Buckling of shear deformable polymer/clay nanocomposite columns with uncertain material properties by multiscale modeling

Buckling of shear deformable columns is studied taking the variations in the material properties into account. The material of the column is specified as a polymer/clay nanocomposite and the properties of the components, i.e., elastic constants of the polymer and clay platelets, are taken as uncertain-but-bounded. The elastic constants of the nanocomposite are determined via a micromechanical approach. The uncertainties in the matrix and the reinforcement propagate to the bending and shear stiffnesses which, in turn, lead to an uncertain buckling load expression. The least favorable value of the buckling load is obtained via convex modeling corresponding to the worst case material properties. The effects of the uncertain material parameters of the polymer/clay nanocomposite on the buckling load are investigated numerically.