Geometric nonlinear substructuring for dynamics of flexible mechanical systems. (English) Zbl 0661.73059
A substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric nonlinear 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 nonlinear 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.
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74B20 | Nonlinear elasticity |
Keywords:
substructure synthesis formulation; flexible multibody dynamic analysis computer codes; structural geometric nonlinear effects; Large relative displacement; small strain elastic deformation; substructures; Normal vibration; static correction deformation modes; Compatibility conditions; constraint equations; equations of motion; geometric nonlinear effects of large rotation; set of deformation modesReferences:
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