Contact problem for periodically stratified half-space and rigid foundation possessing geometrical surface defect

• Autorzy: Kaczyński A. , Monastyrskyy B.

Warianty tytułu

PL

Zagadnienie kontaktowe dla periodycznie uwarstwionej półprzestrzeni i sztywnego podłoża z geometrycznym defektem powierzchniowym

• Języki publikacji: EN

Abstrakty

EN

A three-dimensional problem of frictionless contact interaction of a periodic two-layered elastic half-space and a rigid foudation with a local sloping surface recess is examined. The analysis is performed within the framework of a homogenized model with microlocal parameters. By constructing appropriate harmonic functions, the resulting boundary-value problem is reducet to some mixed problem of the potential theory. In dealing with its solution, the integro-differential singular equation of Newton's potential type for the function of gap height is obtained. To determine the unknown region of the gap the condition of smooth running of its faces is used. As an example, a certain form of the initial defect is considered and in this case the solution of the equation is found analytically by using an analogue of Dyson's theorem.

PL

W pracy rozważono trójwymiarowe zagadnienie ściskania prowadzące do jednostronnego kontaktu bez tarcia periodycznie dwuwarstwowej półprzestrzeni sprężystej ze sztywnym podłożem zawierającym lokalny defekt (gładkie niewielkie wgłębienie). Zastosowano przybliżone podejście opata na zhomogenizowanym modelu z parametrami lokalnymi. Wynikające zagadnienie brzegowe sformułowano w postaci mieszanego problemu teorii potencjału, który sprowadzono do osobliwego równania całkowo-różniczkowego na głębokość defektu z nieznaną powierzchnią kontaktu. Dla szczególnego kształtu wgłębienia uzyskano jego rozwiązanie z użyciem analogu twierdzenia Dysona.

Słowa kluczowe

EN

periodic two-layered half-space; local surface defect; singular integro-differential equation

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2002
• Tom: Vol. 40 nr 4
• Strony: 985--999
• Opis fizyczny: Bibliogr. 20 poz., rys.

Twórcy

autor

Kaczyński A.

• Faculty of Mathematics and Information Sciences, Warsaw University of Technology

autor

Monastyrskyy B.

• Pidstryhacli Institute for Applied Problems of Meckanics and Mathematics, NASU, Lviv, Ukraine

Bibliografia

• 1. BAKHVALOV N.S., PANASENKO G.P., 1984, Processes Averaging in Periodic Media (in Russian), Nauka, Moscov
• 2. BENSOUSSAN A., LIONS J.L., PAPANICOLAU G., 1978, Asymptotic Analysis for Periodic Systems, North Holland, Amsterdam
• 3. CHRISTENSEN R.M., 1979, Mechanics of Composite Materials, John Wiley and Sons., New York
• 4. JOHNSON K.L., 1985, Contact Mechanics, Cambridge University Press, Cambridge
• 5. KACZYŃSKI A., 1993, On the three-dimcnsional interface crack problems in periodic two-layered composites, Int. J. Fracture, 62, 283-306
• 6. KACZYŃSKI A., 1994, Three-dimensional thermoelastie problems of interface cracks in periodic two-layered composites, Engng Fract. Mech., 48, 783-800
• 7. KACZYŃSKI A., MATYSIAK S.J., 1988, On crack problems in periodic two-layered elastic composites, Int. J. Fracture, 37, 31-45
• 8. KACZYŃSKI A., MATYSIAK S.J., 1994, Analysis of stress intensity factors in crack problems of periodic two-layered elastic composites, Acta Mech., 107, 1-16
• 9. KACZYŃSKI A., MATYSIAK S.J., PAUK V.I., 1994, Griffith crack in laminatcd elastic layer, Int.. J. Fracture, 67, R81-R86
• 10. KIIAY M.V., 1993, Two-Dimensional Integral Eqtiations of Newton's Potentials Type and Its Applications (in Russian), Naukova Dumka, Kiev
• 11. KIT H.S., MARTYNYAK R.M., MONASTYRSKYY B.YE., 2001, Potentials method in problems of local contact absence (in Ukrainian), Visn. Dnipr. Univ., (in press)
• 12. KIT H.S., MONASTYRSKYY B.YE., 1998, Contact problem for a half-space and rigid substrate with axisymmetrical recess (in Ukrainian), Mathematical Methods and Physicomechanical Fields, 41, 4, 7-11
• 13. MARTYNYAK R.M., 1985, Intcraction of elastie bodies provided imperfect mechanical contact (in Ukrainian), Mathematical Methods and Physicomechanical Fields, 22, 89-92
• 14. MARTYNYAK R.M., 2000. Method of functions of intercontact gaps in problcms of local separation of elastic half-spaces (in Ukrainian), Mathematical Methods and Physicomechanical Fields, 43, 1, 109-114
• 15. MATYSIAK S.J., 1995, On the microlocal parameter method in modelling of pcriodically laycred thermoelastic composites, .J. Theor. Appl. Mech., 33, 2, 481-487
• 16. MATYSIAK S.J., WOŹNIAK C, 1988, On the microlocal modelling of thermoelastic periodic composites, J. Tech. Phys., 29, 85-97
• 17. MONASTYRSKYY B.YE., 1999, Axially symmetric contact problem for half-spaces with geometrically disturbed surface, J. Materiał ScL, 35, 6, 777-782
• 18. SHVETS R.M., MARTYNYAK R.M., 1995, Integral equations of thermoelasticity contact problems for rough bodies (in Ukrainian), Dop. AN URSR, A, 11, 59-63
• 19. SHVETS R.M., MARTYNYAK R.M., KRYSHTAFOVYCH A.A., 1996, Discontinuous contact. of anisotropic half-plane and a rigid base with disturbed surface, Int. J. Engng ScL, 34, 184-200
• 20. WOŹNIAK C, 1987, A nonstandard method of modelling of thermoelastic periodic composites, Int. J. Engng ScL, 25, 483-499