Buckling of Unstiffened Steel Cones Subjected to Axial Compression and External Pressure

This is the first study into elastic-plastic buckling of unstiffened truncated conical shells under simultaneously acting axial compression and an independent external pressure. This is both a numerical and experimental study. Domains of combined stability are obtained using the finite element method for a range of geometrical parameters. Cones are clamped at one end and free to move axially at the other end, where all the other degrees of freedom remain constrained. Shells are assumed to be from mild steel and the material is modeled as elastic perfectly plastic. The FE results indicate that the static stability domains remain convex. The failure mechanisms, i.e., asymmetric bifurcation and axisymmetric collapse are discussed together with the spread of plastic strains through the wall thickness. Also, the combined stability domains are examined for regions of purely elastic behavior and for regions where plastic straining exists. The latter is not convex and repercussions of that are discussed. The spread of plastic strain is computed for a range of the (radius-to-wall-thickness) ratios. Experimental results are based on laboratory scale models. Here, a single geometry was chosen for validation of numerically predicted static stability domain. Parameters of this geometry were assumed as follows: the ratio of the bigger radius, r 2 , to the smaller radius, r 1 , was taken as (r 2 /r 1 ) ¼ 2.02; the ratio of radius-to-wall-thickness, (r 2 /t), was 33.0, and the cone semiangle was 26.56 , while the axial length-to-radius ratio was (h/r 2 ) ¼ 1.01. Shells were formed by computer numerically controlled machining from 252 mm diameter solid steel billet. They had heavy integral flanges at both ends and models were not stress relieved prior to testing. Details about the test arrangements are provided in the paper