High‐Order Bending of Sandwich Beams with Transversely Flexible Core and Nonparallel Skins

Abstract

The bending behavior of a general tapered sandwich beam with a flexible core in the vertical direction and a piecewise uniform sandwich beam with tapered transition zones between the uniform regions is analytically investigated. The structure is modeled as a combination of a core that is assumed to be a two‐dimensional elastic medium, in the longitudinal and transverse directions, and skins considered as one‐dimensional inclined beams. Thus the effects of the flexibility of the core in the vertical direction and that of the vertical component of the longitudinal and the shear forces in the inclined skins on the local and the overall behavior are considered. The field equations and the boundary and the continuity conditions are rigorously derived using variational principles. The proposed analysis accounts for higher‐order effects due to the flexibility of the core in the form of nonlinear displacements fields through its height that comprises a parabolic distribution of the vertical deformation, which changes the distance between the skins, as well as the height of the core and a cubic variation of the longitudinal displacement. These high‐order effects are especially pronounced in the vicinity of concentrated or localized distributed loads or supports as well as at the ends of tapered transition zones and are usually associated with stress concentration in the form of high peeling and shear stresses at the skin‐core interfaces and high bending stresses in the skins. These effects also exist at the ends of taper transition zones of a piecewise uniform beam due to the concentrated resultant of the shear and longitudinal internal forces of the skins even in the case of a distributed load. The characteristic behavior of a tapered sandwich beam and a piecewise uniform beam with a tapered transition region are studied in terms of deflections, shear forces and bending moments in the skins, normal transverse and shear stresses in the core, and shear and peeling stresses at the interfaces between the core and the skins. Numerical results of stress concentration effects for some typical cases are presented and discussed.