Shape sensing of plate structures through coupling inverse finite element method and scaled boundary element analysis

Abstract

This study proposes an enhanced inverse finite element method (iFEM) to reconstruct the structural displacements based on strain data collected from single surface (top/bottom) of the structure. The method eliminates the drawback of existing iFEM formulations for which the strain sensors must be symmetrically installed on both top and bottom surfaces of the structure with respect to its mid-plane. Therefore, the present approach increases the practical application of shape sensing with a lower number of sensors. To this end, the least-squares variational principle of iFEM is established using scaled boundary method, which represents the displacement field of structure by scaling the boundary in the radial direction with a scaling factor. Moreover, a novel five-node inverse plate element is developed to discretize the geometry and approximate the kinematic variables of the present approach. This element increases the order of interpolation function and thus reduces the number of strain sensors used in shape-sensing process. Overall, the accuracy and applicability of the present iFEM is numerically and experimentally validated by performing shape sensing analyses of various plate structures.