Buckling of thermalized cylindrical shells

We explore how thermal fluctuations affect the buckling of thin cylindrical shells. It is known that for flat solid sheets thermal fluctuations effectively increase the bending rigidity and reduce the bulk and shear moduli. As a consequence, thermal fluctuations increase the critical buckling load. In cylindrical shells, thermal fluctuations also increase the bending rigidity and reduce the in-plane elastic constants. However, the additional coupling between the shell curvature, the in-plane stretching modes and the out-of-plane undulations leads to novel phenomena. In shells thermal fluctuations effectively generate compressive load. As a consequence, the critical axial buckling load for cylindrical shells is reduced due to thermal fluctuations, which is similar to the reduced buckling pressure for spherical shells, but different from the enhanced buckling load for flat sheets. Similar to spherical shells, we find that for cylindrical shells with a sufficiently large radius the thermally generated compression can be large enough that shells become unstable even in the absence of external load. Furthermore, we find that the critical radius also depends on the aspect ratio (length/perimeter) of cylindrical shells.