Modelling of Random Geometrical Imperfections and Reliability Calculations for Thin Cylindrical Shell Subjected to Lateral Pressure

Document Type : Research Paper


1 Department of Mechanical Engineering, Pondicherry Engineering College, Pillaichavady Puducherry, India

2 Department of Mechanical Engineering , Pondicherry Engineering College, Pondicherry



It is well known that it is very difficult to manufacture perfect thin cylindrical shell. Initial geometrical imperfections existing in the shell structure is one of the main determining factor for load bearing capacity of thin cylindrical shell under uniform lateral pressure. As these imperfections are random, the strength of same size cylindrical shell will also random and a statistical method can be preferred to find the allowable load of these shell structures and therefore a In this work the cylindrical shell of size R/t = 228, L/R = 2 and t=1mm is taken for study. The random geometrical imperfections are modeled by linearly adding the first 10 eigen mode shapes using 2kfullfactorial design matrix of DoE. By adopting this method 1024 FE random imperfect cylindrical shell models are generated with tolerance limit of ± 1 mm. Nonlinear static FE analysis of ANSYS is used to find the buckling strength of these 1024 models. FE results of 1024 models are used to predict the reliability based on MVFOSM method.


Main Subjects

[1] Prabu B., Rathinam N., Srinivasan R., Naarayen K.A.S., 2009, Finite element analysis of buckling of thin cylindrical shell subjected to uniform external pressure, Journal of Solid Mechanics 2(2): 148-158.
[2] Rathinam N., Prabu B., 2015, Numerical study on influence of dent parameters on critical buckling pressure of thin cylindrical shell subjected to uniform lateral pressure, Thin Walled Structures 88: 1-15.
[3] Ranganathan R., 2000, Structural Reliability: Analysis & Design, Jaico Publishing House, New Delhi, India.
[4] Caitriona de P., Kevin C., James P. G., Denis K., 2012, Statistical characterisation and modelling of random geometric imperfections in cylindrical shells, Thin Walled Structures 58: 9-17.
[5] Sadovsky Z., Teixeira A.P., Guedes Soares C., 2005, Degradation of the compressive strength of rectangular plates due to initial deflections, Thin-Walled Structures 43: 65-82.
[6] Sadovsky Z., Teixeira A.P., Guedes Soares C., 2006, Degradation of the compressive strength of square plates due to initial deflections, Journal of Constructional Steel Research 62: 369-377.
[7] Athiannan K., Palaninathan R., 2004, Experimental investigations of buckling of cylindrical shells under axial compression and transverse shear, Sadhana 29: 93-115.
[8] Singer J., 1999, On the importance of shell buckling experiment, Journal of Applied Mechanics Review 52(6): 17-25.
[9] Schneider M.H. Jr., 1996, Investigation of stability of imperfect cylinders using structural models, Engineering Structures 18(10): 792-800.
[10] Arbocz J., Hol J.M.A.M., 1991, Collapse of axially compressed cylindrical shells with random imperfections, AIAA Journal 29(12): 2247-2256.
[11] Kirkpatrick S.W., Holmes B.S., 1989, Axial buckling of a thin cylindrical shell: Experiments and calcualtions, Computational Experiments 176: 67-74.
[12] Featherston C.A., 2003, Imperfection sensitivity of curved panels under combined compression and shear, International Journal of Non-Linear Mechanics 38: 225-238.
[13] Kim S.-E., Kim Ch.-S., 2002, Buckling strength of the cylindrical shell and tank subjected to axially compressive loads, Thin-Walled Structures 40: 329-353.
[14] Khelil A., 2002, Buckling of steel shells subjected to non-uniform axial and pressure loadings, Thin-Walled Structures 40: 955-970.
[15] Teng J.G., Song C.Y., 2001, Numerical models for nonlinear analysis of elastic shells with eigen mode-affine imperfections, International Journal of Solids and Structure 38: 3263-3280.
[16] Ikeda K., Kitada T., Matsumura M., Yamakawa Y., 2007, Imperfection sensitivity and ultimate buckling strength of elastic-plastic square plates under compression, International Journal of Non-Linear Mechanics 42: 529-541.
[17] Khamlichi A., Bezzazi M., Limam A., 2004, Buckling of elastic cylindrical shells considering the effect of localized axisymmetric imperfections, Thin-Walled Structures 42: 1035-1047.
[18] Pircher M., Berry P.A., Ding X., Bridge R.Q., 2001, The shape of circumferential weld-induced imperfections in thin walled steel silos and tanks, Thin-Walled Structures 39(12): 999-1014.
[19] Chrysanthopoulos M.K., 1998, Probabilistic buckling analysis of plates and shells, Thin-Walled Structures 30(1-4): 135-157.
[20] Elishakoff I., 1979, Buckling of a stochastically imperfect finite column on a nonlinear elastic foundation: A reliability study, Journal of Applied Mechanics-Transactions of ASME 46: 411-416.
[21] Elishakoff I., Van Manen S., Vermeulen P.G., Arbocz J., 1987, First-order second-moment analysis of the buckling of shells with random imperfections, AIAA Journal 25(8): 1113-1117.
[22] Chryssanthopoulos M.K., Baker M.J., Dowling P.J., 1991, Imperfection modeling for buckling analysis of stiffened cylinders, Journal of Structural Engineering Division 117(7): 1998-2017.
[23] Sadovsky Z., Bulaz I., 1996, Tolerance of initial deflections of welded steel plates and strength of I- cross section in compression and bending, Journal of Constructional Steel Research 38(3): 219-238.
[24] Warren J.E. Jr., 1997, Nonlinear Stability Analysis of Frame-Type Structures with Random Geometric Imperfections Using a Total-Lagrangian Finite Element Formulation, Ph.D. Thesis, Virginia Polytechnic Institute and State University, USA.
[25] Náprstek J., 1999, Strongly non-linear stochastic response of a system with random initial imperfections, Probabilistic Engineering Mechanics 14(1-2): 141-148.
[26] Bielewicz E., Gorski J., 2002, Shells with random geometric imperfections simulation - based approach, International Journal of Non-Linear Mechanics 37: 777-784.
[27] Schenk C.A., Schueller G.I., 2003, Buckling analysis of cylindrical shells with random geometric imperfections, International Journal of Non-Linear Mechanics 38: 1119-1132.
[28] Papadopoulos V., Papadrakakis M., 2004, Finite-element analysis of cylindrical panels with random initial imperfections, Journal of Engineering Mechanics 130(8): 867-876.
[29] Craig K.J., Roux W.J., 2007, On the investigation of shell buckling due to random geometrical imperfections implemented using Karhunen-Loève expansions, International Journal for Numerical Methods in Engineering 73(12): 1715-1726.
[30] Sadovsky Z., Guedes Soares C., Teixeira A.P., 2007, Random field of initial deflections and strength of thin rectangular plates, Reliability Engineering & System Safety 92: 1659-1670.
[31] Papadopoulos V., Stefanou G., Papadrakakis M., 2009, Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties, International Journal of Solids and Structures 46: 2800-2808.
[32] Rzeszut K., Garstecki A., 2009, Modeling of initial geometrical imperfections in stability analysis of thin-walled structures, Journal of Theoretical and Applied Mechanics 47(3): 667-684.
[33] Bahaoui J.El., Khamlichi A., Bakkali L.El., Limam A., 2010, Reliability assessment of buckling strength for compressed cylindrical shells with interacting localized geometric imperfections, American Journal of Engineering and Applied Sciences 3(4): 620-628.
[34] Brar G. S., Hari Y., Dennis K. W., 2012, Calculation of working pressure for cylindrical vessel under external pressure, Proceedings of the ASME 2012 Pressure Vessels & Piping Division Conference.
[35] Chryssanthopoulos M.K., Poggi C., 1995, Probabilistic imperfection sensitivity analysis of axially compressed composite cylinders, Engineering Structures 17(6): 398-406.
[36] Croll J.G.A., 2006, Stability in shells, Nonlinear Dynamics 43: 17-28.
[37] Combescure A., Gusic G., 2001, Nonlinear buckling of cylinders under external pressure with non axisymmetric thickness imperfections using the COMI axisymmetric shell element, International Journal of Solids and Structures 38: 6207-6226.
[38] Windernburg D.F., Trilling C., 1934, Collapse by instability of thin cylindrical shells under external pressure, ASME Transactions 56(11): 819-25.
[39] Forde W. R. B., Stiemer S. F., 1987, Improved arc length orthogonality methods for nonlinear finite element analysis, Computers & Structures 27(5): 625-630.
[40] Verderaime V., 1994, Illustrated Structural Application of Universal First Order Reliability Method, NASA Technical Paper 3501.