A nonlinear theory for doubly curved anisotropic sandwich shells with transversely compressible core

In the present paper, an advanced geometrically nonlinear shell theory of doubly curved structural sandwich panels with transversely compressible core is presented. The model is based on the adoption of the Kirchhoff theory for the face sheets and a second/third order power series expansion for the core displacements. The theory accounts for dynamic effects as well as for initial geometric imperfections. In the v. Kármán sense, large displacement theory is employed with respect to the transverse direction while the displacement gradients with respect to the tangential directions are assumed to be small. The equations of motion are derived by means of Hamilton’s principle and hold valid for all types of elastic and elastic–plastic material models. The theory is illustrated by an analysis of the elastic buckling and postbuckling behavior of flat and curved sandwich panels using an extended Galerkin scheme. Owing to the assumed transverse flexibility of the core, both the global and the local (face wrinkling) instability modes can be addressed.