Investigation into the nonlinear structural behavior of tapered axially functionally graded material beams utilizing absolute nodal coordinate formulations

Abstract This study investigates the nonlinear structural behavior of axially functionally graded material beams composed of steel and aluminum through a systematic computational approach. Three absolute nodal coordinate formulation (ANCF)-based approaches were applied: the first employs a planar ANCF shear deformable beam element, the second utilizes an enhanced continuum mechanics-based ANCF element, and the third leverages a higher order ANCF beam element. The research methodology follows a rigorous stepwise analysis: first, the accuracy of the ANCF beam elements was verified through a convergence study; second, a large deformation analysis was carried out focusing on the effect of material nonlinearity; third, comprehensive buckling analyses were conducted, including both nonlinear postbuckling evaluation using Crisfield’s arc-length method and nonlinear eigenvalue buckling estimation via a dichotomy scheme, identifying the complex nonlinear behavior and demonstrating the variation in critical loads depending on material gradation profiles, respectively. The overall results demonstrate the ANCF framework’s effectiveness in capturing complex geometric and material nonlinearities. This study highlights the mechanical tradeoffs between steel dominated regions and aluminum rich zones, providing insights for the design of graded structural components in advanced engineering applications. It was also found that the ANCF-based higher order beam element provides more accurate and reliable deflection curves than other beam models.