An enhanced inverse beam element for shape estimation of beam-like structures

The inverse finite element method (iFEM) is a mechanics-based algorithm for deformed-shape estimation of structures. In this paper, an enhanced inverse beam element named iEBT2 is developed based on classical beam theory. The element formulation is derived by minimizing a weighted-errors functional that consists of experimental and numerical section strains. The improved coefficient matrix KR is always non-singular, assuring that the solution of iFEM formulation exists. Location-independent feature of matrix KR simplifies the inverse finite element modeling, especially for complicated structures. Weighting constants are utilized to define error functional, aiming to penalize the contributions from measure-less stations. Numerical and experimental cases have been performed and demonstrated excellent predictive capability when iEBT2 model has complete strain measures. In the case of missing strain components, iEBT2 enables deformation estimation and its accuracy is acceptable in general. The enhanced inverse element extends the practical usefulness of iFEM in shape-sensing analysis of civil infrastructures.

Automated summary

The enhanced inverse beam element, iEBT2, developed in this paper based on classical beam theory, minimizes a weighted-errors functional to accurately estimate the deformed shape of structures using the inverse finite element method. The improved coefficient matrix KR ensures the existence of solutions in iFEM formulation, making it a practical tool for shape-sensing analysis of civil infrastructures.