Analytical solutions to buckling analysis of sandwich composite plates with uncertain material properties and dimensions

Structures that have thin cross-sections and are prone to compressive loads may buckle suddenly at critical load values. To calculate the critical buckling load, researchers have reported many analytical solutions which are related mainly to the deterministic approach. However, the important geometric and material parameters highly affect critical buckling loads of structures and they should be considered as uncertain in order to obtain realistic estimations. This is due to the fact that imperfections in the geometry and material properties may occur during the production stages of a component or under operational conditions. In the present study, which is based on first-order shear deformation theory (FSDT), in the first step the deterministic buckling equation of symmetric sandwich composite plates consisting of two identical carbon/epoxy skins and a foam core between the skins is formulated considering the uncertainties which can occur in the nondeterministic state. In the next step, closed-form analytical buckling equations including the geometric and material uncertainties are derived using the convex modeling and Lagrange multiplier method and based on the worst-case scenario leading to the lowest buckling loads. Sensitivity analysis is also conducted to understand which uncertain parameters have the most negative effect on the critical buckling load. Finite element analysis (FEA) is implemented to validate the derived equations. It is seen that even minor variations in the material properties and geometric dimensions lead to considerable variations in the critical buckling load. The significance of involving the uncertainty in the analysis is explained both qualitatively and quantitatively.