Buckling and sensitivity analysis of nonlocal orthotropic nanoplates with uncertain material properties

Abstract

Accurate estimates of the orthotropic properties of nano-materials are usually not available due to the difficulties in making measurements at nano-scale. However the values of the elastic constants may be known with some level uncertainty. In the present study an ellipsoidal convex model is employed to study the biaxial buckling of a rectangular orthotropic nanoplate with the material properties displaying uncertain-but-bounded variations around their nominal values. Such uncertainties are not uncommon in nano-sized structures and the convex analysis enables to determine the lowest buckling loads for a given level of material uncertainty. The nanoplate considered in the present study is modeled as a nonlocal plate to take the small-size effects into account with the small-scale parameter also taken to be uncertain. Method of Lagrange multipliers is applied to obtain the worst-case variations of the orthotropic constants with respect to the critical buckling load. The sensitivity of the buckling load to the uncertainties in the elastic constants is also investigated. Numerical results are given to study the effect of material uncer- tainty on the buckling load.