Shear Buckling of Sandwich, Fiber Composite and Lattice Columns, Bearings, and Helical Springs: Paradox Resolved

[+] Author and Article Information
Z. P. Bažant

McCormick School of Engineering and Applied Science, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208 e-mail: z-bazant@northwestern.edu

J. Appl. Mech 70(1), 75-83 (Jan 23, 2003) (9 pages) doi:10.1115/1.1509486 History: Received January 30, 2002; Revised May 09, 2002; Online January 23, 2003
Copyright © 2003 by ASME
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Biot, M. A., 1965, Mechanics of Incremental Deformations. John Wiley and Sons, New York.
Bažant, Z. P., and Cedolin, L., 1991, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories, Oxford University Press, New York (and 2nd updated Ed., Dover, New York, 2002).
Bažant,  Z. P., 1968, “Conditions of Deformation Instability of a Continuum and Their Application to Thick Slabs and a Half Space” (in Czech, with English summary), Stavebnı́cky Časopis (SAV, Bratislava), 16, pp. 48–64.
Bažant,  Z. P., 1971, “A Correlation Study of Incremental Deformations and Stability of Continuous Bodies,” ASME J. Appl. Mech., 38, pp. 919–928.
Goodier,  J. N., and Hsu,  C. S., 1954, “Nonsinusoidal Buckling Modes of Sandwich Plates,” J. Aeronaut. Sci., 21, pp. 525–532.
Plantema, F. J., 1966, Sandwich Construction: The Bending and Buckling of Sandwich Beams, Plates and Shells, John Wiley and Sons, New York.
Allen, H. G., 1969, Analysis and Design of Sandwich Panels, Pergamon Press, Oxford, UK.
Kovařı́k, V., and Šlapák, P., 1973, Stability and Vibrations of Sandwich Plates, Academia, Prague (in Czech).
Michiharu,  O., 1976, “Antisymmteric and Symmetric Buckling of Sandwich Columns Under Compressive Loads,” Trans., Jap. Soc. of Aeronaut. Space Sci., 19, pp. 163–178.
Chong, K. P., Wang, K. A., and Griffith, G. R., 1979, “Analysis of Continuous Sandwich Panels in Building Systems,” Building and Environment 44.
Frostig,  Y., and Baruch,  M., 1993, “Buckling of Simply Supported Sandwich Beams With Transversely Flexible Core—A High Order Theory,” J. Eng. Mech. 119, pp. 955–972.
Engesser,  F., 1889, “Die Knickfestigkeit gerader Stäbe,” Zentralblatt des Bauverwaltung., 11, p. 483–486.
Engesser,  F., 1889, “Die Knickfestigkeit gerader Stäbe,” Z. Architekten und Ing. Verein zu Hannover, 35, p. 455.
Engesser,  F., 1891, “Die Knickfestigkeit gerader Stäbe,” Zentralblatt der Bauverwaltung, 11, pp. 483–486.
Haringx, J. A., 1942, “On the Buckling and Lateral Rigidity of Helical Springs,” Proc., Konink. Ned. Akad. Wetenschap., 45 , p. 533.
Haringx, J. A., 1948–1949, Phillips Research Reports, Vols. 3–4, Phillips Research Laboratories, Eindhoven.
Kardomateas,  G. A., 1995, “Three Dimensional Elasticity Solution for the Buckling of Transversely Isotropic Rods: The Euler Load Revisited,” ASME J. Appl. Mech., 62, pp. 346–355.
Kardomateas,  G. A., and Dancila,  D. S., 1997, “Buckling of Moderately Thick Orthotropic Columns: Comparison of an Elasticity Solution With the Euler and Engesser/Haringx/Timoshenko Formulas,” Int. J. Solids Struct., 34(3), pp. 341–357.
Kardomateas,  G. A., 2001, “Elasticity Solutions for Sandwich Orthotropic Cylindrical Shell Under External Pressure, Internal Pressure and Axial Force,” AIAA J., 39(4), pp. 713–719.
Kardomateas, G. A., 2001, “Three-Dimensional Elasticity Solutions for the Buckling of Sandwich Columns,” ASME Intern. Mechanical Engrg. Congress, pp. 1–6.
Kardomateas, G. A., and Huang, H., 2002, “Buckling and Initial Postbuckling Behavior of Sandwich Beams Including Transverse Shear,” AIAA J., in press.
Kardomateas, G. A., Simitses, G. J., Shen, L., and Li, R., 2002, “Buckling of Sandwich Wide Columns,” Int. J. Non-Linear Mech., (special issue on “Nonlinear Stability of Structures”), in press.
Simitses, G. J., and Shen, L., 2000, “Static and Dynamic Buckling of Sandwich Columns,” Mechanics of Sandwich Structures, Y. D. S. Rajapakse et al., eds., ASME, New York, AD-Vol. 62/AMD-Vol. 245, pp. 41–50.
Timoshenko, S. P., and Gere, J. M., 1961, Theory of Elastic Stability, McGraw-Hill, New York, pp. 135, 142.
Bažant,  Z. P., 1992, discussion of “Stability of Built-up Columns,” by A. Gjelsvik, J. Eng. Mech., 118(6), pp. 1279–1281.
Bažant,  Z. P., 1993, discussion of “Use of Engineering Strain and Trefftz Theory in Buckling of Columns,” by C. M. Wang and W. A. M. Alwis ASME J. Appl. Mech., 119(12), pp. 2536–2537.
Ziegler,  F., 1982, “Arguments for and Against Engesser’s Buckling Formulas,” Ingenieur-Archiv, 52, pp. 105–113.
Reissner,  E., 1972, “On One-Dimensional Finite-Strain Beam Theory: The Plane Problem,” J. of Applied Mathematics and Physics, 23, pp. 795–804.
Reissner,  E., 1982, “Some Remarks on the Problem of Column Buckling,” Ingenieur-Archiv, 52, pp. 115–119.
Simo,  J. C., and Kelly,  J. M., 1984, “The Analysis of Multilayer Elastomeric Bearings,” ASME J. Appl. Mech., 51, pp. 256–262.
Simo,  J. C., Hjelmstad,  K. D., and Taylor,  R. L., 1984, “Numerical Formulation of Elasto-Viscoplastic Response of Beams Accounting for the Effect of Shear,” Comput. Methods Appl. Mech. Eng., 42, pp. 301–330.
Gjelsvik,  A., 1991, “Stability of Built-Up Columns,” J. Eng. Mech., 117(6), pp. 1331–1345.
Wang,  C. M., and Alwis,  W. A. M., 1992, “Use of Engineering Strain and Trefftz Theory in Buckling of Columns,” J. Eng. Mech., 118(10), pp. 2135–2140.
Attard, M. A., 2002, draft of a manuscript on “Finite Strain Beam Theory,” University of New South Wales, Australia (private communication to Bažant, 2002).
Buckle,  I., Nagarajaiah,  S., and Ferell,  K., 2002, “Stability of Elastomeric Isolation Bearings: Experimental Study,” J. Eng. Mech., 128(1), pp. 3–11.
Timoshenko,  S. P., 1921, “On the Correction for Shear in the Differential Equation of Transverse Vibrations of Prismatic Bars,” Philos. Mag., 21, p. 747.


Grahic Jump Location
Shear deformation of an element of sandwich column under initial axial forces F=P/2; (a) with second-order axial extension γ2/2, and (b) at no axial extension
Grahic Jump Location
(a) Lateral view of a helical spring and cross sections on which the shear force is defined in Haringx and Engesser theories; (b) shear buckling of an elastomeric bridge bearing
Grahic Jump Location
Left: Column with battens and pin-jointed lattice column. Middle: Shearing of a cell of batten column. Right: Shearing of a cell of lattice column. Top: Shearing with second-order axial extension. Bottom: Shearing with no axial extension.
Grahic Jump Location
Sandwich column in (a) initial state and (b) deflected state; (c,d) cross-section rotation, shear angle and shear force due to axial load
Grahic Jump Location
Column loaded (a) under load control (e.g., by gravity) and (b) displacement control



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