Experimental and numerical investigation on large deformation reconstruction of thin laminated composite structures using inverse finite element method

The inverse finite element method (iFEM) is one of the best candidates to perform displacement monitoring (shape sensing) of structures using a set of on-board/embedded strain sensors. This study demonstrates the high efficiency, robustness, and accuracy of the iFEM approach to reconstruct geometrically non-linear deformations of thin laminated plates and shells by performing experimental measurements and numerical analyses. The iFEM formulation is derived based on the first-order shear deformation theory of plates. A weighted least-squares variational principle is utilized with incremental non-linear strains while performing the geometrical update of the model using predicted incremental deformations. Moreover, a quadrilateral inverse-shell element (iQS4) is employed to discretize the whole domain of the laminated panels and solve the numerical/experimental shape-sensing problems. Further, a polynomial strain pre-extrapolation technique is incorporated with the iQS4 formulation to smoothen the discrete strain data obtained from a few strain rosettes placed along the entire length of the structures. For each case study, a high-fidelity finite element analysis is performed to establish a reference displacement solution. Finally, the qualitative and quantitative comparison of reconstructed displacement results with reference solutions confirms the superior potential of the iFEM-iQS4 approach for full-field shape sensing of thin laminates undergoing non-linear deformations.