Size-dependent snap buckling behavior of functionally graded sinusoidal shallow nano-arches supported by elastic horizontal springs using the stress-driven nonlocal approach

Abstract

This study investigates the nonlocal nonlinear snap-through instability of functionally graded (FG) sinusoidal shallow nano-arches with horizontal spring supports under sinusoidal vertical loading. To capture sizedependent behavior, the stress-driven nonlocal elasticity theory is employed, as it addresses the inconsistencies associated with the strain-driven nonlocal model. The geometric nonlinearity is incorporated via the von Karman strain theory within the framework of the Euler-Bernoulli beam theory. The principle of virtual work is used to derive the equilibrium equations and the boundary conditions for the spring supports. The resulting governing differential equations are transformed into algebraic equations via the generalized differential quadrature method. Nonlinear equilibrium paths are traced by surpassing the limit points using the displacement-controlled Newton-Raphson method. The snap-through buckling load, corresponding central deflection, the intensity of the snap-through buckling, and the horizontal support reactions are determined numerically. The results reveal that the nonlinear response of the elastically supported FG sinusoidal shallow nano-arches is significantly influenced by the combined effects of the nonlocal parameter, support stiffness, modular ratio, power-law index, and modified slenderness. Each parameter exhibits distinct effects in the local and nonlocal regimes, emphasizing the importance of accounting for their interaction in the design of nanostructural systems.