Stress-Driven Nonlocal Modeling and Arc-Length Simulation of Post-Buckling Behavior of Functionally Graded Shallow Nano-Arches Under Partial Loading

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.