Nonlinear structural stability of functionally optimized sandwich structures

Abstract

Sandwich structures arc an efficient form of construction but can suffer from nonlinear interaction phenomena that can erode their load carrying capacity. This interaction is triggered at a secondary bifurcation point and is manifested as a localized deformation wave in the most compressed face plate which destabilizes and drastically reduces its load carrying capacity. The current work advances some recent analytical work on mode interaction and localization in sandwich struts by extending and developing the model for different geometries and material parametric design. In the first part, a nonlinear analytical model for investigating localized interactive buckling in simply supported, thin-face plate sandwich struts with weak cores, is extended to account for local deformations in both face plates, which have been observed in experiments and finite element simulations. The original model is based on the total potential energy principles with large displacement assumptions. It assumes Timoshenko shear deformable theory for the core and approximates the overall mode as a half-sine wave along the length of the strut while the local face plate displacements are initially unknown and are found as solutions of the governing equations. The extended model is able to capture measurable local face plate displacements in the less compressed face plate, beyond the secondary bifurcation which leads to localized interactive buckling, for the case where overall buckling is critical. Moreover, the allowance of local displacements in both face plates allows the extended model to predict the postbuckling behavior better in cases where local buckling is critical. The results from this model compare very well with nonlinear finite element simulations with respect to both the equilibrium paths and panel deformations. In the second part, two analytical model for interactive buckling in sandwich struts with cores made from a functionally graded material based on the total potential energy principles are presented. Each model is derived from a different shear deformation theory, namely Timoshenko Beam Theory (TBT) and Reddy-Bickford Theory (RBT). Parametric results from the analytical models are compared with geometrically nonlinear simulations using ANSYS general purpose finite clement package. Good agrement is found, and this offers encouragement for more elaborate models to be devised that can account for face-core interface dclamination, an area where functionally graded materials could offer mitigating design solutions.