On 3D symmetrical thermoelastic anticrack problems

• Autorzy: Kaczyński A.
• Języki publikacji: EN

Abstrakty

EN

A potential theory method is developed to solve a symmetrical thermoelastic problem of a cooling temperature field applied over the faces of a rigid sheet-like inclusion (an anticrack) in an elastic space. The governing boundary two-dimensional (2D) singular integral equations for an arbitrarily shaped anticrack are derived in terms of unknown thermal shear stress jumps. As an illustration, a complete solution expressed in elementary functions to the problem of a circular rigid inclusion subjected to a uniform temperature is presented and interpreted from the point of view of fracture theory.

Słowa kluczowe

EN

three-dimensional anticrack; symmetrical temperature problem; potential theory method; thermal stress singularity

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2016
• Tom: Vol. 68, nr 2
• Strony: 99--112
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Kaczyński A.

• Faculty of Mathematics and Information Science Warsaw University of Technology Koszykowa 75 00-662 Warsaw, Poland

Bibliografia

• 1. Z.Q. Yue, A.P.S. Selvadurai, On the mechanics of a rigid disc inclusion embedded in a fluid saturated poroelastic medium, International Journal of Engineering Science, 33, 11, 1633–1662, 1995.
• 2. R.A. Chaudhuri, Three-dimensional asymptotic stress field in the vicinity of the circumference of a penny-shaped discontinuity, International Journal of Solids and Structures, 40, 13-14, 3787–3805, 2003.
• 3. H. Altenbach, J. Altenbach, W. Kissing, Mechanics of Composite Structural Elements, Springer, Berlin-Heidelberg, 2004.
• 4. H.M. Shodja, F. Ojaghnezhad, A general unified treatment of lamellar inhomogeneities, Engineering Fracture Mechanics, 74, 1499–1510, 2007.
• 5. P. Pingle, J. Sherwood, L. Gorbatikh, Properties of rigid-line inclusions as building blocks of naturally occurring composites, Composite Science and Technology, 68, 2267–2272, 2008.
• 6. T.C.T. Ting, Anisotropic Elasticity: Theory and Applications, Oxford University Press, New York, 1996.
• 7. L.T. Berezhnitskii, V.V. Panasyuk, N.G. Stashchuk, The Interaction of Rigid Linear Inclusions and Cracks in a Deformable Body, Naukova Dumka, Kiev, 1983 [in Russian].
• 8. M.K. Kassir, G.C. Sih, Mechanics of fracture, Three-Dimensional Crack Problems, Noordhoff International Publishing, Leyden, 1975.
• 9. H.S. Kit, M.V. Khay, Method of Potentials in Three-Dimensional Thermoelastic Problems of Bodies with Cracks, Naukova Dumka, Kiev, 1989 [in Russian].
• 10. A. Kaczyński, W. Kozłowski, Thermal stresses in an elastic space with a perfectly rigid flat inclusion under perpendicular heat flow, International Journal of Solids and Structures, 46, 1772–1777, 2009.
• 11. A. Kaczyński, Thermal stress analysis of a three-dimensional anticrack in a transversely isotropic solid, International Journal of Solids and Structures, 51, 2382–2389, 2014.
• 12. Z. Olesiak, I.N. Sneddon, The distribution of thermal stress in an infinite elastic solid containing a penny-shaped crack, Archive for Rational Mechanics and Analysis, 4, 238–254, 1960.
• 13. Y.M. Tsai, Thermal stress in a transversely isotropic medium containing a penny-shaped crack, Transactions of the ASME: Journal of Applied Mechanics, 50, 24–28, 1983.
• 14. W.Q. Chen, H.J. Ding, D.S. Ling, Thermoelastic field of transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution, International Journal of Solids and Structures, 41, 1, 69–83, 2004.
• 15. O.P. Niraula, B.L. Wang, A magneto-electro-elastic material with a penny-shaped crack subjected to temperature loading, Acta Mechanica, 187, 151–168, 2006.
• 16. A.L. Florence, J.N. Goodier, The linear thermoelastic problem of uniform heat flow disturbed by a penny-shaped crack, International Journal of Engineering Science, 1, 533–540, 1963.
• 17. J.R. Barber, Steady-state thermal stresses in an elastic solid containing an insulated penny-shaped crack, Journal of Strain Analyses, 10, 1, 19–24, 1975.
• 18. Y.M. Tsai, Transversely isotropic thermoelastic problem of uniform heat flow disturbed by a penny-shaped crack, Journal of Thermal Stresses, 6, 379–389, 1983.
• 19. J. Yang, X. Jin, N. Jin, A penny-shaped crack in an infinite linear transversely isotropic medium subjected to uniform anti-symmetric heat flux: closed form-solution, European Journal of Mechanics A/Solids, 47, 254–270, 2014.
• 20. M.K. Kassir, G.C. Sih, Three-dimensional thermoelastic problems of planes discontinuities or cracks in solids, [in:] W. A. Shaw, (Ed.) Developments in Theoretical and Applied Mechanics, vol. 3, Pergamon Press, London, 117–146, 1967.
• 21. M.K. Kassir, Thermal crack propagation, Transactions of the ASME: Journal of Basic Engineering, 93, 14, 643–648, 1971.
• 22. V.S. Kirilyuk, The thermoelastic equilibrium of a transversally isotropic medium with an elliptical crack under symmetric loading, International Applied Mechanics, 36, 4, 509–517, 2000.
• 23. Yu. N. Podil’chuk, Exact analytical solutions of three-dimensional static thermoelastic problems for a transversally isotropic body in curvilinear coordinate, International Applied Mechanics, 37, 6, 728–761, 2001.
• 24. A. Kaczyński, On 3D anticrack problems in a transversely isotropic solid, European Journal of Mechanics A/Solids, 43, 142–151, 2014.
• 25. W. Nowacki, Thermoelasticity, PWN and Pergamon Press, Oxford, 1986.
• 26. A. Kaczyński, Three-dimensional thermoelastic problems of interface cracks in periodic two-layered composites, Engineering Fracture Mechanics, 48, 6, 783–800, 1994.
• 27. O.D. Kellogg, Foundation of Potential Theory, Springer, Berlin, Heidelberg, 1967.
• 28. V.I. Fabrikant, Applications of Potential Theory in Mechanics: A Selection of New Results, Kluwer Academic Publishers, Dordrecht, 1989.
• 29. V.I. Fabrikant, Mixed Boundary Value Problems of Potential Theory and Their Applications in Engineering, Kluwer Academic Publishers, Dordrecht, 1991.
• 30. M. Rahman, A rigid elliptical disc-inclusion, in an elastic solid, subjected to a polynomial normal shift, Journal of Elasticity, 66, 207–235, 2002.
• 31. M. Rahman, Bonded contact of a flexible elliptical disk with a transversely isotropic half-space, International Journal of Solids and Structures, 36, 1965–1983, 1999.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.