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

Abstract

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.