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Improved minimal augmentation procedure for the direct computation of critical points
KTH, Superseded Departments, Structural Engineering.ORCID iD: 0000-0003-2104-382X
KTH, Superseded Departments, Structural Engineering.
KTH, Superseded Departments, Structural Engineering.ORCID iD: 0000-0002-5819-4544
2003 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 192, no 16-18, 2169-2185 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents a new numerical procedure for the direct computation of critical points for elastic beam structures undergoing large displacements and rotations. Compared to the approach described by Wriggers et al. [Comput. Methods Appl. Mech. Engrg. 70 (1988) 329; Int. J. Numer. Methods Engrg. 30 (1990) 1551, two main modifications are introduced. First, following Eriksson [Comput. Methods Appl. Mech. Engrg. 114 (1994) 77; Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynam. l(l) (2001)], the condition of criticality is expressed by a scalar equation instead of a vectorial one. Next, the present procedure does not use exclusively the extended system obtained from the equilibrium equations and the criticality condition, but also introduces intermediate iterations based purely on equilibrium equations under load or displacement control, Eight numerical examples, presenting bifurcation and limit points, are used in order to compare the performances of this new method and the one presented in [Comput. Methods Appl. Mech. Engrg. 70 (1988) 329; Int. J. Numer. Methods Engrg. 30 (1990) 155].

Place, publisher, year, edition, pages
2003. Vol. 192, no 16-18, 2169-2185 p.
Keyword [en]
NON-LINEAR EQUATIONS, STRUCTURAL INSTABILITY, BIFURCATION POINTS, TURNING-POINTS, PATH
National Category
Construction Management
Identifiers
URN: urn:nbn:se:kth:diva-12811DOI: 10.1016/S0045-7825(03)00254-8ISI: 000182794800012OAI: oai:DiVA.org:kth-12811DiVA: diva2:318955
Note
QC 20100512Available from: 2010-05-12 Created: 2010-05-12 Last updated: 2017-12-12Bibliographically 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.
Series
Trita-MEK, ISSN 0348-467X ; 2002:01
Keyword
instability, co-rotational mehtod, branch-switching, beam element, warping, plastic buckling. post-bifurcation
National Category
Natural Sciences
Identifiers
urn:nbn:se:kth:diva-3284 (URN)
Public defence
2002-01-18, 00:00 (English)
Note
QC 20100512Available from: 2002-01-14 Created: 2002-01-14 Last updated: 2010-05-12Bibliographically approved

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Battini, Jean-MarcEriksson, Anders

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