Analysis of a generalized kinematic impact law for multibody-multicontact systems, with application to the planar rocking block and chains of balls

Brogliato, Bernard; Zhang, Hongjian; Liu, Caishan

doi:10.1007/s11044-012-9301-3

Cited by 31 publications

(51 citation statements)

References 44 publications

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“…The present study considers structures designed to exhibit planar rocking and it assumes no sliding between the contacting bodies takes place [5]. Consider the rocking frame of Fig.…”

Section: Analytical Modellingmentioning

confidence: 99%

The Role of the Prestressed Tendons on the Seismic Performance of Hybrid Rocking Bridge Bents

Giouvanidis¹,

Dimitrakopoulos²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Allowing structural members to uplift and rotate around pre-defined pivot points isolates and relieves the structure from deformation and damage during strong earthquakes. Such rocking behavior has been examined as damage avoidance seismic design for bridges. Rocking structures, either freestanding or hybrid (supplemented with energy dissipation and re-centering devices), have been proposed by several researchers as high-performance systems that can survive major earthquakes without substantial damage. This paper investigates, analytically and numerically, the seismic performance of a hybrid rocking bridge bent which exhibits flag-shaped hysteretic behavior. The rocking frame is enhanced with elastic prestressed central tendons to provide re-centering capacity and hysteretic buckling restrained braces to dissipate energy. The present study examines its seismic behavior under both pulse-type and non-pulse-type ground motions. The focus of the present analysis is on the role of the prestressing force on the seismic performance. The results reveal the diverse influence of prestress. Specifically, prestress is beneficial for small rocking rotations, but could become detrimental when the frame sustains large rotations and as the size of the columns increases. Finally, the results reveal the sensitivity of the different rocking design solutions to the characteristics of the considered ground motion. As a consequence, none of the examined rocking frames can be considered as the optimal design solution under all ground motions. 4983

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“…The present study considers structures designed to exhibit planar rocking and it assumes no sliding between the contacting bodies takes place [5]. Consider the rocking frame of Fig.…”

Section: Analytical Modellingmentioning

confidence: 99%

The Role of the Prestressed Tendons on the Seismic Performance of Hybrid Rocking Bridge Bents

Giouvanidis¹,

Dimitrakopoulos²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…One sees from (10) (11) that the normal part of the dynamics is strongly influenced by the kinetic angles matrix. This is known to play a crucial role in existence and uniqueness of solutions [6], continuous dependence on initial data [1,31,74], couplings between unilateral and bilateral constraints [20], and dynamics at impacts [19].…”

Section: The Kinetic Anglesmentioning

confidence: 99%

“…Glocker [35] later interpreted Frémond's idea as a restitution matrix, recovering (as far as chains of balls are concerned) the normal part of the generalized law presented in the sequel of this paper: this restitution matrix should not in general be diagonal, but should contain off-diagonal entries representing the "distance effects". More recently, it has been shown that even more may sometimes be needed [19], because the normal part of the restitution law may not be sufficient to describe some motions like perfect rocking of a planar block. Recent results on multiple impacts with or without friction have also been obtained in [11,55,65,66,75,[80][81][82]87].…”

Section: Introductionmentioning

confidence: 99%

“…Issues of energetical consistency, uniqueness of coefficients of restitution, link with Moreau's impact law, tangential restitution and Coulomb's friction at impacts are analyzed. In passing, we provide a correct version of a result stated in [19], where some crucial assumptions are missing. Also a general and constructive criterion for the energetical consistency when normal restitution and Coulomb's friction are used, is proposed.…”

Section: Introductionmentioning

confidence: 99%

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Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction

Brogliato

2013

Multibody Syst Dyn

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Quasi-velocities computed with the kinetic metric of a Lagrangian system are introduced, and the quasi-Lagrange equations are derived with and without friction. This is shown to be very well suited to systems subject to unilateral constraints (hence varying topology) and impacts. Energetical consistency of a generalized kinematic impact law is carefully studied, both in the frictionless and the frictional cases. Some results concerning the existence and uniqueness of solutions to the so-called contact linear complementarity problem, when friction is present, are provided.

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“…[3]), a non-smooth dynamics (e.g. [4]) and a stochastic dynamics (e.g. [5] and references therein in all the above) perspective.…”

Section: Introductionmentioning

confidence: 99%

Closed-form rocking overturning conditions for a family of pulse ground motions

Dimitrakopoulos¹,

Fung²

2016

Proc. R. Soc. A.

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This paper characterizes the stability of a rigid rocking block subjected to a family of multi-lobe pulse ground motions. It unveils a counter to intuition plurality of overturning (OT) modes despite the short duration and bounded energy of the examined ground motions. Accordingly, it describes with original closed-form expressions the critical conditions of all OT modes involving a finite number of impacts. It also proposes pertinent semi-analytical, exact analytical and approximate analytical solutions with respect to the determination of the (unknown) times of impact, as appropriate. The analysis reveals that the first, or lower bound, critical OT mode is in most cases toppling during free rocking after one impact specifically before the end of the pulse. For this case, it elucidates the physical mechanism behind the timing of impact that produces minimum amplitude and maximum amplitude critical OT, respectively, and proposes pertinent closed-form approximations. Finally, the study derives, in 'universal' terms, global 'safety walls' against rocking OT considering a large number of different pulse shapes.

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Analysis of a generalized kinematic impact law for multibody-multicontact systems, with application to the planar rocking block and chains of balls

Cited by 31 publications

References 44 publications

The Role of the Prestressed Tendons on the Seismic Performance of Hybrid Rocking Bridge Bents

The Role of the Prestressed Tendons on the Seismic Performance of Hybrid Rocking Bridge Bents

Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction

Closed-form rocking overturning conditions for a family of pulse ground motions

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