Local instability of shallow sandwich shells for the general case of orthotropy, curvature and loading

The paper considers wrinkling of orthotropic faces of a shallow sandwich shell with an isotropic core for a general case of in-plane multi-axial loading. The principal axes of loading do not necessarily coincide with the principal axes of orthotropy and curvature. Analytical closed-form solutions are obtained for anti-symmetric (both faces wrinkle in phase) and non-symmetric (one-sided wrinkle) local instabilities, that represent the most probable patterns of behaviour of sandwich shells. The solutions coincide with the known classical solutions for the limiting cases of constitution, geometry and loading. Multiple examples of various combinations of values of the introduced main structural parameters are considered.