Geometrically nonlinear deformation reconstruction based on iQS4 elements using a linearized iterative iFEM algorithm

Official URL: https://dx.doi.org/10.1007/s10338-022-00369-6

Structural shape monitoring plays a vital role in the structural health monitoring systems. The inverse finite element method (iFEM) has been demonstrated to be a practical method of deformation reconstruction owing to its unique advantages. Current iFEM formulations have been applied to small deformation of structures based on the small-displacement assumption of linear theory. However, this assumption may be inapplicable to some structures with large displacements in practical applications. Therefore, geometric nonlinearity needs to be considered. In this study, to expand the practical utility of iFEM for large displacement monitoring, we propose a nonlinear iFEM algorithm based on a four-node inverse quadrilateral shell element iQS4. Taking the advantage of an iterative iFEM algorithm, a nonlinear response is linearized to compute the geometrically nonlinear deformation reconstruction, like the basic concept of nonlinear FE analysis. Several examples are solved to verify the proposed approach. It is demonstrated that large displacements can be accurately estimated even if the in-situ sensor data includes different levels of randomly generated noise. It is proven that the nonlinear iFEM algorithm provides a more accurate displacement response as compared to the linear iFEM methodology for structures undergoing large displacement. Hence, the proposed approach can be utilized as a viable tool to effectively characterize geometrically nonlinear deformations of structures in real-time applications.