Out‐of‐plane static analysis of curved nanobeams resting on an elastic foundation using the method of initial values

Abstract The unique mechanical properties and versatile applications of curved nanobeams have gained significant attention among researchers, as understanding their mechanical behavior is essential for precise control at the atomic scale. In this study, the out‐of‐plane static behavior of curved nanobeams resting on an elastic foundation is investigated for small displacements within the framework of nonlocal elasticity theory. Nonlocal constitutive equations are derived and solved using the initial value method, with the approximate transfer matrix approach employed to obtain the principal matrix, ensuring systematic and accurate solutions. A detailed parametric study is conducted to highlight the effects of the nonlocal parameter, opening angle, and elastic foundation interactions on displacements, rotation angles, bending moments, and shear forces. The findings emphasize the critical role of these effects in accurately predicting the mechanical behavior of curved nanoscale structures. The results of this study offer valuable insights for the design and development of curved nanobeam components in nano‐engineered materials and devices.