Shape Sensing for the Large Deflection of Euler-Bernoulli Beam Structure Using Inverse Finite Element Method

In this paper, an innovative iFEM algorithm is presented to investigate the large deformation based on Lagrangian displacement theory. Initially, the components of displacement vector are presented, and the differential relations are deduced based on the geometrical relations. Then, Variational Iteration Method-II (VIM-II) are employed to solve the governing equations and the rotation function is presented, where isogeometric analysis is used to study the deformation filed. Next, the reconstruction model is established and the corrected method for the axial strain measurement is proposed. Finally, static validation cases regarding cantilever beam with rectangle cross-section subjected to different transverse loads are discussed, and the nonlinear and linear iFEM method are employed to reconstruct the deformation, respectively, which are compared with theoretical displacements. The experimental results demonstrate that the nonlinear iFEM can accurately and robustly predict the displacements and provide promising applicability potential in the structural health monitoring system of smart structure.