Elliptical and Circular Cylindrical Sandwich Shells with Different Facings

The Sanders-type theory of elliptical sandwich shells with different facings is formulated. The governing equations account for transverse shear strains and for rotations about the normal to the middle surface of the shell. The constitutive equations correspond to a sandwich shell where each facing is formed of an even number of regular symmetrically laminated layers. Accordingly, the matrix of extensional, coupling and bending stiffnesses is fully populated, except for the elements A ₁₆ and A ₂₆ that are equal to zero. In addition, a geometrically nonlinear formulation is presented for an elliptical facing resting on an elastic foundation, based on the Sanders nonlinear shell theory. In this formulation, the rotations about the normal to the middle surface as well as transverse shear strains are disregarded. Both the governing equations for the sandwich shell and the nonlinear solution for a facing are reduced to the corresponding results for a circular cylindrical shell if the radius of curvature of the shell is constant. Numerical examples are presented for the problem of buckling of a long cylindrical shell subjected to a lateral pressure. This solution, developed by using the energy method, illustrates the penalty involved in using different facings, which may nevertheless be necessary to improve the design by reinforcing the facing exposed to low-velocity impact and other loads.