In this paper a procedure leading to a one-dimensional continuum that describes the nonlinear elastic behaviour of thin walled beams with open cross-sections, is introduced. The starting point is the theory proposed by Koiter which describes the deformation of the plate in a kinematically exact way. By assuming some fair constraints on the plate motion, its deformation measures can be described by means of the standard strain measures of nonlinear beam theory and their first gradients. Given that the plate is thin and made up by a material that is isotropically elastic and linear in the twodimensional finite strains, its strain energy is written in terms of the one-dimensional strains leading to a hyper elastic model of grade two. The buckling and postbuckling behaviour of a simply supported, axially loaded channel beam, is analyzed and the results compared with those obtained using ABAQUS and those reported in previous work by some of the authors.
Gabriele, S., Rizzi, N.L., Varano, V. (2014). A One-Dimensional Nonlinear Thin Walled Beam Model derived from Koiter Shell Theory. In B.H.V. Topping and P. Iványi (Editors) (a cura di), Proceedings of theTwelfth International Conference onComputational Structures Technology. STIRLINGSHIRE : Civil-Comp Press [10.4203/ccp.106.156].
A One-Dimensional Nonlinear Thin Walled Beam Model derived from Koiter Shell Theory
GABRIELE, STEFANO;RIZZI, Nicola Luigi;Varano V.
2014-01-01
Abstract
In this paper a procedure leading to a one-dimensional continuum that describes the nonlinear elastic behaviour of thin walled beams with open cross-sections, is introduced. The starting point is the theory proposed by Koiter which describes the deformation of the plate in a kinematically exact way. By assuming some fair constraints on the plate motion, its deformation measures can be described by means of the standard strain measures of nonlinear beam theory and their first gradients. Given that the plate is thin and made up by a material that is isotropically elastic and linear in the twodimensional finite strains, its strain energy is written in terms of the one-dimensional strains leading to a hyper elastic model of grade two. The buckling and postbuckling behaviour of a simply supported, axially loaded channel beam, is analyzed and the results compared with those obtained using ABAQUS and those reported in previous work by some of the authors.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
