Biomechanics of cellular solids.

On the collapse of inelastic tubes under combined bending and pressure

Bifurcation and localization instabilities in cylindrical shells under bending—I. Experiments

Purpose I order to produce efficient, reliable designs and to avoid unexpected catastrophic failure of structures of which thin shells are important components, the engineer must understand the physics of shell buckling. The objective of this survey is to convey to the reader a "feel" for shell buckling, whether it be due to nonlinear collapse, bifurcation buckling, or a combination of these modes. This intuitive understanding of instability is communicated by a large number of examples involving practical shell structures which may be stiffened, segmented, or branched and which have complex wall constructions. With such intuitive knowledge the engineer will have an improved ability to foresee situations in which buckling might occur and to modify a design to avoid it. He will be able to set up more appropriate models for tests and analytical predictions. The emphasis here is not on the development of equations for the prediction of instability. For such material the reader is referred to the book by Brush and Almroth. n Emphasis is given here to nonlinear behavior caused by a combination of large deflections and plasticity. Also illustrated are stress redistribution effects, stiffener and loadpath eccentricity effects, local vs general instability, imperfection sensitivity, and modal interaction in optimized structures. Scattered throughout the text are tips on modeling for computerized analysis. The survey is divided into nine major sections describing: 1) several examples of catastrophic failure of expensive shell structures; 2) the basics of buckling behavior; 3) "classical" buckling and imperfection sensitivity; 4) nonlinear collapse and the appropriateness of linear bifurcation buckling analyses for general shells; 5) bifurcation buckling with significant nonlinear prebuckling behavior; 6) effects of boundary conditions, load eccentricity, transverse shear deformation, and stable postbuckling behavior; 7) optimization of buckling-critical structures with consequent modal interaction; 8) a suggested design method for axially compressed cylinders with stiffeners, internal pressure, or other special characteristics; and 9) two examples in which sophisticated buckling analyses are required in order to derive improved designs. The paper focuses on static buckling problems.

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Buckling of Shells-Pitfall for Designers

Behaviour of axially crushed corrugated tubes

: The stability of circular cylindrical shells under pure bending is investigated by means of Batdorf's modified Donnell's equation and the Galerkin method. The results have shown that contrary to the commonly accepted value, the maximum critical bending stress is for all practical purposes equal to the critical compressive stress. (Author)

On the Buckling of Circular Cylindrical Shells Under Pure Bending

: The stability under axial compressionoion and lateral prpressure of a finite ciircular-cylindrical shell with an elastic core is treated by means of Donnell's equations. For lateral pressure it is found that a previous solution treating the cylinder as a ring or a long cylinder is adequate for a wide range of combinations of length-radius ratio, radius-thickness ratio, and ratio of moduli of core and cylinder. Results for axial compression are included for completeness and to correct a previous analysis of the same problem. (Author)

The stability under axial compression and lateral pressure of circular-cylindrical shells with a soft elastic core.

A, B = constants appearing in deflection functions b = width of plate c = fraction of half-buckle wavelength representing length of region of plate in which the foundation is compressed D = flexural stiffness of plate [D = Et*/12(1 v)} E = Young's modulus of plate material F(x) = function representing variation in ^-direction of the plate deflection k = buckling load coefficient (k = bN/wD) k = foundation modulus N = critical compressive load per inch of plate width t = plate thickness w = plate deflection x = distance along plate longitudinal axis [see Fig. 1(b)] y = distance along width of plate 7 = foundation modulus parameter (7 = bk/irD) V^ = (d/dx) + 2(d/dxdy) + ( d 4 / ^ 4 ) X = ' half-wavelength of buckle v = Poisson's ratio

Compressive Buckling of a Long Simply Supported Plate on an Elastic Foundation

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Paul Seide

Papers

On the Buckling of Circular Cylindrical Shells Under Pure Bending

The stability under axial compression and lateral pressure of circular-cylindrical shells with a soft elastic core.

Compressive Buckling of a Long Simply Supported Plate on an Elastic Foundation

Discussion: “Buckling of Circular Cones Under Axial Compression” (Lackman, Leslie, and Penzien, Joseph, 1960, ASME J. Appl. Mech., 27, pp. 458–460)

Buckling of Circular Rings and Long Cylinders Enclosing an Elastic Material Under Uniform External Pressure