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Buckling, postbuckling and imperfection-sensitivity: Old questions and some new answers. (English) Zbl 1158.74361
Summary: From the point-of-view of economy and safety it is desirable to employ structural configurations with a favorable strength-to-weight ratio and a sufficiently small imperfection-sensitivity. The presentation focuses on two examples falling into this category: The axially compressed cylindrical shell filled with – and/or surrounded by – a compliant core, and auxetic structures. Both exhibit unexpected aspects in their load-carrying behavior and have a significant weight-savings potential.

74G60 Bifurcation and buckling
74H55 Stability of dynamical problems in solid mechanics
74K25 Shells
Full Text: DOI
[1] Koiter WT (1945) On the stability of elastic equilibrium (in Dutch), Thesis, Delft University of Technology, H.J. Paris, Amsterdam, 1945. English translation NASA TT-F10833
[2] Koiter WT (1963) The effect of axisymmetric imperfections on the buckling of cylindrical shells under axial compression. Proc Kon Ned Akad Wet B66:265–279 · Zbl 0117.19103
[3] Hutchinson JW, Koiter WT (1970) Postbuckling theory. Appl Mech Rev 23:1353–1366
[4] Budiansky B, Hutchinson JW (1972) Buckling of circular cylindrical shells under axial compression. In: Contributions to the Theory of Aircraft Structures. Delft University Press, Delft 239–260
[5] Budiansky B (1974)Theory of buckling and post-buckling behavior of elastic structures. Adv Appl Mech 14:1–65
[6] Thompson JMT (1972) Optimization as a generator of structural instability. Int J Mech Sci 14:627–629
[7] Thompson JMT, Supple WJ (1973) Erosion of optimum designs by compound branching phenomena. J Mech Phys Solids 21:135–144
[8] Arbocz J, Singer J (2000) Professor Budiansky’s contributions to buckling and postbuckling of elastic structures. AIAA-Paper 2000–1322
[9] Brush DO, Almroth BO (1962) Buckling of core-stabilized cylinders under axisymmetric external loads. J Aerospace Sci 1164–1170 · Zbl 0104.19202
[10] Almroth BO, Brush DO (1963) Postbuckling behavior of pressure- or core-stabilized cylinders under axial compression. AIAA J 1:2338–2341
[11] Goree WS, Nash WA (1962) Elastic stability of circular cylindrical shells stabilized by a soft elastic core. Exper Mech 142–149
[12] Seide P (1962) The stability under axial compression and lateral pressure of circular cylindrical shells with a soft elastic core. JAerospace Sci 1962:851–862 · Zbl 0106.17203
[13] Yao JC (1962) Buckling of axially compressed long cylindrical shell with elastic core. J Appl Mech 29:329–334 · Zbl 0118.41402
[14] Agarwal BL, Sobel LH (1977) Weight comparisons of optimized stiffened, unstiffened and sandwich cylindrical shells. J Aircraft 14:1000–1008
[15] Budiansky B (1999) On the minimum weight of compression members. Int J Solids Structures 36:3677–3708 · Zbl 0933.74050
[16] Hutchinson JW, He MY (2000) Buckling of cylindrical sandwich shells with metal foam cores. Int J Solids Structures 37:6777–6794 · Zbl 0994.74026
[17] Evans AG, Hutchinson JW, Ashby MF (1999) Multifunctionality of cellular metal systems. Prog Mater Sci 43:171–221
[18] Karam GN, Gibson LJ (1995) Elastic buckling of cylindrical shells with elastic cores. I Analysis Int J Solids Structures 32:1259–1263 · Zbl 0872.73016
[19] Karam GN, Gibson LJ (1995) Elastic buckling of cylindrical shells with elastic cores, II. Experiments. Int J Solids Structures 32:1285–1306 · Zbl 0872.73016
[20] Anon (1968) Buckling of thin-walled cylinders. NASA Space Vehicle Design Criteria, NASA SP-8007, 1965
[21] Lakes RS (1992) No contractile obligations. Nature 358:713–714
[22] Lakes RS (1993) Advances in negative Poisson’s ratio materials. Adv Mater 5:293–296
[23] Evans KE Alderson A (2000) Auxetic materials: Functional materials and structures from lateral thinking. Adv Mater. 12:617–628
[24] Evans KE, Alderson KL (2000) Auxetic materials: The positive side of being negative. Eng Sci Educ J Aug:148–154
[25] Almgren RF (1985) An isotropic three dimensional structure with Poisson’s ratio = . J Elasticity 15:427–430
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