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Finite element analysis is carried out for cylindrical shells with large openings subjected to axial tension. By utilizing a parametric study, the paper investigates the effect of the opening, on the stresses in cylindrical shells. It has been found that any increase in (a/R) ratio has produced a correspondent increase in the stress concentration factor. This is particularly true for higher values of curvature parameter. Comparing with analytical solutions are also made and the overall agreement between the two sets of results is reasonably good.
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Presentation 1
- 1. FINITE ELEMENT ANALYSIS OF LARGE OPENINGS IN CYLINDRICAL SHELLS T.MAHDI Building and Housing Research Centre, Tehran, Iran
- 2. Content Introduction Verification of the results Shells with small circular openings Shells with small and large elliptical openings Shells with large openings Shells with reinforced openings Conclusion
- 3. Introduction
- 6. Analytical Work on Shells with Small Openings Lure (1946) Savin (1961) Lekkerkerker (1965) Van Dyke (1965) Tsai & Sanders (1975)
- 8. Analytical Work on Shells with Large Openings Mizooguchi et al. (1972) Steele et al. (1986) Mokhtarian & Endicott (1991) Xue et al. (1991) Xue et al. (1996)
- 9. Verification of the results SHELLS WITH SMALL CIRCULAR OPENINGS
- 14. curvature parameter SCF present Tsai & Sanders Van Dyke
- 15. Bending stresses are negligible compared with membrane ones. Any increase in () has a correspondent increase in the S.C.F. Shells with <1
- 16. For between 2 and 8 The perturbed stresses die within a shallow region of the shell. Any increase in () has a a correspondent increase in the S.C.F. Bending stresses become more important but membrane ones remain dominant. The stress concentration factors (S.C.F.) obtained by the finite element method show excellent agreements with those obtained by the shallow shell theory.
- 17. Verification of the results SHELLS WITH ELLIPTICAL OPENINGS
- 18. Models used Model No. R (cm) h (cm) b (cm) a (cm) b/a SH 2510 100 2.5 10 10.02 ≈1 0.57 SH 2520 100 2.5 20 20.14 0.99 1.15 SH 2530 100 2.5 30 30.47 0.98 1.74 SH 2540 100 2.5 40 41.15 0.97 2.35 SH 2550 100 2.5 50 52.36 0.95 2.99 SH 2560 100 2.5 60 64.35 0.93 3.68 SH 2570 100 2.5 70 77.54 0.90 4.43
- 19. . . . . . . . . a/R SCF finite element Xue et al.-elliptical Xue et al.-circular
- 20. Tangential membrane stresses around the opening (SH2540 model) - Angle SCF
- 21. Tangential bending stresses around the opening (SH2540 model) - - . - - . . . Angle SCF
- 22. RESULTS For Small Openings The finite element method predicts higher stresses than those given by Xue etal. (1991). For Medium Openings The finite element results show excellent agreements with those obtained by Xue etal. (1991). For Large Openings The differences with the shallow shell theory are found within the order of (a2/R2) expected by Lekkerkerker (1965) and the results are quite comparable with Xue etal. (1991).
- 23. Shells with large openings Parametric Study
- 34. Any increase in the radius of the opening produces a correspondent increase in the S.C.F. Any increase in (a/R) ratio has a direct effect on the increase of the relative size of zones of high stresses GENERAL CONCLUSION
- 36. Geometrical properties of Group # 1 Radius of the shell 100cm. Radius of the opening 10 cm. Width of the reinforced zone 0.5172 cm Curvature parameter 6
- 37. Models of group # 1 Thickness of the reinforced zone compared to the thickness of the cylinder % reinforcements 1 0 3 23.5 5 47 7 70.5 10 105.75
- 38. 0 2 4 6 8 10 0 10 20 30 40 50 60 70 80 90 10 0 11 0 % reinforcement SCF membrane bending total
- 39. Geometrical properties of Group # 2 Radius of the shell 100cm. Radius of the opening 10 cm. Width of the reinforced zone 1.428 cm. Curvature parameter 6
- 40. Models of group # 2 Thickness of the reinforced zone compared to the thickness of the cylinder % reinforcements 1 0 1.768 23.5 2.536 47 3.304 70.5 4.456 105.75
- 41. Comparsion of models group #1 & group #2
- 42. Geometrical properties of Group # 3 (Thickness of reinforced zone = 4 times the thickness of the shell) Radius of the shell 100cm. Radius of the opening 50 cm. Curvature parameter 6
- 43. Models of group # 3 % reinforcement Width of the reinforced zone (cm.) 0.0 - 26.61 2.17 68.7 5.43 136.62 10.33 249.35 17.66 442.49 28.66
- 44. 0 3 6 9 12 15 0 100 200 300 400 500 % reinforcements SCF membrane bending total
- 45. CONCLUSION The use of reinforcements for large openings is found less effective in reducing stresses By using reinforcement in the immediate area near the opening, the membrane stresses are reduced dramatically