On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3D geometrically exact beam model

Ibrahimbegović, Adnan; Mamouri, Said

doi:10.1016/s0045-7825(99)00363-1

Cited by 72 publications

(45 citation statements)

References 25 publications

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“…in Mamouri (2000 and, Ibrahimbegović et al (2003), Romero (2008), Ghosh andRoy (2009), Betsch andSteinmann (2003), Jelenić and Crisfield (2001) and Romero and Armero (2002). Most of those studies state that the Newmark time integration procedure cannot be used in nonlinear dynamics as a whole, however, finite rotation based methods are not the unique strategy to solve nonlinear dynamics.…”

Section: Latin American Journal Of Solids and Structures 14 (2017) 52-71mentioning

confidence: 99%

Flexible Multibody Dynamics Finite Element Formulation Applied to Structural Progressive Collapse Analysis

Sanches

Coda

2017

Lat. Am. j. solids struct.

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This paper presents a two-dimensional frame finite element methodology to deal with flexible multi-body dynamic systems and applies it to building progressive collapse analysis. The proposed methodology employs a frame element with Timoshenko kinematics and the dynamic governing equation is solved based on the stationary potential energy theorem written regarding nodal positions and generalized vectors components instead of displacements and rotations. The bodies are discretized by lose finite elements, which are assembled by Lagrange multipliers in order to make possible dynamical detachment. Due to the absence of rotation, the time integration is carried by classical Newmark algorithm, which reveals to be stable to the position based formulation. The accuracy of the proposed formulation is verified by simple examples and its capabilities regarding progressive collapse analysis is demonstrated in a more complete building analysis.

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Section: Latin American Journal Of Solids and Structures 14 (2017) 52-71mentioning

confidence: 99%

Flexible Multibody Dynamics Finite Element Formulation Applied to Structural Progressive Collapse Analysis

Sanches

Coda

2017

Lat. Am. j. solids struct.

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“…This type of solution is not practical for our purpose and is replaced with Levenberg-Marquardt procedure for determination of relevant structure parameters [8].…”

Section: Similarity In Operator Spacementioning

confidence: 99%

Similarity of structures based on matrix similarity

2017

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Original scientific paper The paper presents a numerical procedure for relating the behaviour of two different structures, i.e. determining a scale between two structures. This novel solution is based on the notion of matrix similarity and linear transformations, with the restriction that the scale between structures is determined only after structural discretization, and that both structures have to be in the elastic regime. The structure scale can be determined in loading space or displacement space (i.e. structure forces or displacements are put into relation) where the scaling of the static structure model is based on the matrix equivalence principle, and scaling of the dynamic structure model is based on the Smith normal form. The structure scale in operator space (structure stiffness or flexibility matrices are put into relation) should be based on the Sylvester matrix equation. However, that approach is not practical and is replaced with the Levenberg-Marquardt method for obtaining only approximately equivalent stiffness matrices. Numerical examples illustrate the proposed novel approach.Keywords: Levenberg-Marquardt method; matrix equivalence; similarity of structures; Smith normal form; structure scales; Sylvester equation Sličnost konstrukcija zasnovana na sličnosti matricaIzvorni znanstveni članak Rad prikazuje numerički postupak za uspostavljanje odnosa između ponašanja dvije različite konstrukcije, odnosno određivanje mjerila (faktora skaliranja) između dvije konstrukcije. Ovo novo rješenje zasnovano je na ideji sličnosti matrica i linearnim transformacijama, uz ograničenja da se mjerilo između konstrukcija određuje tek nakon provođenja diskretizacije te da obje konstrukcije moraju biti u elastičnom području. Mjerilo konstrukcije može se odrediti u polju opterećenja ili pomaka (ovisno o tome dovode li se u vezu sile ili pomaci konstrukcije) gdje se skaliranje statičkog modela konstrukcije zasniva na principu ekvivalentnosti matrica, dok je skaliranje dinamičkog modela konstrukcije bazirano na Smith normalnoj formi. Skaliranje konstrukcije u operatorskom prostoru (matrice krutosti ili fleksije stavljaju se u međuodnos) trebalo bi biti bazirano na Sylvester matričnoj jednadžbi. Međutim, takav pristup nije praktičan te je zamijenjen Levenberg-Marquardt metodom za dobivanje približno ekvivalentnih matrica krutosti. Numerički primjeri ilustriraju predloženi drugačiji pristup.

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“…[13,14]) is chosen. In the following section we describe the time integration of the coupled rigid flexible system in minimal coordinates with the Energy Momentum Method with a specific reference to Zienkiewicz and Taylor [16], Ibrahimbegovic et al [10] and Ibrahimbegovic and Mamouri [8]. The formulation of the weak form requires the expression of the displacement degrees of freedom u g of the nodes of those flexible elements that are directly adjacent to rigid bodies (in global coordinates) by the translational and rotational degrees of freedom of the rigid body r s and h s for the discretized structure in accordance with Fig.…”

Section: Time Integration Of the Coupled Structurementioning

confidence: 99%

“…A corresponding procedure using Lagrange multipliers was worked out in detail in [2,15] and can also be found in [10]. The latter article includes an efficient formulation for the integration of general constraint conditions on the basis of minimal coordinates that are explained more closely in [8]. For an extensive discussion we also refer to Gö ttlicher [6].…”

Section: Introductionmentioning

confidence: 99%

Analysis of flexible structures with occasionally rigid parts under transient loading

Göttlicher

Schweizerhof

2005

Computers & Structures

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In the computation of solid structures under long duration transient loading it is often advisable to treat parts of the structure at least for some time of the analysis as rigid bodies. Such a procedure increases first the efficiency of the analysis considerably and second the numerical condition of the system of equations benefits substantially within the numerical solution process. In particular structural modeling capabilities concerning boundary conditions and load transfer are considerably extended compared to a straightforward modeling with rigid bodies. The parts assumed rigid with small strains and sharing almost only a rigid body motion can be found in systems with high difference in stiffness as well as in systems with modestly loaded parts.A methodology based on the Energy Momentum Method is developed for creating occasionally rigid bodies within the computation. A criterion based on strain rates is used to decide for the modification from flexible to rigid. For optimal reduction of the number of degrees of freedom the rigid bodies are formulated using a transformation to minimal coordinates, also called master slave concept. The numerical examples involving long duration motion and large rotations demonstrate the possibilities of the developed procedure.

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On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3D geometrically exact beam model

Cited by 72 publications

References 25 publications

Flexible Multibody Dynamics Finite Element Formulation Applied to Structural Progressive Collapse Analysis

Flexible Multibody Dynamics Finite Element Formulation Applied to Structural Progressive Collapse Analysis

Similarity of structures based on matrix similarity

Analysis of flexible structures with occasionally rigid parts under transient loading

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