Warping-inclusive bending behavior of out-of-plane loaded axially functionally graded circular and cycloidal nanobeams

Hadidane A. C., NOORI A. R., ASLAN T. A.

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2026 (SCI-Expanded, Scopus)

Özet

This study conducts an out-of-plane bending analysis of axially functionally graded (AFG) circular and cycloidal nanobeams utilizing nonlocal elasticity theory. Regarding the methodology the governing equations are expressed in curvilinear coordinates and resolved utilizing the Complementary Functions Method (CFM) in conjunction with a fifth-order Runge–Kutta (RK5) algorithm, facilitating precise assessment of displacements, rotations, and internal forces without discretizing the domain. This study primarily contributes to the existing literature by obtaining the canonical equations for AFG nano circular and cycloidal beams. Additionally, it marks the initial implementation of the CFM to address this particular class of problems.The influence of key parameters on the structural response is evaluated. The findings indicate that elevating the beam height significantly diminishes transverse displacement and rotations, demonstrating improved stiffness. Larger curvature radii lead to enhanced deformation, signifying increased structural flexibility. The nonlocal parameter induces a distinct softening effect, primarily influencing displacement fields, whereas material gradation significantly governs stiffness, particularly under clamped–clamped boundary conditions. Cycloidal nanobeams demonstrate heightened sensitivity to geometric and material alterations relative to circular designs, underscoring their potential for adjustable structural performance. In conclusion, the suggested formulation establishes an effective and dependable framework for the analysis of curved nanostructures and yields significant insights for the creation of sophisticated nano-engineered systems.