Oval cylindrical shells under asymmetric bending: a singular-perturbation solution

A singular asymptotic limit of the bifurcation instability experienced by short oval cylindrical shells under asymmetric pure bending is explored both analytically and numerically. Of primary interest here is the interplay between the variable geometrical stiffness of the cross section and the arbitrary orientation of the applied bending moments. By using boundary layer arguments, it is shown that the localised cross-sectional eigen-deformations are concentrated around a point determined by the solution of a simple trigonometric equation. The non-symmetric shape of the eigenmodes is also captured by a reduced fourth-order ordinary differential equation, which represents a generalisation of an earlier form found previously for the case of circular cylindrical shells under the same type of loading.