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This paper is concerned with the “Study of photoelasticity and a photoelastic theoretical investigation of the stress distribution in Square Blocks subjected to concentrated diagonal loads”, a thesis topic by M.M. Frocht who developed the well-known semi empirical Shear Stress Difference method. Indeed, the use of the Beltrami-Michell methodology remains quick, when complemented by photoelasticity to acquire Dirichlet’s conditions. The synergy of both methods is enhanced with the use of the finite difference method. In addition, a finite element analysis has provided results that will be a supplementary reference for validation. The results obtained have been of lower cost than those obtained by Frocht.
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Tom
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847—858
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Bibliogr. 28 poz., rys., tab.
Twórcy
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- LCGE Laboratory, USTO – Mohamed Boudiaf University of Oran, Algeria
autor
- LRTTFC Laboratory, USTO – Mohamed Boudiaf University of Oran, Algeria
autor
- Metallurgy Department, USTO – Mohamed Boudiaf University of Oran, Algeria
autor
- LRTTFC Laboratory, USTO – Mohamed Boudiaf University of Oran, Algeria
Bibliografia
- 1. Ajovalasit A., Zuccarello B., 2000, Limitation of Fourier transform photoelasticity: influence of isoclinics, Experimental Mechanics, 4, 384-392
- 2. Ajovalasit A., Barone S., Petrucci G., 1998, A review of automated methods for the collection and analysis of photoelastic data, Strain, 33, 75-91
- 3. Boresi A.P., Chong K.P., Lee J.D., 2011, Elasticity in Engineering Mechanics, 3rd Edit., John Wiley & Sons, Inc.
- 4. Collatz L., 1960, The Numerical Treatment of Differential Equations, Springer
- 5. Dahlquist G., Bjorck A., 1974, Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ
- 6. Duff I., Erisman A., Reid J., 1986, Direct Methods for Sparse Matrices, Oxford University Press, England
- 7. Fernandez M.S.-B. ` , 2011, Towards uncertainty evaluation in photoelastic measurements, Journal of Strain Analysis, 45, 275-285
- 8. Fernandez M.S-B., Alegre Calderón J.M., Bravo Diez P.M., Cuesta Se ` gura I.I., 2010, Stress-separation techniques in photoelasticity, Strain, 1, 1-17
- 9. Frocht M., 1931, A Study of Photoelasticity and a Photoelastic Theoretical Investigation of the Stress Distribution in Square Blocks Subjected to Concentrated Diagonal Loads, Dissertation Topic, Advisor Stephen Prokofyevich Timoshenko. Ph.D. Dissertation, University of Michigan, USA
- 10. Frocht M., 1941, Photoelasticity, Volume I, John Wiley & Sons, New York
- 11. Frocht M., 1948, Photoelasticity, Volume II, John Wiley & Sons, New York
- 12. Hetnarski R.B., Ignaczak J., 2011, The Mathematical Theory of Elasticity, Taylor Francis
- 13. Kuske A., 1959, Introduction of Photoelasticity (in German), Stuttgart, Wissenschaftliche Verlagsgesellschaft
- 14. Kuske A., 1971, Handbook of Photoelasticity (in German), Stuttgart: Wiss. Verl. Ges.
- 15. Kuske A., Robertson G., 1974, Photoelastic Stress Analysis, London, New York, Sydney John Wiley & Sons
- 16. Madenci E., Guven I., 2005, The Finite Element Method and Applications in Engineering Using ANSYS, Springer
- 17. Mangal S.K., Ramesh K., 1999, Use of multiple loads to extract continuous isoclinic fringes by phase-shifting, Strain, 35, 15-17
- 18. McKenney A., Greengard L., Mayo A., 1996, A fast Poisson solver for complex geometries, Journal of Computation Physics, 2, 348-355
- 19. Muskhelishvili N.I., 1975, Some Basic Problems of the Mathematical Theory of Elasticity, 4th Edit., English translation, L. Noordhoff International Publishing, Leyden
- 20. Petrucci G., 1997, Full-field automatic evaluation of an isoclinic parameter in white light, Experimental Mechanics, 37, 4, 420-426
- 21. 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
- 22. Ramesh K., 2008, Photoelasticity, Springer Handbook of Experimental Solid Mechanics, Springer Handbook of Experimental Solid Mechanics
- 23. Rezini D., 1984, Randisochromaten als ausreichende Information zur Spannungstrennung und Spannungsermittelung in der Spannungsoptik, Ph.D. Dissertation, TU-Clausthal, FR Germany
- 24. Sharafutdinov G. Z., 2012, Basic relations of photoelasticity (I. Allerton Press, Ed.), Allerton Press, Inc., 67, 1, 1-4
- 25. Shortley G. H., Weller R., 1938, The numerical solution of Laplace’s equation, Appl. Phys.
- 26. Siegmann P., Colombo C., Daz-Garrido F., Patterson E., 2011, Determination of the isoclinic map for complex photoelastic fringe patterns, Experimwntal and Applied Mechanics, 6, 79-85, Conf. Proc. of the SEM Series 17
- 27. Smith G., 1985, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford Ed., Clarendon Press
- 28. Zhang J., 1998, Fast and high accuracy multigrid solution of the three dimensional Poisson equation, Journal of Computation Physics, 2, 449-461
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Bibliografia
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