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1

Modeling and simulations for quasistatic frictional contact of a linear 2D bar

Barboteu M., Djehaf N., Shillor M., Sofonea M.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

897--910

EN

This work considers a mathematical model that describes quasistatic evolution of an elastic 2D bar that may come in frictional contact with a deformable foundation. We present the model and some of its underlying assumptions. In particular, the novelty in the model is that both vertical and horizontal motions are taken into account, which makes it especially useful when frictional contact is concerned. Contact is described with the normal compliance condition and friction with the Coulomb law of dry friction. We introduce a hybrid variational formulation of the problem and a numerical discretization based on a uniform time step and the finite element method in space. The numerical algorithm has been implemented, and we present computer simulations that illustrate the mechanical behavior of the system with emphasis on frictional aspects of the problem.

2

A Damageable Spring

Chipman J. C., Roux A., Shillor M., Sofonea M.

Machine Dynamics Research

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2011

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Vol. 35, No. 1

82-96

EN

The evolution of material damage in a nonlinear spring is modeled, analyzed, and numerically simulated. The material damage is described by a damage function whose evolution depends on the mechanical energy in the system and the damage threshold. The model is in the form of two coupled nonlinear ordinary differential equations. The existence of the unique solution is proved using arguments for evolutionary equations with maximal monotone operators, differential equations, and fixed points. The scaling properties of the model are discussed. A numerical algorithm for the problem is presented and four simulations of the system behavior depicted. In particular, the changes in the oscillations of the system as damage progresses are shown.

3

Analysis of the dependence between a temperature and working parameters of the MR damper

Bajkowski J., Bajkowski M., Grzesikiewicz W., Sofonea M., Shillor M., Zalewski R.

Mechanics / AGH University of Science and Technology

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2007

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Vol. 26, no. 4

149-155

EN

In this paper detailed description of temperature influence on MR damper working parameters has been described. Prototype of such a device and its mathematical description taking into considerations a thermal balance, have been proposed. Basing on experimental results, a connection between temperature and operating parameters of tested MR damper has been revealed.

PL

W pracy szczegółowo omówiono wpływ temperatury na charakterystyki dyssypacji energii amortyzatora wypełnionego cieczą magnetoreologiczną. Zaproponowano pewne rozwiązanie konstrukcyjne prototypowego amortyzatora MR oraz jego model matematyczny, uwzględniający bilans cieplny. Na podstawie wyników badań eksperymentalnych wykazano ścisłe powiązanie parametrów eksploatacyjnych amortyzatora MR z jego temperaturą pracy.

4

Quasistatic Problems in Contact Mechanics

Shillor M.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 1

189-204

EN

We describe some of our recent results concerning the modeling and analysis of quasistatic contact problems between a deformable body and a foundation. We concentrate mainly on frictional contact, and in some of the problems thermal effects and the wear of the contacting surfaces are also taken into account. We describe the physical processes involved, the mathematical models, their variational formulation and then present statements of our results. We conclude with a description of some unresolved problems.

5

Numerical Analysis and Simulations of Quasistatic Frictionless Contact Problems

Fernandez Garcia J. R., Han W., Shillor M., Sofonea M.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 1

205-222

EN

A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.