Static and sensitivity analysis of nonlocal nanobeams subject to load and material uncertainties by convex modeling

At the nano-scale, loads acting on a nanobeam and its material properties are likely to be not known precisely, i.e., uncertain. In the present paper, the deflection of a nanobeam subject to load and material uncertainties is studied by convex modeling of the uncertainties. The level of uncertainty is taken to be bounded and the maximum deflection corresponding to the worst-case of loading or material properties is obtained, that is, the uncertainties are determined so as to maximize the deflection. The sensitivity of the deflection to the uncertainty in the material properties is also investigated. Numerical results are given relating the level of uncertainty to maximum deflection.