On the first boundary value problem of the photoelastic thin ring

• Autorzy: Rezini D. , Tamine T.

Warianty tytułu

PL

Wyznaczanie pierwszej wartości brzegowej w zagadnieniu fotoelastyczności cienkiego pierścienia

• Języki publikacji: EN

Abstrakty

EN

Analytical solutions to the piane problems in terms of stresses for thin annular domains under compression loading are well known in several papers. Moreover, the large majority of the two-dimensional problems in the theory of elasticity are reducible to the solution of their boundary value problems. The two-dimensional photoelasticity methods easily provide the stress tensor components on the boundary, from one photograph only. The Beltrami-Michell equations with the Dirichlet photoelastic data state a well-posed hybrid problem in stress terms. It has been shown that the results obtained from the hybrid method developed in this paper, are applicable to any irregular shaped photoelastic domain of interest. Successful results have been obtained for more complicated forms and loads. The correctness of the results for the circular ring is confirmed and will be discussed in details.

PL

Analityczne rozważania płaskiego stanu naprężeń w cienkich strukturach pierścieniowych poddanych obciążeniu ściskającemu są szeroko znane w literaturze. Co więcej, większość przypadków tego typu zagadnień teorii sprężystości daje się zredukować do problemu wyznaczania wartości własnych zagadnienia brzegowego. Metody dwuwymiarowej fotoelastyczności umożliwiają łatwą identyfikację składowych tensora naprężeń na brzegu elementu w oparciu o pojedynczą fotografię. Równania Beltramiego-Michella warz i parametrami fotoelastyczności Dirichleta pozwalają poprawnie sformułować hybrydowy model badanego układu w kontekście poszukiwanych naprężeń. W pracy wykazano, że taki model jest stosowalny do dowolnie nieregularnego kształtu próbki. Otrzymano bardzo dobre wyniki dla elementów o skomplikowanym obrysie i poddanych złożonemu stanowi obciążenia. W szczegółowej analizie potwierdzono dokładność rezultatów dla pierścienia kołowego.

Słowa kluczowe

EN

photoelasticity; Beltrami-Michell eąuation; annulus

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2013
• Tom: Vol. 51 nr 1
• Strony: 131--141
• Opis fizyczny: Bibliogr. 35 poz., rys.

Twórcy

autor

Rezini D.

• University of UST-MB Oran, Faculty of Mechanical Engineering, Laboratoire LCGE, Algeria

autor

Tamine T.

• University of UST-MB Oran, Faculty of Mechanical Engineering, Laboratoire LCGE, Algeria

Bibliografia

• 1. Boresi A.P., Chong A.P., Lee J.D., 2011, Elasticity in Engineering Mechanics, 3rd Ed., John Wiley and Sons, Inc.
• 2. Doyle J.F., 2004, Modern experimental stress Analysis, John Wiley and Sons Ltd.
• 3. Fern´andez M.S-B., 2011, Towards uncertainty evaluation in photoelastic measurements, J. Strain Analysis, 45, 275-285
• 4. Fern´andez M.S-B., Alegre Calderón J.M., Bravo Diez P.M., Cuesta Segura I.I., 2010, Stress-separation techniques in photoelasticity: a review, Strain, 1, 1-17
• 5. Filon L.N.G., 1924, The stresses in a circular ring, Inst. Civil Eng. London: Selected Engineer. Papers, 1, 12, 4-26
• 6. Frocht M.M., 1948, Photoelasticity, Vol. II, John Wiley and Sons, New York
• 7. Gao S., 2010, In-Plane Stress Analysis using Tensor Field Photoelasticity, Thesis, University of British Columbia, Vancouver
• 8. Gerlach H.-D., 1968, Eleklronische Hilfsmittel zur Automalisierung spannungsoptischer Messungen (Electronic Aids for the Automation of Photoelastic Measurements), Doctoral thesis, University of Karlsruhe, FR Germany
• 9. Hetnarski R.B., Ignaczak J., 2011, The Mathematical Theory of Elasticity, Taylor Francis
• 10. Jacob K.A., 1978, Experimental numerical hybrid technique for stress analysis, VDI-Berichte, 335, 335-341
• 11. Kuske A., 1979, Separation of principal stresses in photoelasticity by means of a computer, Strain, 2, 43-49
• 12. Mahfuz H., Caser O., Wong T.-L., 1990, Hybrid stress analysis by digitized photoelastic data and numerical methods, Experimental Mechanics, 2, 90-194
• 13. McKenney A., Greengard L., Mayo A., 1996, A fast Poisson solver for complex geometries, Journal of Computation Physics, 2, 348-355
• 14. Muskhelishvili N.I., 1975, Some Basic Problems of the Mathematical Theory of Elasticity, 4th Ed. English translation, Noordhoff International Publishing, Leyden
• 15. Navneet Kumar L., Khobragade N.W., 2011, Analysis of thermal stresses and displacement in a thick annular disc, Int. J. of Latest Trends in Mathematics, 2, 1, 39-46
• 16. Nomura Y., Pinit P., Umezaki E., 2008, Digital simulation of a circular ring loaded by a diametric compression for photoelastic analysis, Journal of JSEM, 8, Special Issue 83-87
• 17. Nurse P., Allison I.M., 1972, Automatic acquisition of photoelastic data, J.B.C.S.A. Conference
• 18. Pinit P., 2007, Automated detection of singularities from orientation map of isoclinics in Digital photoelasticity, 21st Conf.of Mech. Eng., Chonburi, Thailand
• 19. Pinit P., Umezaki E., 2005, Full-field determination of principal-stress directions using photoelasticity with plane polarized RGB lights, Optical Review, 12, 3, 228-232
• 20. Pinit P., Umezaki E., 2007, Digitally whole field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique, Optics and Lasers in Engineering, 45, 7, 795-807
• 21. Ramesh K., 2000, Digital Photoelasticity: Advanced Techniques and Applications, Springer
• 22. Ramesh K., Kasimayan T., Simon B.N., 2011, Digital photoelasticity – A comprehensive review, Journal of Strain Analysis for Engineering Design, 46, 245-266
• 23. Redner S., 1974, New automatic polariscope system, Experimental Mechanics, 14, 12, 486-491
• 24. Rezini D., 1984, Randisochromaten als ausreichende Information zur Spannungstrennung und Spannungsermittlung, Doctoral thesis, Tech. University of Clausthal (TUC), FR Germany
• 25. Sangdong Kim, Soyoung Ahn, Philsu Kim, 2011, Local boundary element based a new finie difference representation for Poisson equations, Applied Mathematics and Computation, 217, 12, 5186-5198
• 26. Sciammarella C.A., Gilbert J.A., 1973, Strain analysis of a disk subjected to diametral compression by means of holographic interferometry, Applied Optics, 8, 12, 1951-1956
• 27. Segerlind L.J., 1971, Stress-difference elasticity and its application to photomechanics, Experimental Mechanics, 11, 440-445
• 28. Shortley G.H., Weller R., 1938, The numerical solution of Laplace’s equation, Appl. Phys.
• 29. Timoshenko S.P., Goodier J.N., 1970, Theory of Elasticity, 3-rd Ed., New York, Mc-Graw Hill
• 30. Tokovyy Yu.V., Hung K.-M., Ma C.-C., 2010, Determination of stresses and displacements in a thin annular disk subjected to diametral compression, J. of Math. Sciences, 3, 342-354
• 31. Ugural A.C., Fenster S.K., 2011, Advanced Mechanics of Materials and Applied Elasticity, 5-th Ed., Prentice Hall
• 32. Wolf H., 1976, Spannungsoptik, Band 1 Grundlagen. Zweite Auflage, Springer
• 33. Zhang Dongsheng, Min Maa, Dwayne D. Arola., 2002, Fringe skeletonizing using an improved derivative sign binary method, Optics and Lasers in Eng., 37, 51-62
• 34. Zhang Dongsheng, Yongsheng Han, Bao Zhang, Dwayne Arola, 2007, Automatic determination of parameters in photoelasticity, Optics and Lasers in Eng., 45, 860-867
• 35. Zhang J., 1998, Fast and high accuracy multigrid solution of the three dimensional Poisson equation, Journal of Computation Physics, 2, 449-461