Buckling and Initial Postbuckling Behavior of Sandwich Beams Including Transverse Shear

An asymptotic solution is presented for the buckling and initial postbuckling behavior of sandwich beams. The effect of transverse shear is included, and the shear correction is calculated from energy equivalency. The asymptotic procedure is based on the nonlinear beam equation (with transverse shear included ), and closed-form solutions are derived for the critical load and for the load and midpoint dee ection and axial shortening vs applied compressiveload during theinitial postbuckling phase.Illustrativeresultsarepresented fora few typical sandwich construction cone gurations, in particular, with regard to the effect of face sheet and core material system. Nomenclature A = total cross-sectional area c = subscript for the core E = Young’ s modulus e = distance of the neutral axis of the section from the core midline .EI/eq = equivalent rigidity f1 = subscript for the top face sheet f2 = subscript for the bottom face sheet G = shear modulus N G = “ effective” shear modulus of the section L = beam length P = axial force Pcr = critical load s = distance along the dee ected beam V = shear force (normal to the dee ected beam axis) v = vertical displacement ® = shear correction coefe cient ¯ = slope of the dee ected beam axis °eq = equivalent for the section shear angle µ = rotation of the cross section due to bending