Coupling of discrete shear projection method and inverse finite element method for accurate deformation reconstruction of plates with different thickness

Official URL: https://dx.doi.org/10.1016/j.tws.2026.115063

The inverse finite element method (iFEM) is a powerful framework for structural shape perception. However, thin and thick plates exhibit different deformation behaviors, requiring corresponding adjustments to the iFEM formulation to achieve high-precision deformation reconstruction. This thickness dependency limits its applicability across diverse engineering scenarios. To overcome this limitation, this study proposes an enhanced iFEM capable of achieving high-accuracy deformation reconstruction for both thin and thick plates with a unified algorithm. The proposed approach introduces two key advancements. First, the Discrete Shear Projection Method (DSPM) is integrated into the conventional iFEM formulation to establish a shear-strain correction matrix that adaptively calibrates theoretical strains according to plate thickness, thereby bridging thin- and moderately thick-plate theories within a single unified model. Second, for triangular inverse elements, temporary mid-side nodes are incorporated to construct a higher-order displacement field, significantly improving the representation of complex deformation modes. The numerical and experimental validations confirm the accuracy, robustness, and generality of the proposed method. Compared with traditional iFEM formulations, the unified enhanced iFEM achieves up to 55% improvement in reconstruction accuracy, demonstrating its strong engineering relevance and broad potential for practical implementation in real-world structural monitoring applications.