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A geometrically-exact rod model incorporating shear and torsion-warping deformation. (English) Zbl 0731.73029

The authors start with a critical survey of the relevant research done within the last twenty years. In the paper under consideration, the deformation of the rod is determined by three functions: The first one accounts for finite displacement of the centroid and the other two for finite rotation and twist of the cross section and finite warping, respectively. The next step is the establishment of stress resultants and couples. Considering the stress power, one obtains the conjugate strains therewith. The hyperelastic constitutive equation connecting these quantities and the balance laws complete the set of equations. Final point is the construction of the weak form of the local field equations with the help of variational formulation, their linearization and iterative solution by Newton’s method. Numerical examples are given. The reseach reported is an important contribution to rod theory.
Reviewer: U.Gamer (Wien)

MSC:

74B20 Nonlinear elasticity
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
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