This study examines the nonlinear buckling response of functionally graded shallow circular nano-arches within the framework of the stress-driven nonlocal elasticity theory and Euler–Bernoulli beam kinematics. Geometric nonlinearity is incorporated through von Kármán strain–displacement relations, and the governing equations are discretized using the generalized differential quadrature method (GDQM). A possible equilibrium path, including the post-buckling regime, is traced via the arc-length method to capture potential instability phenomena. A parametric investigation is conducted to explore the influence of boundary conditions, geometric characteristics, nonlocal material length scale, gradation profile, and the extent of a partially applied transverse load on the buckling behavior. The results reveal that shallow nano-arches may exhibit multiple instability patterns, snap-back, and looping—depending on the combined effects of small-scale parameters, material gradation, loading characteristics and boundary conditions (BCs). To the authors’ knowledge, this is the first study to analyze the post-buckling behavior of functionally graded shallow nano-arches subjected to non-uniform partial loading using the stress-driven nonlocal elasticity model in conjunction with an arc-length solution strategy.
Atacan et al. (Fri,) studied this question.