Geometrically nonlinear deformation reconstruction of based on Euler-Bernoulli beam theory using a nonlinear iFEM algorithm

Deformation reconstruction plays a vital role in the structural health monitoring systems. The inverse finite element method (iFEM) has been demonstrated to be an accurate and robust method of deformation reconstruction. Current iFEM formulations have been applied to the linear deformation of structures based on small-displacement assumption. However, the assumption is inapplicable to some structures with large displacements in practical engineering. Therefore, the geometric nonlinearity needs to be considered in deformation reconstruction model. In this paper, a novel nonlinear iFEM algorithm is proposed based on strain gradient theory. The advantage of the proposed iFEM is that the nonlinear responses does not need to be linearized, which eliminates the influence of the improper strain linearization on stability of reconstruction displacements. The simulation analyses and experimental tests are used to verify the proposed nonlinear iFEM method. Numerical results show that the large displacements can be accurately predicted and the nonlinear iFEM algorithm can improve the reconstruction accuracy by 9% as compared to the linear iFEM strategy. Hence, the proposed nonlinear iFEM approach can be used as a viable tool to accurately reconstruct geometrically nonlinear deformations of structures in real-time applications.