Sandwich buckling formulas and applicability of standard computational algorithm for finite strain

Although, for homogeneous columns, the differences between Engesser’s and Haringx’s formulas for shear buckling have been explained in 1971 by the dependence of shear modulus on the axial stress, for soft-core sandwich columns the choice of the correct formula has baffled engineers for half a century. Recently, Bažant explained this difference by a variational analysis which showed that an agreement is achieved if the shear modulus of the light core is considered to depend on the compressive stress in the skins even when small-strain elasticity applies. To clarify this paradoxical dependence, first the variational framework is briefly reviewed. Subsequently, the mathematical results from Bažant’s recent study are physically reinterpreted, with the conclusion that only the Engesser-type theory (rather than Haringx-type theory) corresponds to constant shear moduli as obtained, for example, by the torsional test of a tube made from the foam. This is a rather fundamental point for applications because the discrepancy between these two theories can be very large in the case of short columns with thin skins. The implications for standard finite element programs are then explored by computing the critical loads of several sandwich columns with different material and geometric properties. The finite element computations show agreement with the Engesser-type formula predictions, while the Haringx-type prediction can be obtained with the finite element program somewhat artificially—by updating the core modulus as a function of the axial stress in the skins. q 2004 Elsevier Ltd. All rights reserved.