use of the formulation is illustrated on the classical problem of a spinning beam with geometric stiffening and on a space structure that experiences large deformation.