Geometry-Exact Inverse Finite Element Method for Flexible Curved Beam Structures: The Method for Strain Decoupling and Dynamic Reconstruction

To address the failure of strain-displacement de-coupling in the existing inverse finite element method (iFEM) framework for dynamically evolving curved structures, this study proposes a geometrically nonlinear deformation reconstruction method for curved beams based on the geometrically exact beam theory. The proposed method innovatively integrates the Frenet–Serret kinematic framework to establish a strain-decoupled model in the manifold coordinate system, which can accurately describe the characterization of the geometrically nonlinear deformation of curved beams. A coupled framework between the Frenet frame and iFEM is proposed and a transformation relationship between the deformation field of curved beams and the curvature tensor is established. Additionally, a curvature-threshold-controlled incre-mental iterative algorithm is presented and the curvature-adap-tive displacement functions are constructed based on the NURBS basis functions to effectively improve displacement reconstruction accuracy under large deflection conditions. Experimental test re-sults demonstrate that the proposed method maintains the recon-struction accuracy within 5% suffered from small to large defor-mation based on cantilevered and simply supported curved beams under multiple loading conditions. Therefore, the curvature-driven iFEM framework can be used as a significant approach to enhance the deformation sensing capability of complex curved structures and provide a robust theoretical tool for real-time shape monitoring of flexible curved structures.