Accurate and flexible shape sensing of shell structures with polygonal inverse finite element method

The inverse Finite Element Method (iFEM) based on triangular and quadrilateral elements faces significant challenges in complex shell structures due to slow convergence or poor mesh quality. In this study, a novel variable-node polygonal iFEM is developed to enhance the accuracy and flexibility of shape sensing for complex shell structures. Shear and membrane behaviors are respectively improved by the Mixed Interpolation of Tensorial Components (MITC) method and the Strain-Smoothed Element (SSE) method. Moreover, the precision of shape sensing at low mesh densities is improved through a polygonal Smoothing Element Analysis (SEA) method and an iFEM paradigm for curved shell elements based on MITC. Finally, numerical examples demonstrate that the polygonal iFEM achieves high-precision deformation reconstruction with less strain data, supports flexible mesh refinement and strain sensor deployment, and meets the shape sensing demands of shell structures with complex shapes and load conditions.