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general buckling mode of ring and stringer stiffened cylindrical shell

Shown here is a general buckling mode obtained from a STAGS model of an optimized axially compressed cylindrical shell with external stringers and internal rings. (The optimum design was obtained by PANDA2.)

This general buckling mode shape can be used as an initial imperfection in a subsequent STAGS execution with use of the same model for static nonlinear equilibrium with step-wise increasing applied load.

As the axial compression increases the imperfect stiffened shell bends, giving rise to the following two effects:

1. stresses are redistributed over the skin and stiffeners, affecting the local buckling behavior and maximum stresses in the skin, in the rings, and in the stringers, and

2. where there exist inward lobes of the buckling modal imperfection pattern, which is amplified by the compressive loading, there exist locally flattened areas where the effective circumferential radius of curvature of the imperfect shell exceeds the nominal radius of the perfect cylindrical shell, causing a reduction in the general buckling load of the imperfect shell compared with that of the perfect shell.


Almroth, B. O. and Brogan, F. A., "The STAGS computer code", NASA CR-2950, NASA Langley Research Center, Hampton, VA, 1978.

STAGS Brochure (2002) available online by request: (pdf format).

(A) Rankin, C.C., Stehlin, P., and Brogan, F.A., "Enhancements to the STAGS computer code", NASA CR-4000, NASA Langley Research center, Hampton, VA, 1986. See also: (B) Rankin, C.C, “Application of Linear Finite Elements to Finite Strain Using Corotation.” AIAA Paper AIAA-2006-1751, 47th AIAA Structures, Structural Dynamics and Materials Conference, May 2006; (C) Rankin, C.C., Brogan, F.A., Loden, W.A., Cabiness, H.D., “STAGS User Manual – Version 5.0,” Rhombus Consultants Group, Inc., Palo Alto, CA, Revised January 2005 (on-line). Previously Report No. LMSC P032594, Lockheed Martin Missiles and Space Company, Palo Alto, CA, June 1998; (D) Rankin, C.C., “The use of shell elements for the analysis of large strain response, AIAA Paper 2007-2384, 48th AIAA Structures, Structural Dynamics and Materials Conference, Hawaii, April 2007.

Riks, E., Rankin C. C., Brogan F. A., "On the solution of mode jumping phenomena in thin walled shell structures", First ASCE/ASM/SES Mechanics Conference, Charlottesville, VA, June 6-9, 1993, in: Computer Methods in Applied Mechanics and Engineering, Vol. 136, 1996.

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