Plastic Buckling of Various Shells

The phenomenon of plastic buckling is first illustrated by the behavior of a fairly thick cylindrical shell, which under axial compression deforms at first axisymmetrically and later nonaxisymmetrically. Plastic buckling encompasses two modes of behavior, nonlinear collapse at the maximum point in a load versus deflection curve and bifurcation buckling. Accurate prediction of critical loads corresponding to either mode in the plastic range requires a simultaneous accounting for moderately large deflections and nonlinear, irreversible, path-dependent material behavior. A thumbnail survey is given of plastic buckling which spans three areas: asymptotic analysis of postbifurcation behavior of perfect and imperfect simple structures, general nonlinear analysis of arbitrary structures, and nonlinear analysis for collapse and bifurcation buckling of shells and bodies of revolution. Comparisons between test and theory are presented for elastic-plastic buckling of axially compressed unstiffened and ring-stiffened cylindrical shells, internally pressurized torispherical and ellipsoidal pressure vessel heads, and pipes under combined external pressure and bending. The effect on buckling of fabrication processes such as cold forming and welding is discussed for the case of ring-stiffened cylindrical shells. Two examples are given of rather complex shell structures in which considerations of plastic buckling affect the design.