Wave motion in a thick cylindrical rod undergoing longitudinal impact

Červ, Jan; Adámek, Vítězslav; Valeš, František; Gabriel, D.; Plešek, Jiřı́

doi:10.1016/j.wavemoti.2016.05.007

Cited by 12 publications

(4 citation statements)

References 22 publications

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“…We verify in Figure 9 (top‐left) that the computed numerical solution is very close to the semianalytical solution obtained by Červ et al 61 for three representative values of time

t^{*} = \{0.25, 1, 2\}

. On the right, it is represented the evolution of contact pressure in the contact zone.…”

Section: Numerical Examplessupporting

confidence: 79%

See 1 more Smart Citation

Partitioned formulation of contact‐impact problems with stabilized contact constraints and reciprocal mass matrices

González

Kopačka

Kolman

et al. 2021

Numerical Meth Engineering

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This work presents an efficient and accuracy‐improved time explicit solution methodology for the simulation of contact‐impact problems with finite elements. The proposed solution process combines four different existent techniques. First, the contact constraints are modeled by a bipenalty contact‐impact formulation that incorporates stiffness and mass penalties preserving the stability limit of contact‐free problems for efficient explicit time integration. Second, a method of localized Lagrange multipliers is employed, which facilitates the partitioned governing equations for each substructure along with the completely localized contact penalty forces pertaining to each free substructure. Third, a method for the direct construction of sparse inverse mass matrices of the free bodies in contact is combined with the localized Lagrange multipliers approach. Finally, an element‐by‐element mass matrix scaling technique that allows the extension of the time integration step is adopted to improve the overall performance of the algorithm. A judicious synthesis of the four numerical techniques has resulted in an increased stable explicit step‐size that boosts the performance of the bipenalty method for contact problems. Classical contact‐impact numerical examples are used to demonstrate the effectiveness of the proposed methodology.

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“…We verify in Figure 9 (top‐left) that the computed numerical solution is very close to the semianalytical solution obtained by Červ et al 61 for three representative values of time

t^{*} = \{0.25, 1, 2\}

. On the right, it is represented the evolution of contact pressure in the contact zone.…”

Section: Numerical Examplessupporting

confidence: 79%

“…As a second benchmark problem we adopt the Taylor test of a perfectly elastic cylinder, a classical problem with semianalytical solution 61 . In particular, we consider the case of a cylinder with radius a = 1m and initial velocity v 0 = 1m/s impacting on a rigid wall, as schematically represented in Figure 7.…”

Section: Numerical Examplesmentioning

confidence: 99%

Partitioned formulation of contact‐impact problems with stabilized contact constraints and reciprocal mass matrices

González

Kopačka

Kolman

et al. 2021

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…As a benchmark problem we adopt the Taylor test of a perfectly elastic cylinder, a problem with semi-analytical solution [6]. We consider the particular case of an cylinder of radius a = 2 m and length L = 10 m with an initial velocity v 0 = 0.1 m/s impacting on a rigid wall, represented in Figure 2.…”

Section: Numerical Example (Taylor Test)mentioning

confidence: 99%

Partitioned Formulation of Contact-Impact Problems With Stabilized Contact Constraints and Reciprocal Mass Matrices

González¹,

Kolman²,

Kopačka³

et al. 2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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This work proposes an extremely efficient and accurate time explicit solution algorithm for the simulation of contact-impact problems with finite elements. The methodology combines three existent techniques. First, for the treatment of the contact problem, a bipenalty contact-impact algorithm for explicit dynamics with stabilization of the contact constraints through the addition of stiffness and mass penalties [1]. Second, for the reduction of the contact problem to the interface, the method of localized Lagrange multipliers [2], that is able to formulate the contact problem in partitioned form, uncoupling the contact terms from the free body matrices. And finally, for an efficient construction of the free-free inverse mass matrices, the method based on localized Lagrange multipliers to generate inverse mass matrices [3] with specific projectors for the application of boundary conditions. It is also demonstrated that the resultant methodology is very well suited for parallelization in multicore machines. Different numerical experiments will be used to prove the effectiveness of the proposed formulation. 786 COMPDYN 2019 7 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.

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“…This algorithm was tested in [13] on different problems of elastodynamics and it was showed that it is very efficient and robust and that it can be used to obtain results of accuracy comparable to those from analytical approach (see e.g. [14]). …”

Section: Solving Proceduresmentioning

confidence: 99%

Propagation of Non-Stationary Waves in Viscoelastic Strip Composed of Orthotropic Layers

Adámek¹,

Valeš²,

Červ³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The analytical solution for transient waves caused by transverse impact on an infinite layered strip with free-free boundaries is presented in this work. The strip is composed of two horizontal layers of different heights. The materials of both layers are assumed to be linear viscoelastic and orthotropic. The case of special orthotropy is assumed for simplicity. The dissipative behaviour of each layer is modelled by the discrete model of standard linear viscoelastic solid in Zener configuration. The solving procedure used in this work follows the methods applied in previously published works dealing with the problems of a viscoelastic orthotropic strip and the symmetric case of a layered strip. The system of four linear partial integro-differential equations describing the non-stationary state of plane stress in the strip is solved by means of integral transform method. Concretely, the Laplace transform in time domain and the Fourier transform in spatial domain are applied. As a results of this procedure, the final formulas for displacement components in both layers are derived in Laplace domain. These transforms contain eight spectra of Fourier integrals which can be found as the solution of the system of eight complex equations arising from boundary conditions of the problem. When the spectra are known, the resulting formulas for the Laplace transforms of displacement components are obtained.The presented new formulation of non-symmetric problem enables to study the wave phenomena in general two-layered solids of strip-like geometry and it is fundamental for solving a problem with arbitrary number of layers.

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Wave motion in a thick cylindrical rod undergoing longitudinal impact

Cited by 12 publications

References 22 publications

Partitioned formulation of contact‐impact problems with stabilized contact constraints and reciprocal mass matrices

Partitioned formulation of contact‐impact problems with stabilized contact constraints and reciprocal mass matrices

Partitioned Formulation of Contact-Impact Problems With Stabilized Contact Constraints and Reciprocal Mass Matrices

Propagation of Non-Stationary Waves in Viscoelastic Strip Composed of Orthotropic Layers

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