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Doktorsdisputation

Co-rotational beam elements in instability problems


Respondent	Huvudhandledare	Bihandledare	Datum
Jean-Marc Battini	Anders Eriksson	Costin Pacoste	2002-01-18

Opponent
Eduard Riks, Delft University of Technology, Netherlands

Betygsnämd
Jean-Louis Batoz, InSIC, France Reijo Kouhia, Helsinki University of Technology Adam Zdunek, FOI

Abstract

The purpose of the work presented in this thesis is to implement co-rotational beam elements and branch-switching procedures in order to analyse elastic and elasto-plastic instability problems. For the 2D beam elements, the co-rotational framework is taken from Crisfield [23]. The main objective is to compare three different local elasto-plastic elements. The 3D co-rotational formulation is based on the work of Pacoste and Eriksson [73], with new items concerning the parameterisation of the finite rotations, the definition of the local frame, the inclusion of warping effects through the introduction of a seventh nodal degree of freedom and the consideration of rigid links. Different types of local formulations are considered, including or not warping effects. It is shown that at least some degree of non-linearity must be introduced in the local strain definition in order to obtain correct results for certain classes of problems. Within the present approach any cross-section can be modelled, and particularly, the centroid and shear center are not necessarily coincident. Plasticity is introduced via a von Mises material with isotropic hardening. Numerical integration over the cross-section is performed. At each integration point, the constitutive equations are solved by including interaction between the normal and shear stresses. Concerning instabilities, a new numerical method for the direct computation of elastic critical points is proposed. This is based on a minimal augmentation procedure as developed by Eriksson [32-34]. In elasto-plasticity, a literature survey, mainly concerned with theoretical aspects is first presented. The objective is to get a complete comprehension of the phenomena and to give a basis for the two branch-switching procedures presented in this thesis. A large number of examples are used in order to assess the performances of the elements and the path-following procedures.
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