The Buckling Load of Cylindrical Shells Under Axial Compression Depends on the Cross-Sectional Curvature

It is known that the famous theoretical formula by Koiter for the critical buckling load of circular cylindrical shells under axial compression does not coincide with the experimental data. Namely, while Koiter's formula predicts linear dependence of the buckling load lambda(h) of the shell thickness h (h > 0 is a small parameter), one observes the dependence lambda(h) -h(3/2) in experiments; i.e., the shell buckles at much smaller loads for small thickness. This theoretical prediction failure is believed to be caused by the so-called sensitivity to imperfections phenomenon (both, shape and load). Grabovsky and the first author have rigorously proven in (J Nonlinear Sci 26(1):83-119, 2016) , that in the problem of circular cylindrical shells buckling under axial compression, a small load twist leads to the buckling load scaling lambda(h) -h(5/4), while shape imperfections are likely to result in the scaling lambda(h) -h(3/2). In this work, we prove that in fact the buckling load lambda(h) of cylindrical (not necessarily circular) shells under vertical compression depends on the curvature of the cross section curve. When the cross section is a convex curve with uniformly positive curvature, then lambda(h) -h, and when the cross-sectional curve has positive curvature except at finitely many points, then C(1)h(8/5) <= lambda(h) <= C(2)h(3/2) for h small thickness h > 0.

Automated summary

This study proves that the buckling load of cylindrical shells under vertical compression depends on the curvature of the cross section curve. For convex curves with uniformly positive curvature, the buckling load has a linear relationship with the shell thickness. For curves with positive curvature at finitely many points, the buckling load lies between C(1)h(8/5) and C(2)h(3/2) for small thickness h > 0.