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Co-rotational beam elements in instability problems
KTH, Superseded Departments, Structural Engineering.ORCID iD: 0000-0003-2104-382X
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 [en]
instability, co-rotational mehtod, branch-switching, beam element, warping, plastic buckling. post-bifurcation
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:kth:diva-3284OAI: oai:DiVA.org:kth-3284DiVA: diva2:9068
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
List of papers
1. Co-rotational beam elements with warping effects in instability problems
Open this publication in new window or tab >>Co-rotational beam elements with warping effects in instability problems
2002 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 191, no 17-18, 1755-1789 p.Article in journal (Refereed) Published
Abstract [en]

The present paper investigates the formulation of 3D co-rotational beam elements for the buckling and post-buckling analysis of frame structures. Following Pacoste and Eriksson [Comput. Methods Appl. Mech. Engrg. 144 (1997) 163], the term co-rotational relates here to the provision of a local reference frame that continuously rotates and translates with the element. Within this context, several issues are emphasised. The first one refers to the parameterisation of finite 3D rotations. The alternative put forth in the paper is based on the spatial form of the incremental rotational vector. The second issue concerns warping effects which are introduced by adding a seventh degree of freedom at each node. Different types of local formulations are considered and 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 the centroid and shear center of the cross-section are not necessarily coincident. Finally, in the context of instability problems, a method for the direct computation of critical points is also briefly discussed, This is based on a minimal augmentation procedure as developed by Eriksson [Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynamic 1 (1) (2001)]. Ten examples, including large displacement and stability problems, are used in order to assess the performances of the elements.

Keyword
finite element and matrix methods; nonlinear mechanics; numerical solution procedures; stability in structural mechanics; structural mechanics
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-12346 (URN)10.1016/S0045-7825(01)00352-8 (DOI)000174316200001 ()
Note
QC 20100409Available from: 2010-04-09 Created: 2010-04-09 Last updated: 2017-12-12Bibliographically approved
2. Plastic instability of beam structures using co-rotational elements
Open this publication in new window or tab >>Plastic instability of beam structures using co-rotational elements
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.

Keyword
BEHAVIOR; BIFURCATION; SOLIDS
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-12348 (URN)10.1016/S0045-7825(02)00498-X (DOI)000179800200002 ()
Note
QC 20100409Available from: 2010-04-09 Created: 2010-04-09 Last updated: 2017-12-12Bibliographically approved
3. Improved minimal augmentation procedure for the direct computation of critical points
Open this publication in new window or tab >>Improved minimal augmentation procedure for the direct computation of critical points
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].

Keyword
NON-LINEAR EQUATIONS, STRUCTURAL INSTABILITY, BIFURCATION POINTS, TURNING-POINTS, PATH
National Category
Construction Management
Identifiers
urn:nbn:se:kth:diva-12811 (URN)10.1016/S0045-7825(03)00254-8 (DOI)000182794800012 ()
Note
QC 20100512Available from: 2010-05-12 Created: 2010-05-12 Last updated: 2017-12-12Bibliographically approved
4. Parameterisation of rotations in co-rotational elements
Open this publication in new window or tab >>Parameterisation of rotations in co-rotational elements
2000 (English)In: Proceedings Euromech 2000, Metz / [ed] Aeby-Gautier, E. Clavel, M. Dunne, F, Les Ulis: EDP Sciences , 2000Conference paper, Published paper (Refereed)
Abstract [en]

This paper presents some theoretical aspects related to the parameterisation of finite 3D rotations in the formulation of co-rotational beam and shell elements. In this context, the term "co-rotational" means that the motion of the element is decomposed into a rigid body motion followed by a pure deformation in the local coordinate system which continuously translates and rotates with the element.

Place, publisher, year, edition, pages
Les Ulis: EDP Sciences, 2000
Series
Journal de physique. IV, Proceedings, 99-2641810-4
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-12812 (URN)2-86883-550-3 (ISBN)
Conference
4th European Mechanics of Materials Conference on Processes, Microstructures and Mechanical Properties
Note
QC 20100512Available from: 2010-05-12 Created: 2010-05-12 Last updated: 2010-05-12Bibliographically approved
5. Elements poutres co-rotationels avec gauchissement
Open this publication in new window or tab >>Elements poutres co-rotationels avec gauchissement
2001 (French)In: Proceedings CSMA 5éme colloque national en calcul des structures, Giens, 2001Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Giens: , 2001
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-12813 (URN)
Conference
CSMA 5éme colloque national en calcul des structures
Note
QC 20100512Available from: 2010-05-12 Created: 2010-05-12 Last updated: 2010-05-12Bibliographically approved
6. Calcul des chemins d'équilibres post-critiques
Open this publication in new window or tab >>Calcul des chemins d'équilibres post-critiques
2001 (French)In: Proceedings CSMA 5éme colloque national en calcul des structures, Giens, 2001Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Giens: , 2001
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-12814 (URN)
Conference
CSMA 5éme colloque national en calcul des structures
Note
QC 20100512Available from: 2010-05-12 Created: 2010-05-12 Last updated: 2010-05-12Bibliographically approved
7. Plastic instability analysis of plane frames using a co-rotational approach
Open this publication in new window or tab >>Plastic instability analysis of plane frames using a co-rotational approach
1999 (English)Licentiate thesis, monograph (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH, 1999. viii, 86 p.
Series
Trita-BKN. Bulletin, ISSN 1103-4270 ; 48
Keyword
Plastic instability, Co-rotational method, Branch-switching, Beam element, Plastic buckling, Post-bifurcation
National Category
Building Technologies
Identifiers
urn:nbn:se:kth:diva-924 (URN)KTH/BKN/B--48--SE (ISRN)
Presentation
(English)
Note
QC 20100506Available from: 2000-09-26 Created: 2000-09-26 Last updated: 2010-05-12Bibliographically approved

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