A Unified Measurement Method for Shape Sensing of Plate Structure

This study proposes an enhanced inverse finite-element method (iFEM) for reconstructing the deformation of homogeneity structures, including thin to thick plate models. The methodology develops the explicit relation between the structural mid-plane deformation field by biharmonic function and discrete surface strain measurements consistent with scaled boundary element theory. The present method fills the gap in existing iFEM for the deployment of strain sensors and expands the engineering application of iFEM based on single-surface (top/bottom) strain information. In addition, the algorithm accommodates for the effect of transverse shear strain measurements on reconstructing accuracy, and the calculated process of shear strain measurement based on discrete surface strain is formulated by the equilibrium equations of elasticity theory and strain–stress constitutive relation. Overall, by performing the shape sensing of an array antenna plate model subjected to different loading cases, the accuracy and applicability of the present method are numerically and experimentally validated for various thickness–width ratio plate structures.