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Numerical Simulation of Buckling of Thin Cylindrical Shells

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- 1. Numerical Simulation of Buckling of Thin Cylindrical Shells Master of Technology (M.Tech) in Structural Engineering By Khaja misba uddin oct 1st, 2013 Department of Civil Engineering JNTUH College of Engineering, Kukatpally, Hyderabad
- 2. Outline of the Presentation • • • • • • • • • • • Introduction Importance Literature Review Lacuna in the field Present work Numerical modeling and analysis Results Conclusions Scope for future work References Acknowledgement
- 3. Introduction It is well known that thin walled cylinders are proven efficient structures with a variety of applications in - construction - chemical & - aero-space industry.
- 4. The strength of these structures is limited to their buckling strength when subjected to axial compressive loads and external pressures. Failure of these thin cylindrical shells under buckling loads is a matter of concern for engineers, while predicting the reliability of these structures.
- 5. Definition -Thin Shells If the wall thickness of the shell is less that 10% of the diameter of the shell then it can be treated a thin shell. When the shell is subjected to internal Pressure the stresses developed are assumed to be uniform throughout the wall thickness.
- 6. Importance Knowledge of - Stress distribution - Vibration Pattern - Buckling Behaviour is very important in the design of thin cylindrical shells.
- 7. Thin cylinder subjected to external pressure (Vacuum inside the cylinder)
- 8. Literature Review There are several research papers and technical reports published in this field. Euler’s research in 18th century gave birth to classical theory of buckling. Successful applications of a variety of the structures is well documented in Theory of Elastic Stability by Timoshenko and Gere.
- 9. A very pertinent literature survey has been conducted in this field. Certain gaps are identified in the open published literature. Some of these gaps are detailed hereunder.
- 10. According to the classical theory of buckling, for axially-loaded thin cylindrical shells, buckling stress is directly proportional to the wall thickness ‘t’, other things being equal. t σ cr = 2 3(1 − υ ) R E Where, “σ” is critical compressive stress, “E” is Young’s modulus, “υ” is Poisson ratio of isotropic material, “t” is the uniform thickness and “R” is the radius of the shell.
- 11. However, from the experimental investigations of the several researchers the empirical data show clearly that the buckling stress is actually proportional to t1.5, other things being equal. 1.5 σ mean t = 5 E R
- 12. Lacuna in the Field It is well known that there is wide scatter in the buckling-stress data, ranging from one half to twice the mean value. Current theories of shell buckling attribute both the scatter and the low buckling stress – in comparison with the classical – to “imperfectionsensitive”, non-linear structural behaviour. All those theories considered classical shell theory as their ideal reference and treated as perfect.
- 13. Present Work The present work deals with the investigation of 1. The stress distribution – Static Analysis 2. Buckling Behaviour using FEM when thin cylindrical shells are subjected to axial compressive loads and external pressures.
- 14. NUMERICAL MODELING AND ANALYSIS A complete ABAQUS analysis flow chart usually consists of three distinct stages: 1) Preprocessing, 2) Simulation, 3) Post-Processing. These three stages are linked together by the corresponding files.
- 15. FLOW CHART
- 16. MODELING AND MESHING
- 17. MESHING (Four node shell element)
- 18. Applying loads and boundary conditions
- 19. RESULTS AND DISCUSSIONS
- 20. Buckling pattern of thin walled (0.1mm) cylindrical shell subjected to axial compression
- 21. Stress distribution in thin cylinder (0.3mm) subjected to axial compression.
- 22. DEFORMATION PATTERN OF THIN WALLED SHORT CYLINDRICAL SHELL SUBJECTED TO EXTERNAL PRESSURE
- 23. Buckling pattern of thin cylindrical shell subjected to external pressure
- 24. Deformed shape of the cylindrical shell under axial compression
- 25. Deformed shape of the cylindrical shell
- 26. Deformed shape of the cylindrical shell
- 27. Deformed shape of the cylindrical shell
- 28. Deformed shape of the cylindrical shell
- 29. Shell subjected to axial compression of 100 N and varying the thickness of the shell the buckling load is calculated. Length in mm Thickness mm Radius mm Eigen value for Mode 1 Buckling Load in N 6000 0.1 500 31.592 3159.2 6000 0.3 500 237.24 23724 6000 0.5 500 618.9 61890
- 30. CONCLUSIONS The following are the important conclusions drawn from the present study on numerical simulation of buckling of thin cylindrical shells. During buckling, half sine waves will be formed along the generator and along the circumference. The number of half sine waves formed along the generator and along the circumference are independent of the length of the cylindrical shell. The number of half sine waves formed along the generator and along the circumference are dependent on the radius and thickness of the shell.
- 31. SCOPE FOR FUTURE WORK As an extension to the present work: A number of variations of the problem specifications can be tried with the available soft wares in estimating the critical buckling loads. There is always a need for the experimental data to be generated to validate the numerical results. In these endeavors an experimental test facility can be built with data acquisition and recording systems.
- 32. There is a wide scope to further investigate the effect of geometric nonlinearity and material nonlinearity on the critical buckling loads. Buckling of thin shells, made of functionally graded materials, subjected to internal/ external loads. Vibration behaviour and impact resistance of thin cylindrical shells.
- 33. References 1. 2. 3. 4. Euler, L., 1744. Methodus inveniend lincas curves maxim: minimive proprietate gaudentes (Appendix, de curvis elastics). Marcum Michaelem Bousquet, Lausanne and Geneva. Timoshenko SP, Gerri JM. Theory of elastic stability, 2nd ed. New York: McGraw-Hill, 1961 Von Karman, T., Dunn, L.G., Tsien, H., 1940. The influence of curvature on the buckling characteristics of structures. Journal of the Aeronautical Sciences 7, 276289.. Koiter WT. On the stability of elastic equilibrium (in Dutch with English summary). Ph.D. thesis, Delft, H.J. Paris, Amsterdam, 1945. Air Force Dynamics Laboratory, Technical Report, AFFDL-TR-70-25, Ohio, February 1970(English translation)
- 34. 5. 6. 7. 8. 9. Arbocz., J., 1974. The effect of initial imperfections on shell stability. In: Fung, Y.C., Sechler, E.E. (Eds), thin shell structures. Abramovich H, Singer J, Weller T. The influence of initial imperfections on the buckling of stiffened cylindrical shells under combined loading. In: Jullian JF, editor. Buckling of shell structures on land, in the sea, and on the air. London: Elsevier Applied Science, 1991.p. 205-45. Yamaki, N., 1984. Elastic Stability of Circular Cylindrical Shells. North – Holland, Amsterdam. Heyman J. Equilibrium of shell structures. Oxford: Clarendon Press, 1977 Lancaster, E.R., Calladine, C.R., Palmer S.C., 1998. Experimental observations on the buckling of a thin cylindrical shell subjected to axial compression. International Journal of Mechanical Sciences.
- 35. 10. 11. 12. 13. T.D. Park and S.Kyriakides, “On the collapse of dented cylinders under external pressure”, Int.J.Mech.Sci. v.38, No.5, pp. 557-558 (1996) Y. Bai, R.T.Igland, T.Moan, “Tube Collapse Under Combined External Pressure, Tension and Bending”, Marine Structures, v.10, 389-410 (1997) G.Forasassi, R.Lo Frano., “Buckling of imperfect thin cylindrical shells under lateral pressure”, Journal of Achievements in Materials and Manufacturing Engineering, pp287-290, Vol.18, Issue 1-2, September – October 2006. R.Lo Frano and G.Forasassi,., “Buckling of imperfect thin cylindrical shells under lateral pressure”, Journal of Achievements in Materials and Manufacturing Engineering, pp1-8, Vol.20, 2008.
- 36. ACKNOWLEDGEMENT I profusely thank Dr. N. V. Ramana Rao, PRINCIPAL & PROFESSOR, JNTUH College of Engineering, Kukatpally, Hyderabad, for his valuable guidance and constant inspiration at every stage of this dissertation. I sincerely thank for supporting my work. I am indebted to Dr. M.V. Seshagiri Rao, the Head of the Department of Civil Engineering for his valuable suggestions and co-operation during the entire period of work, without whom, this project could not have been completed.
- 37. I would like to express my gratitude to the then Head of the Department of Civil Engineering Dr. G. K. Viswanadh, for his support in a number of ways to M.Tech Program in the department during the entire period of my course. I sincerely express my thanks to all the faculty members of Civil Engineering Department who all helped me at different stages of my M.Tech course work and project work.
- 38. I would like to sincerely thank all my classmates who made my stay in JNTUH College of Engineering, really a memorable one. V.L.S. BANU
- 39. Thank You

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