On interactive buckling in a sandwich structure

Abstract

This work revisits an interactive buckling model for sandwich beams proposed relatively recently by Hunt and Wadee (Proc R Soc Lond A 454:1197-1216, 1998). Our asymptotic investigations reveal an interesting resonant behaviour which is shown to lie at the origin of the corresponding localised deformations reported in the literature. The very good agreement between the asymptotic results and various direct numerical simulations reinforces the validity of our theoretical arguments and provides an incentive for further research. (2000). 34E13 · 65L15 · 74G60 · 74K99. Mathematics Subject Classification

Discussion: “On interactive buckling in a sandwich structure” by C. D. Coman

“…This is supposed to occur beyond a threshold of a certain parameter within those equations, given as a ratio involving the flexural rigidity of the individual face plates, the core stiffness and the strut length ( Figure 5 of that paper); a fact apparently "overlooked" by the original authors of [2]. It then discusses some observed resonant phenomena that the equations exhibit, which we have also observed in our solution procedure and generally concur with those specific findings presented in [1].…”

“…Phys. [1]; it takes the linearized equations from some of our earlier work on interactive buckling in sandwich struts [2] and one of its claims is that rather than symmetric solutions being important, sometimes antisymmetric solutions become the preferred mode. This is supposed to occur beyond a threshold of a certain parameter within those equations, given as a ratio involving the flexural rigidity of the individual face plates, the core stiffness and the strut length ( Figure 5 of that paper); a fact apparently "overlooked" by the original authors of [2].…”

“…Before opening the detailed discussion, there follows a summary list of our observations: • The observed antisymmetric modes in [1] are clearly triggered when local buckling, rather than global (overall) buckling, is critical. • The linearized system of equations used for all the arguments in [1] cannot be used to model the case where local buckling is critical, since the load is fixed to the global critical buckling load within that system.…”

“…• The linearized system of equations used for all the arguments in [1] cannot be used to model the case where local buckling is critical, since the load is fixed to the global critical buckling load within that system. The local buckling modes at other axial loads would be different [3], since these would be governed by an equation for a structure similar to the strut on a Pasternak foundation.…”

“…This model is more intricate than the simpler Winkler foundation, since it includes the effect of shear within the foundation [4]. • The boundary condition used in [1] for the in-plane displacement gradient u is not an energy minimizer. Hence, the solutions are not valid equilibrium states for the mechanical system modeled.…”