Shape sensing of the thin-walled beam members by coupling an inverse finite element method with a refined quasi-3D zigzag beam theory

Abstract

In structural safety field, the inverse finite element method (iFEM) is an effective methodology to reconstruct full-field displacement on beam, plate and shell structures, independently of the loading conditions and of the material properties. However, the current iFEM in principle requires uniform shear distribution over the thickness of beam, which is practically hardly possible due to these thin-walled beam with the general cross-section shape, such as I-section beam, hat-section beam and box-section beam, and there is no effective method to realize deformation online monitoring at home and abroad. To relieve this issue, a novel iFEM strategy is proposed to establish the shape sensing model of the thin-walled beam, where the thin-walled beam is replaced with an equivalent layered composite one based on a generalized layered global-local beam (GLGB) theory, and the improved quasi-3D zigzag shear deformation theory is presented to describe deformation field of the equivalent layered composite beam. The proposed iFEM method accounts for not only thickness stretching but also interlaminar continuity of shear stresses and displacements. Besides, the proposed iFEM formulation does not need any shear correction factors. Accuracy and effectiveness of the established shape sensing model are demonstrated through several case studies. The numerical results show that the proposed iFEM can accurately reconstruct the deformation of the thin-walled structure and the reconstruction accuracy can be improved by 5 %.