Equilibrium of Heavy Elastic Cylindrical Shells

Abstract

An originally circular, heavy elastic shell rests on a horizonal surface. The equilibrium shape is governed by the heavy elastica equations. The solutions depend heavily on the parameter B, which represents the relative importance of density and perimeter length to flexural rigidity. There are four distinct cases. A perturbation analysis is obtained for small B while a similarity solution exists for large B. The general solution is obtained by accurate numerical integration using a least change secant update quasi-Newton method and a new homotopy method.