Models of dynamic contact of a 2D thermoelastic bar

• Autorzy: Shillor Meir

Identyfikatory

DOI

10.15632/jtam-pl/118310

• Języki publikacji: EN

Abstrakty

EN

This work is based on a part of the plenary lecture I gave in the PCM-CMM-2019 conference in Krakow, Poland. It presents a new mathematical model for a thermoelastic 2D bar and proposes three problems for the processes of: (i) dynamic contact of the bar with an obstacle below it; (ii) vibrations of the right end between two stops; and (iii) debonding of two bars because of vibrations, humidity and thermal effects. The models are new and questions of existence of weak solutions, analysis of the solutions, effective numerical methods and simulations, as well as possible control, are unresolved yet.

Słowa kluczowe

EN

2D bar; dynamic contact; Barber’s heat exchange condition; debonding; humidity diffusion

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2020
• Tom: Vol. 58 nr 2
• Strony: 295--305
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Shillor Meir

• Oakland University, Department of Mathematics and Statistics, Rochester, Michigan, USA

Bibliografia

• 1. Ahn J., Kuttler K.L., Shillor M., 2012, Dynamic contact of two Gao beams, Electronic Journal of Differential Equations, 2012, 194, 1-42.
• 2. Andrews K.T., M’Bengue M.F., Shillor M., 2009, Vibrations of a nonlinear dynamic beam between two stops, Discrete and Continuous Dynamical System, DCDS-B, 12, 1, 23-38.
• 3. Andrews K.T., Shi P., Shillor M., Wright S., 1993, Thermoelastic contact with Barber’s heat exchange condition, Applied Mathematics and Optimization, 28, 1, 11-48.
• 4. Barboteu M., Djehaf N., Shillor M., Sofonea M., 2017, Modeling and simulations for quasistatic frictional contact of a linear 2D bar, Journal of Theoretical and Applied Mechanics, 55, 3, 897-910.
• 5. Dumont Y., Kuttler K.L., Shillor N., 2003, Analysis and simulations of vibrations of a beam with a slider, Journal of Engineering Mathematics, 47, 1, 61-82.
• 6. Duvaut G., Lions J.L., 1976, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin.
• 7. Eck C., Jarusek J., Krbec M., 2005, Unilateral Contact Problems: Variational Methods and Existence Theorems, CRC Press, Taylor & Francis Group, ISBN: 9780429121210.
• 8. Frémond M., 2002, Non-Smooth Thermomechanics, Springer.
• 9. Gao D.Y., 1998, Bi-complementarity and duality: A framework in nonlinear equilibria with applications to the contact problems of elastoplastic beam theory, Journal of Mathematical Analysis and Applications, 221, 2, 672-697.
• 10. Gao D.Y., Russell D.L., 1994, A finite element approach to optimal control of a ‘smart’ beam, [In:] International Conference on Computational Methods in Structural and Geotechnical Engineering, P.K.K. Lee, L.G. Tham and Y.K. Cheung (Eds.), Hong Kong, 135-140.
• 11. Han W., Sofonea M., 2002, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, Studies in Advanced Mathematics, AMS, Providence, RI and International Press, Somerville, MA.
• 12. Kuttler K.L., Park A., Shillor M., Zhang W., 2001, Unilateral dynamic contact of two beams, Mathematical and Computer Modelling, 34, 3-4, 365-384.
• 13. Kuttler K.L., Shillor M., 2001, Vibrations of a beam between two stops, Dynamics of Continuous, Discrete and Impulsive Systems, 8, 1, 93-110.
• 14. Kuttler K.L., Kruk S., Marcinek P., Shillor M., 2017, Modeling, analysis and simulations of debonding of bonded rod-beam system caused by humidity and thermal effects, Electronic Journal of Differential Equations, 2017, 301, 1-42.
• 15. Martins J.A.C., Oden J.T., 1983, A numerical analysis of a class of problems in elastodynamics with friction, Computer Methods in Applied Mechanics and Engineering, 40, 3, 327-360.
• 16. Migórski S., Ochal A., Shillor M., Sofonea M., 2018, Nonsmooth dynamic frictional contact of a thermoviscoelastic body, [In the special issue:] Mathematical Analysis of Unilateral and Related Contact Problems, L. Paoli and M. Shillor M. (Eds.), Applicable Analysis, 97, 8, 1228-1245.
• 17. Migórski S., Ochal A., Sofonea M., 2013, Nonlinear Inclusions and Hemivariational Inequalities, Advances in Mechanics and Mathematics, Vol. 26, Springer, New York.
• 18. Paoli L., Shillor M., 2018, Vibrations of a beam between two rigid stops: vector valued measures solutions, [In the special issue:] Mathematical Analysis of Unilateral and Related Contact Problems, L. Paoli and M. Shillor M. (Eds.), Applicable Analysis, 97, 8, 1299-1314.
• 19. Schatzman M., Bercovier M., 1989, Numerical approximation of a wave equation with unilateral constraints, Mathematics of Computation, 53, 187, 55-79.
• 20. Shillor M., 2017, Models of debonding caused by vibrations, heat and humidity, [Chapter 15 in:] Mathematical Modelling in Mechanics, Advanced Structured Materials, 69, F. dell’Isola, M. Sofonea and D. Steigmann (Eds.), Springer, Singapore, 233-250.
• 21. Shillor M., Sofonea M., Telega J.J., 2004, Models and Analysis of Quasistatic Contact, Springer, Berlin.
• 22. Sofonea M., Han W., Shillor M., 2006, Analysis and Approximations of Contact Problems with Adhesion or Damage, Pure and Applied Mathematics, Chapman & Hall/CRC Press, Boca Raton, Florida.
• 23. Sofonea M., Shillor M., 2018, Model and analysis for quasistatic frictional contact of a 2D elastic bar, Electronic Journal of Differential Equations, 2018, 107, 1-19.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).