Nonlinear deformation monitoring of elastic beams based on isogeometric iFEM approach

Abstract

Shape sensing plays a key role in Structural Health Monitoring (SHM) and has become an excellent methodology for large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an accurate and efficient method for shape sensing to reconstruct the three-dimensional displacements using in situ surface strain data. This study proposes a novel shape sensing method for large deformation monitoring based on strain gradient theory and iFEM method. Initially, the nonlinear displacement fields are described, and Green–Lagrange strain theory is employed to deduce the theoretical section strains, and then the strain–displacement relation is established by using a least-squares variational principle. Next, isogeometric displacement functions and the measured section strain formulations are deduced, and a decoupling method for high order section strains is proposed. Finally, a cantilever beam is used to demonstrate the accuracy and effectiveness of the refined isogeometric iFEM method for large deformations. The numerical results show the superior reconstruction capability and potential applicability of the proposed model for accurate shape prediction of the non-linear deformation of beam structure.