The bending behavior of a unidirectional sandwich panel with flat and generally curved faces and a flexible core in the vertical direction is investigated. The studied panels consist of an upper flat face sheet, a core of variable thickness, and a lower face sheet that can take any geometrical layout described by an analytical function. The core is assumed a two-dimensional elastic medium with shear and transverse vertical rigidities only, and the face sheets are considered as membrane and bending members made of metallic or composite materials. The term unidirectional refers here either to a beam (narrow panel) or to a wide beam (panel) undergoing a cylindrical bending. The field equations and the boundary conditions are derived via the variational principle of the virtual work and transformed from the local polar coordinate system of the curved face into the global Cartesian one. Higher order effects due to flexibility of the core in the form of nonlinear deformation fields are incorporated in the proposed analysis as a result of the closed-form solution of the field equations and are not postulated a priori. Numerical results in terms of deformations, stresses, and stress resultants are presented for some typical cases of flat-curved panels. The effect of a wide range of layouts, various boundary conditions, and the influence of manufacturing imperfections in the form of initially wrinkled face are investigated. The results demonstrate the capabilities and generality of the proposed model and present its ability to predict the high-order localized effects that characterize such panels.
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