Mathematical Modeling and Finite Element Analysis of Torsional Divergence of Carbon Plates with an AIREX Foam Core

This study presents a novel analytical–numerical framework for investigating the torsional divergence of composite sandwich structures composed of carbon fiber-reinforced skins and an AIREX foam core. A divergence differential equation is derived and modified to accommodate the anisotropic behavior of composite materials through an equivalent shear modulus, extending classical formulations originally developed for isotropic structures. The resulting equation is solved using the Galerkin method, yielding structural section rotations as a continuous function along the wing span. These torsional modes are then applied as boundary inputs in a high-fidelity finite element model of the composite fin to determine stress distributions across the structure. The method enables evaluation of not only in-plane (membrane) stresses, but also out-of-plane responses such as interlaminar stresses and local core-skin interactions critical for assessing failure modes in sandwich composites. This integrated workflow links analytical aeroelastic modeling with detailed structural analysis, offering valuable insights into the interplay between global torsional stability and local stress behavior in laminated composite systems.