Stress-driven nonlinear behavior of curved nanobeams

A nonlocal stress-driven model for geometrically nonlinear behavior of a shallow arch under radial pressure is presented. The analytical nonlinear equilibrium equation and also buckling equations by variational principles and virtual work are found. As it has been proven before, the strain-driven models encountered some contradictions with local equilibrium conditions, while stress-driven formulation has solved these difficulties. The simultaneous participation of the constitutive boundary conditions has led to this improvement. To obtain nonlocal strains, local nonlinear strains are incorporated in the nonlocal stress-based equations. In this way, nonlocal loads corresponding to the limit-load and bifurcation instabilities are exactly calculated by considering the effect of nanoscale and geometry parameters. In this article, the geometric limits which determine when and how the arch bifurcates, are found. The results in specific cases are compared with those available in the literature. These comparisons show the accuracy of the work. Finally, the 3D view of the equilibrium nonlinear paths, associated with the pinned curved nanobeam, are presented for different nanoscale and also geometry ratio parameters.