HIGH-ORDER BENDING OF SANDWICH BEAMS WITH TRANSVERSELY FLEXIBLE CORE AND NONPARALLEL SKINS

The bending behavior of a general tapered sandwich beam with a flexibl e core in the vertical direction and a piecewise uniform sandwich beam with tapered transition zones between the uniform regions is analytic ally investigated. The structure is modeled as a combination of a core that is assumed to be a two-dimensional elastic medium, in the longit udinal and transverse directions, and skins considered as one-dimensio nal inclined beams. Thus the effects of the flexibility of the core in the vertical direction and that of the vertical component of the long itudinal and the shear forces in the inclined skins on the local and t he overall behavior are considered. The field equations and the bounda ry and the continuity conditions are rigorously derived using variatio nal principles. The proposed analysis accounts for higher-order effect s due to the flexibility of the core in the form of nonlinear displace ments fields through its height that comprises a parabolic distributio n 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 pro nounced in the vicinity of concentrated or localized distributed loads or supports as well as at the ends of tapered transition zones and ar e usually associated with stress concentration in the form of high pee ling and shear stresses at the skin-core interfaces and high bending s tresses in the skins. These effects also exist at the ends of taper tr ansition zones of a piecewise uniform beam due to the concentrated res ultant of the shear and longitudinal internal forces of the skins even in the case of a distributed load. The characteristic behavior of a t apered sandwich beam and a piecewise uniform beam with a tapered trans ition region are studied in terms of deflections, shear forces and ben ding moments in the skins, normal transverse and shear stresses in the core, and shear and peeling stresses at the interfaces between the co re and the skins, Numerical results of stress concentration effects fo r some typical cases are presented and discussed.