Geometrically nonlinear deformation reconstruction of membrane structures using inverse finite element method

Official URL: https://dx.doi.org/10.1063/5.0329264

Shape sensing (deformation reconstruction) is a crucial step of structural health monitoring, and it can be effectively solved by using the inverse finite element method (iFEM). In this study, a nonlinear iFEM formulation is developed to solve full-field large displacements of plane solids utilizing experimental strain data of sensors. To this end, Green-Lagrange strains are used to calculate analytical section strains, and a Newton-Rapson iterative solution is employed for the displacement predictions. In this context, a nonlinear extension of a well-known iQS4 (four-node inverse quad shell) element is presented by considering membrane (in-plane) deformations. The predictive capability of the nonlinear element is compared with the linear one by solving a fishpole bending problem with sparse strain measurements. It is demonstrated that the nonlinear element outperforms the linear one when the structure undergoes large displacements.