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Plastic instability of beam structures using co-rotational elements
KTH, Superseded Departments, Civil and Architectural Engineering.ORCID iD: 0000-0003-2104-382X
KTH, Superseded Departments, Civil and Architectural Engineering.
2002 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 191, no 51-52, 5811-5831 p.Article in journal (Refereed) Published
Abstract [en]

In a previous paper [Comput. Methods Appl. Mech. Engrg. 191 (2002) 1755], the authors have presented a 3D co-rotational elastic beam element including warping effects. This formulation is now further developed in order to incorporate elasto-plastic deformations. The element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross-sections. Thus, within the present approach, the centroid and shear center of the cross-section are not necessarily coincident. The main purpose of this element is to model elasto-plastic instability problems. In this context, two methods of branch-switching are tested and discussed. In the first one, the bifurcation point is isolated by successive bisections and the branch-switching is operated by using the eigenvector associated to the negative eigenvalue. In the second one, introduced by Petryk, an energy approach is used to select automatically the stable post-bifurcation path. Six examples, including large displacement and stability problems, are used in order to assess the performances of the element.

Place, publisher, year, edition, pages
2002. Vol. 191, no 51-52, 5811-5831 p.
Keyword [en]
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-12348DOI: 10.1016/S0045-7825(02)00498-XISI: 000179800200002OAI: diva2:309857
QC 20100409Available from: 2010-04-09 Created: 2010-04-09 Last updated: 2011-02-04Bibliographically approved
In thesis
1. Co-rotational beam elements in instability problems
Open this publication in new window or tab >>Co-rotational beam elements in instability problems
2002 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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 elastoplasticinstability 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 definitionof the local frame, the inclusion of warping effects through the introduction of aseventh nodal degree of freedom and the consideration of rigid links. Differenttypes of local formulations are considered, including or not warping effects. It isshown that at least some degree of non-linearity must be introduced in the localstrain 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. Numericalintegration over the cross-section is performed. At each integration point, theconstitutive equations are solved by including interaction between the normal andshear stresses. Concerning instabilities, a new numerical method for the direct computation of elasticcritical points is proposed. This is based on a minimal augmentation procedure asdeveloped by Eriksson [32–34]. In elasto-plasticity, a literature survey, mainly concernedwith theoretical aspects is first presented. The objective is to get a completecomprehension of the phenomena and to give a basis for the two branch-switchingprocedures 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.

Place, publisher, year, edition, pages
Stockholm: KTH, 2002. xv, 180 p.
Trita-MEK, ISSN 0348-467X ; 2002:01
instability, co-rotational mehtod, branch-switching, beam element, warping, plastic buckling. post-bifurcation
National Category
Natural Sciences
urn:nbn:se:kth:diva-3284 (URN)
Public defence
2002-01-18, 00:00 (English)
QC 20100512Available from: 2002-01-14 Created: 2002-01-14 Last updated: 2010-05-12Bibliographically approved

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