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Wunderlich, W.; Obrecht, H.; Schrödter, V.

Nonlinear analysis and elastic-plastic load-carrying behaviour of thin- walled spatial beam structures with warping constraints. (English) Zbl 0586.73119

Int. J. Numer. Methods Eng. 22, 671-695 (1986).
An analysis of the elastic-plastic load-carrying behaviour of thin-walled spatial beam structures is presented. It is based on a beam theory valid for large displacements and rotations, which admits arbitrary cross- sections, curved axes, initial imperfections, a general material description, and which fully accounts for the influence of warping constraints as well as the stress-history dependence of the elastic- plastic shear moduli. An incremental updated Lagrangian viewpoint is adopted in the derivation of the basic beam equations from a generalized variational principle, and in the numerical solution procedure the displacement-finite element approach is followed. The associated tangential stiffness matrices are obtained by direct numerical integration of the governing incremental differential equations rather than through the use of shape functions in connection with a virtual work principle. Applications of the theory are given in which the influence of the loading configuration, material parameters, geometric nonlinearities and warping constraints on the load-carrying behaviour and on the bifurcation and ultimate loads of thin-walled beam structures is explored.

Cited in 1 Document

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74R20 Anelastic fracture and damage

Keywords:

elastic-plastic load-carrying behaviour; thin-walled spatial beam structures; large displacements; rotations; arbitrary cross-sections; curved axes; initial imperfections; general material description; influence of warping constraints; stress-history dependence of the elastic-plastic shear moduli; incremental updated Lagrangian viewpoint; generalized variational principle; displacement-finite element approach; tangential stiffness matrices; direct numerical integration; governing incremental differential equations; loading configuration; material parameters; geometric nonlinearities; bifurcation; ultimate loads
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