Hierarchical High-Fidelity Analysis Methodology for Buckling Critical Structures
Publication: Journal of Aerospace Engineering
Volume 18, Issue 3
Abstract
A hierarchical high-fidelity analysis methodology for predicting the critical buckling load of compression-loaded thin-walled isotropic shells is described. This hierarchical procedure includes three levels of fidelity for the analysis. Level 1 assumes that the buckling load can be predicted by the classical shell solution with simply supported boundary condition, and with a linear membrane prebuckling solution. Level 2 includes the effects of a nonlinear prebuckling solution and the effects of traditional clamped or simply supported boundary conditions. Level 3 includes the nonlinear interaction between nearly simultaneous buckling modes and the effects of boundary imperfections and general boundary conditions. Various deterministic and probabilistic approaches are used to account for the degrading effects of unavoidable shell-wall geometric imperfections. The results from the three solution levels are compared with experimental results, and the effects of the assumptions and approximations used for the three solution levels are discussed. This hierarchical analysis approach can be used in the design process to converge rapidly to an accurate prediction of the expected buckling load of a thin-shell design problem.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgment
Part of the research reported in this paper has been carried out during the first writer’s tenure as an NRC Research Associate at the NASA Langley Research Center in 2002. This support is gratefully acknowledged.
References
Almroth, B. O., Brogan, F. A., Miller, E., Zele, F., and Peterson, H. T. (1973). Collapse analysis for shells of general shape; II. User’s manual for the STAGS-A computer code. Technical Rep. AFFDL-TR-71-8, Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio.
Arbocz, J. (1982). “The imperfection data bank, a means to obtain realistic buckling loads.” Buckling of Shells, Proc., State-of-the-Art Colloquium, E. Ramm, ed., Springer-Verlag, Berlin, 535–567.
Arbocz, J. (1992). “The effect of initial imperfections on shell stability—An updated review.” Rep. LR-695, Delft Univ. of Technology, Faculty of Aerospace Engineering, The Netherlands.
Arbocz, J. (2000). “The effect of imperfect boundary conditions on the collapse behavior of anisotropic shells.” Int. J. Solids Struct., 27(46–47), 6891–6915.
Arbocz, J., and Babcock, C. D., Jr. (1969). “The effect of general imperfections on the buckling of cylindrical shells.” J. Appl. Mech., 36, 28–38.
Arbocz, J., and Babcock, C. D., Jr. (1976). “Prediction of buckling loads based on experimentally measured initial imperfections.” Buckling of Structures, Proc., IUTAM Symposium, Harvard Univ., Cambridge, B. Budiansky, ed., Springer-Verlag, Berlin, 291–311.
Arbocz, J., and Babcock, C. D., Jr. (1980). “The buckling analysis of imperfection sensitive structures.” NASA CR-3310.
Arbocz, J., and Hol, J. M. A. M. (1990). “Koiter’s stability theory in a computer aided engineering (CAE) environment.” Int. J. Solids Struct., 26(9/10), 945–973.
Arbocz, J., and Hol, J. M. A. M. (1993). “Shell stability analysis in a computer-aided engineering (CAE) environment.” Proc., 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., La Jolla, Calif., 300–314.
Arbocz, J., and Starnes, J. H. (2002). “Buckling load calculations of the isotropic shell A-8 using a high-fidelity hierarchical approach.” AIAA Paper 2002-1513 in Proc., 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., Denver.
Arbocz, J., Starnes, J. H., and Nemeth, M. P. (1998). “Towards a probabilistic criterion for preliminary shell design.” Proc., 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., Long Beach, Calif., 2941–2955.
Beulsicherheitsnachweise für Schalen, DAST Richtlinie 013. (1980). Deutscher Ausschuss für Stahlbau.
Brogan, F. A., Rankin, C. C., and Cabiness, H. D. (1994). STAGS user manual, Version 2.0, LMSC P032594, Lockheed Palo Alto Research Laboratory, Palo Alto, Calif.
“Buckling of thin-walled cylinders. NASA Space Vehicle Design Criteria (Structures).” (1968). NASA SP-8007.
Budiansky, B., and Hutchinson, J. W. (1966). “Dynamic buckling of imperfection sensitive structures.” Proc., 11th IUTAM Congress, Munich, 1964, Julius Springer-Verlag, Berlin, 636–651.
Bushnell, D. (1972). Stress, Stability and Vibration of Complex Branched Shells of Revolution: Analysis and User’s Manual for BOSOR-4. NASA CR-2116.
Byskov, E. (1988). “Smooth postbuckling stresses by a modified finite element method.” DCAMM Rep. No. 380, Technical Univ. of Denmark, Lyngby.
Cohen, G. A. (1968). “Computer analysis of asymmetric buckling of ring-stiffened orthotropic shells of revolution.” AIAA J., 6(1), 141–149.
Donnell, L. H., and Wan, C. C. (1950). “Effect of imperfections on buckling of thin cylinders and columns under axial compression.” J. Appl. Mech., 17, 73–83.
Fischer, G. (1963). “Über den Einfluss der gelenkingen Lagerung auf die Stabilität dünnwandiger Kreiszylinderschalen unter Axiallast und Innendruck.” Z. Flugwiss., 11, 111–119.
Gellin, S. (1979). “Effect of an axisymmetric imperfection on the plastic buckling of an axially compressed cylindrical shell.” J. Appl. Mech., 46, 125–131.
Hilburger, M. W., and Starnes, J. H. (2000). “Effects of imperfections on the buckling response of compression-loaded composite shells.” AIAA Paper 2000-1382 in Proc., 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., Atlanta, Ga.
Hoff, N. J. (1961). “Buckling of thin shells.” Proc. Aerospace Symposium of Distinguished Lecturers in Honor of Theodore von Kármán on his 80th Anniversary, Institute of Aerospace Sciences, New York, 1–42.
Imbert, J. (1971). “The effect of imperfections on the buckling of cylindrical shells.” Aeronautical Engineer Thesis, California Institute of Technology.
Koiter, W. T. (1945). “On the stability of elastic equilibrium.” PhD thesis (in Dutch), TH-Delft, The Netherlands, H. J. Paris, Amsterdam, English translation NASA TTF-10, 1–833.
Koiter, W. T. (1963). “The effect of axisymmetric imperfections on the buckling of cylindrical shells under axial compression.” Koninkl. Ned. Akad. Wetenschap. Proc., B66, 265–279.
Lorenz, R. (1908). “Achsensymmetrische Verzerrungen in dünnwandigen Hohlzylindern.” Zeitschrift des Vereines Deutscher Ingenieure, 52, 1706–1713.
Nimmer, R. P., and Mayers, J. (1979). “Limit point buckling loads of axially compressed circular cylindrical shells—The effect of nonlinear material behavior.” J. Appl. Mech., 46, 386–392.
Romkes, A. (1997). “Stability and imperfection sensitivity of anisotropic cylindrical shells under general boundary conditions.” Memorandum M-809, Delft University of Technology, Faculty of Aerospace Engineering, The Netherlands.
Singer, J., and Rosen, A. (1976). “The influence of boundary conditions on the buckling of stiffened cylindrical shells.” Buckling of Structures, Proc., IUTAM Symposium, Harvard Univ., Cambridge, B. Budiansky, ed., Springer-Verlag, Berlin, 227–250.
Southwell, R. V. (1914). “On the general theory of elastic stability.” Philos. Trans. R. Soc. London, Ser. A, 213, 187–244.
Stein, M. (1964). “The influence of prebuckling deformations and stresses on the buckling of perfect cylinders.” NASA TR-190.
Stuhlman, C. E., De Luzio, A., and Almroth, B. (1966). “Influence of stiffener eccentricity and end moment on stability of cylinders in compression.” AIAA J., 4(5), 872–877.
Timoshenko, S. (1910). “Einige Stabilitätsprobleme der Elastizitätstheorie.” Zeitschrift für Mathematik und Physik, 58, 337–385.
Weingarten, V. I., Morgan, E. J., and Seide, P. (1965). “Elastic stability of thin-walled cylindrical and conical shells under axial compression.” AIAA J., 3(3), 500–505.
Weustink, A. P. D. (2000). “Stability analysis of anisotropic shells of revolution under axisymmetric load with general boundary conditions.” Memorandum M-881, Delft Univ. of Technology, Faculty of Aerospace Engineering, The Netherlands.
Yaffe, R., Singer, J., and Abramovich, H. (1981). “Further initial imperfection measurements of integrally stringer-stiffened cylindrical shells—Series 2.” TAE Rep. 404, Faculty of Aerospace Engineering, Technion, Israel Institute of Technology, Haifa, Israel.
Zienkiewicz, O. C. (1977). The finite element method. (The third, expanded and revised edition of The Finite Element Method in Engineering Science). McGraw-Hill, London, 504.
Information & Authors
Information
Published In
Copyright
© 2005 ASCE.
History
Received: Jun 27, 2003
Accepted: Feb 24, 2004
Published online: Jul 1, 2005
Published in print: Jul 2005
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.