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On the role of frame invariance in structural mechanics models at finite rotations. (English) Zbl 1023.74048

Summary: We re-examine the so-called geometrically exact models for structures, such as beams, shells or solids with independent rotation field, with respect to invariance under superposed rigid body motion. A special attention is given to clarifying the issues pertaining to the finite element implementation which guarantees that the invariance of the continuum problem is preserved by its discrete approximation. Several numerical simulations dealing with finite rotations of structural models are presented in order to illustrate and confirm the given theoretical considerations.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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