Several aluminum and mild steel torispherical heads were tested by Galletly and by Kirk and Gill and subsequently analyzed by Bushnell with use of the BOSOR5 computer program. The thinnest specimens buckled at pressures for which part of the toroidal knuckle was stressed well beyond the yield point. The analysis includes large deflection effects, nonlinear material behavior, and meridional variation of the thickness. The calculated strains in the thicker specimens agree reasonably well with the test results, but the calculated prebuckling strains in the thinnest specimens are generally greater than the values measured in the torodial knuckle after the onset of plastic flow. Reasonably good agreement between test and theory is obtained for the buckling pressures of aluminum specimens, but the calculated buckling pressures for mild steel specimens are much lower than the observed values, a discrepancy that is attributed to circumferentially varying thickness and possible inability of the analytical model of the elastic-plastic material to predict accurately the state of stress in the toroidal knuckle where loading is nonproportional once yielding has occurred.
Longitudinal-transverse bending of a multilayer bar made of a physically nonlinear material
