Shape Reconstruction Method for Monitoring Large Deformed Beam Structures

Abstract

Shape sensing refers to the deformation reconstruction of structures using measured surface strain. However, there is currently a lack of research on the shape sensing of large deformations, especially for beam structures. To address this issue, this paper proposes a new method called the rotation angle approximation (RAA) for reconstructing large deformations of beam structures. This method utilizes theoretical and actual curvatures to create a least-squares error functional. By minimizing this functional, the rotation angles of the corresponding beam can be obtained, avoiding the accumulation of errors that occurs when using traditional computation methods. The deformed shapes can be predicted utilizing the boundary conditions and the rotation angles along the beam. This method can reconstruct the large deformation of a beam without requiring prior knowledge about the material properties or external loads. The accuracy and effectiveness of this method were validated through numerical simulations and experiments. The results indicate that this method can accurately predict the different deformations of a beam induced by various loading conditions.