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This and the next 2 slides show predictions from BOSOR5 of deformation and buckling of elastic-plastic axisymmetric shells.
This is Fig. 1 from the paper, "Comparisons of test and theory for nonsymmetric elastic-plastic buckling of shells of revolution" by David Bushnell and Gerard D. Galletly, International Journal Solids Structures, Vol. 10, pp. 1271-1286, 1974, called "1974 Galletly paper" in the next two slides.
This slide shows an aluminum torispherical pressure vessel with an axisymmetric nozzle tested under external pressure by Galletly at the University of Liverpool.
The BOSOR5 computer program was used to obtain the buckling load factors and mode shapes for four configurations tested by Galletly and his colleagues at the University of Liverpool.
ABSTRACT FROM THE 1974 GALLETLY PAPER:
Experimental and analytical buckling pressures are presented for very carefully fabricated thin cylindrical shells with 45, 60 and 75° conical heads and for cylindrical shells with torispherical heads pierced by axisymmetric cylindrical nozzles of various thicknesses and diameters. Nonsymmetric buckling occurs at pressures for which some of the material is loading plastically in the neighborhoods of stress concentrations caused by meridional slope discontinuities. The buckling pressures for the cone-cylinder vessels are predicted within 2.6 per cent and for the pierced torispherical vessels within 4.4 per cent with use of BOSOR5, a computer program based on the finite difference energy method in which axisymmetric large deflections, nonlinear material properties and nonsymmetric bifurcation buckling are accounted for. The predicted buckling pressures of the pierced torispherical specimens are rather sensitive to details of the analytical model in the neighborhood of the juncture between the nozzle and the head. The buckling pressures of the cone-cylinder vessels can be accurately predicted by treatment of the wall material as elastic, enforcement of the full compatibility conditions at the juncture in the prebuckling analysis, and release of the rotation compatibility condition in the bifurcation (eigenvalue) analysis.
The following abstract is from the paper: "Bifurcation buckling of shells of revolution including large deflections, plasticity and creep", by David Bushnell, Int. J. Solids Structures, Vol. 10, pp. 1287-1305, 1974
ABSTRACT ABOUT THE BOSOR5 PROGRAM:
A summary is first presented of the conceptual difficulties and paradoxes surrounding plastic bifurcation buckling analysis. Briefly discussed are nonconservativeness, loading rate during buckling, and the discrepancy of buckling predictions with use of J2 flow theory vs J2 deformation theory. The axisymmetric prebuckling analysis, including large deflections, elastic-plastic material behavior and creep is summarized. Details are given on the analysis of nonsymmetric bifurcation from the deformed axisymmetric state. Both J2 flow theory and J2 deformation theory are described. The treatment, based on the finite-difference energy method, applies to layered segmented and branched shells of arbitrary meridional shape composed of a number of different elastic-plastic materials. Numerical results generated with a computer program based on the analysis are presented for an externally pressurized cylinder with conical heads.
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