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A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.ORCID iD: 0000-0003-2104-382X
2014 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 269, 538-565 p.Article in journal (Refereed) Published
Abstract [en]

The purpose of the paper is to present a corotational beam element for the nonlinear dynamic analysis of 3D flexible frames. The novelty of the formulation lies in the use of the corotational framework (i.e., the decomposition into rigid body motion and pure deformation) to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix. As a consequence, cubic interpolations are adopted to formulate both inertia and internal local terms. In the derivation of the dynamic terms, an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained. To enhance the efficiency of the iterative procedure, an approximate expression of the tangent dynamic matrix is adopted. Four numerical examples are considered to assess the performance of the new formulation against the one suggested by Simo and Vu-Quoc (1988) [48]. It was observed that the proposed formulation proves to combine accuracy with efficiency. In particular, the present approach achieves the same level of accuracy as the formulation of Simo and Vu-Quoc but with a significantly smaller number of elements.

Place, publisher, year, edition, pages
2014. Vol. 269, 538-565 p.
Keyword [en]
3D beam elements, Corotational method, Finite rotations, Nonlinear dynamics
National Category
Civil Engineering
Identifiers
URN: urn:nbn:se:kth:diva-131698DOI: 10.1016/j.cma.2013.11.007ISI: 000330815900024Scopus ID: 2-s2.0-84890860488OAI: oai:DiVA.org:kth-131698DiVA: diva2:656761
Note

QC 20140204. Updated from manuscript to article in journal.

Available from: 2013-10-17 Created: 2013-10-17 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Nonlinear dynamics of flexible structures using corotational beam elements
Open this publication in new window or tab >>Nonlinear dynamics of flexible structures using corotational beam elements
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The purpose of this thesis is to develop corotational beam elements for the nonlinear dynamic analyse of flexible beam structures. Whereas corotational beam elements in statics are well documented, the derivation of a corotational dynamic formulation is still an issue.

In the first journal paper, an efficient dynamic corotational beam formulation is proposed for 2D analysis. The idea is to adopt the same corotational kinematic description in static and dynamic parts. The main novelty is to use cubic interpolations to derive both inertia terms and internal terms in order to capture correctly all inertia effects. This new formulation is compared with two classic formulations using constant Timoshenko and constant lumped mass matrices.

In the second journal paper, several choices of parametrization and several time stepping methods are compared. To do so, four dynamic formulations are investigated. The corotational method is used to develop expressions of the internal terms, while the dynamic terms are formulated into a total Lagrangian context. Theoretical derivations as well as practical implementations are given in detail. Their numerical accuracy and computational efficiency are then compared. Moreover, four predictors and various possibilities to simplify the tangent inertia matrix are tested.

In the third journal paper, a new consistent beam formulation is developed for 3D analysis. The novelty of the formulation lies in the use of the corotational framework to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix. Cubic interpolations are adopted to formulate both inertia and internal local terms. In the derivation of the dynamic terms, an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained. Four numerical examples are considered to assess the performance of the new formulation against two other ones based on linear interpolations.

Finally, in the fourth journal paper, the previous 3D corotational beam element is extended for the nonlinear dynamics of structures with thin-walled cross-section by introducing the warping deformations and the eccentricity of the shear center. This leads to additional terms in the expressions of the inertia force vector and the tangent dynamic matrix. The element has seven degrees of freedom at each node and cubic shape functions are used to interpolate local transversal displacements and axial rotations. The performance of the formulation is assessed through five examples and comparisons with Abaqus 3D-solid analyses.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. xii, 79 p.
Series
Trita-BKN. Bulletin, ISSN 1103-4270 ; 119
Keyword
corotational method, nonlinear dynamics, large displacements, finite rotations, time stepping method, thin-walled cross-section, beam element
National Category
Construction Management
Identifiers
urn:nbn:se:kth:diva-131701 (URN)
Public defence
2013-10-18, INSA de Rennes, France, 14:00 (English)
Opponent
Supervisors
Note

QC 20131017

Available from: 2013-10-17 Created: 2013-10-17 Last updated: 2013-10-17Bibliographically approved

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Battini, Jean-Marc

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