Mathematical modelling of a disc weakened by an eccentric circular hole

• Autorzy: Bizić M. , Petrović D. , Pancić D. , Dinović Z.

Warianty tytułu

PL

Modelowanie matematyczne dysku osłabionego mimośrodowo umiejscowionym otworem kołowym

• Języki publikacji: EN

Abstrakty

EN

The task of this paper is identification of stresses in a homogeneous isotropic disc weakened with an eccentric circular hole which is loaded by pressure in the internal contour of the hole. By application of a complex variable method, the mathematical model that allows complete analytical solution of stresses of the disc is formed. The methodology can be applied for the solution of any disc weakened with an eccentric circular hole. The comparative analysis has shown a high accuracy of analytically obtained results with FEM results obtained by calculations in ANSYS 12 software package. The application of the results of this paper is of great importance for quality design and optimization of thin-walled structures of disc type weakened by a circular hole.

PL

Zadaniem podjętym w artykule jest identyfikacja stanu naprężeń w jednorodnym, izotropowym dysku osłabionymmimośrodowo umiejscowionymwycięciem kołowym, obciążonym wzdłuż brzegu wewnętrznym naciskiem. Stosując metodę zmiennej zespolonej, w pracy sformułowano matematyczny model układu, który pozwolił na uzyskanie w pełni analitycznego opisu rozkładu naprężeń w dysku. Zastosowana metodologia, zdaniem autorów, może być użyta dla dowolnego dysku z mimośrodowym otworem o kształcie koła. W pracy przeprowadzono ponadto analizę porównawczą z wynikami uzyskanymi numerycznie za pomocą metody elementów skończonych z wykorzystaniem pakietu ANSYS 12. Otrzymane rezultaty badań mogą mieć duże znaczenie praktyczne z punktu widzenia jakości projektowania i optymalizacji cienkościennych konstrukcji zawierających elementy strukturalne z kołowym wycięciem.

Słowa kluczowe

EN

modelling; disc; eccentric hole

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2012
• Tom: Vol. 50 nr 4
• Strony: 1097--1108
• Opis fizyczny: Bibliogr. 25 poz., rys.

Twórcy

autor

Bizić M.

autor

Petrović D.

autor

Pancić D.

autor

Dinović Z.

• University of Kragujevac, Faculty of Mechanical Engineering Kraljevo, Serbia,

Bibliografia

• 1. Arshadnejad S., Goshtasbi K., Aghazadeh J., 2009, Stress concentration analysis between two neighbouring circular holes under internal pressure of a non-explosive expansion material, Yerbilimleri, 30, 3, 259-270
• 2. Bakhshandeh K., Rajabi I., Rahimi F., 2008, Investigation of stress concentration factor for finite-width orthotropic rectangular plates with a circular opening using three-dimensional finite element model, Strojniski Vestnik – Jour. of Mech. Eng., 54, 2, 140-147
• 3. Batra R.C., Nie G.J., 2010, Analytical solutions for functionally graded incompressible eccentric and non-axisymmetrically loaded circular cylinders, Composite Structures, 92, 1229-1245, doi:10.1016/j.compstruct.2009.10.022
• 4. Bizic M., Petrovic D., 2011, Identification of the effects of circular hole on the stress state of homogeneous isotropic uniaxial tensioned plate, IMK-14 – Istraˇzivanje i Razvoj, 17, 3, 17-22
• 5. Bojic N., Jugovic Z., Popovic M., 2010, Impact form open when uniaxsial straining, IMK-14 – Istrazivanje i Razvoj, 16, 2, 17-22
• 6. Bower F.A., 2010, Applied Mechanics of Solids, CRC Press, Boca Raton
• 7. Chandrashekhara K., Muthanna S.K., 1978, Stress analysis of a thick plate having a circular hole under axisymmetric radial load, Archive of Applied Mechanics, 47, 1, 1-9, doi:10.1007/BF00536613
• 8. Chen K.T., Ting K., Yang W.S., 2000, Stress analysis of two-dimensional perforated plates using boundary element alternating method, Computers and Structures, 75, 5, 515-527, doi:10.1016/S0045-7949(99)00103-0
• 9. Chen P.S., Archer R.R., 1989, Stress concentration factors due to the bending of a thick plate with circular hole, Archive of Applied Mechanics, 59, 6, 401-411, doi:10.1007/BF00534307
• 10. Huan-Chun S., Ju-Yong Z., Guo-Mei Y., Ji-Zhu Z., 1987, Complex variable function method for hole shape optimization in an elastic plane, Journal of Applied Mathematics and Mechanics, 8, 2, 137-146, doi:10.1007/BF02019086
• 11. Kratochvil J., Becker W., 2011, Asymptotic analysis of stresses in an isotropic linear elastic plane or half-plane weakened by a finite number of holes, Archive of Applied Mechanics, doi:10.1007/s00419-011-0587-z
• 12. Lu J.-K., 1995, Complex Variable Methods in Plane Elasticity, World Scientific Publishing, Singapore
• 13. Mitrinovic D.S., 1981, Complex Analysis, Gradjevinska Knjiga, Belgrade
• 14. Mizushima I., Hamada M., 1983, Stress analysis around circular hole in infinite plate with rigid disk, JSME, 26, 218, 1296-1301
• 15. Muskhelishvili N.I., 1963, Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff, Groningen
• 16. Radi E., Strozzi A., 2009, Jeffery solution for an elastic disk containing a sliding eccentric circular inclusion assembled by interference fit, International Journal of Solids and Structures, 46, 4515-4526, doi:10.1016/j.ijsolstr.2009.09.016
• 17. Savin G.N., 1961, Stress Concentration Around Holes, Pergamon Press, London
• 18. Simha K.R.Y., Mohapatra S.S., 1998, Stress concentration around irregular holes using complex variable metod, Sadhana, 23, 4, 393-412
• 19. Timoshenko S., Goodier J.N., 1951, Theory of Elasticity, 2nd ed., McGraw-Hill Book Company, New York
• 20. Timoshenko S., Woinowsky-Kreiger S., 1959, Theory of Plates and Shells, 2nd ed., McGraw-Hill Book Company, New York
• 21. Troyani N., Gomes C., Sterlacci G., 2002, Theoretical stress concentration factors for short rectangular plates with centred circular holes, Journal of Mechanical Design, 124, 1, 126-128, doi:10.1115/1.1412849
• 22. Wang Q.Z., 2004, Stress concentration factors for an eccentric circular hole in a finite-width strip or in a semi-infinite plate in tension, The Journal of Strain Analysis for Engineering Design, 39, 6, 625-630, doi:10.1243/0309324042379284
• 23. Wu L., Markenscoff X., 1996, Singular stress amplification between two holes in tension, Journal of Elasticity, 44, 2, 131-144, doi:10.1007/BF00042474
• 24. Yang Q., Gao C.F., Chen W., 2010, Stress analysis of a functional graded material plate with a circular hole, Archive of Applied Mechanics, 80, 8, 895-907, doi:10.1007/s00419-009-0349-3
• 25. Zhang Y., Shen S., 2011, Influences of surface on the interaction between holes or edge, Archive of Applied Mechanics, 81, 3, 385-395, doi: 10.1007/s00419-010-0416-9