A combined experimental/numerical study on deformation sensing of sandwich structures through inverse analysis of pre-extrapolated strain measurements

Abstract

Real-time reconstruction of displacement field from a network of discrete strain sensors is referred to as “shape (deformation) sensing” for which inverse finite element method (iFEM) has been extensively studied and proven to be an efficient, robust, and accurate algorithm. In this study, practical shape-sensing capability of an enhanced iFEM formulation, which utilizes the kinematics of refined zigzag theory (RZT) as its baseline, is numerically and experimentally investigated for moderately thick sandwich plates/shells. To this end, a novel four-node inverse-shell element (iRZT4) is developed and implemented to discretize the governing equations of the iFEM-RZT formulation. Moreover, the iFEM-RZT approach is coupled with a polynomial-based strain pre-extrapolation technique to achieve a highly precise prediction for numerical and experimental case studies using different sensor deployment strategies. Various test cases namely stiffened plate and curved sandwich shells subjected to bending loads, and a wing-shaped sandwich panel exposed to torsional loading condition are solved to evaluate the performance of the iRZT4 element. For these problems, the results of iFEM-RZT analysis with/without ‘a priori’ smoothing of experimental strain data are compared with high-fidelity FEM reference solutions as well as the results of the classical iFEM formulation. In addition, through-the-thickness full-field displacement maps obtained from digital image correlation (DIC) are used to verify the iFEM and FEM results. These comparisons reveal that using a sparse sensor placement model for an iRZT4 discretization paired with the polynomial smoothing approach leads to the most precise, efficient, and reliable deformation reconstruction for moderately thick sandwich structures, among other strategies.