In-Plane Static Behavior of Nonlocal Curved Nanobeams Resting on an Elastic Foundation Determined Using the Initial Value Method

Curved nanobeams are fundamental components of nanoscale systems, such as nano and microelectromechanical systems, where accurate modeling of small-scale effects is essential for achieving high precision. This study introduces a novel framework for analyzing the in-plane static behavior of curved nanobeams resting on an elastic foundation, particularly for small displacements. Nonlocal constitutive equations are derived based on nonlocal elasticity theory and solved using the initial value method and the approximate transfer matrix approach to address the challenges arising from the high degree of statical indeterminacy. A convergence analysis is conducted, showing that the proposed method provides a systematic and computationally efficient solution. A parametric analysis reveals that the nonlocal parameter, elastic foundation, and opening angle significantly influence the displacements in the tangential and normal directions, the rotation and bending moment in the binormal direction, the shear force in the normal direction, and the axial force in the tangential direction. These findings further elucidate the mechanics of curved nanostructures, contributing to the design and optimization of nanoscale devices.