Shape Sensing of Beams with Complex Cross-sections Using the Inverse Finite Element Method

Abstract

This paper presents the iFEM formulation for beams with complex cross-sectional profiles having at most one plane of symmetry. As the iFEM has already been successfully used for the shape sensing of beams with circular or rectangular cross sections, this work paves the way for formulating a generalized one-dimensional beam element, applicable for any kind of cross-section. Challenges arising due to the asymmetry of the profile, in regard to sensor placement on the surface of the beam and accurate prediction of transverse shear strain measures from experimental strain measurements are addressed. The new formulation is illustrated with the specific case of a beam with a symmetric airfoil profile (NACA 0016), subjected to symmetrically and asymmetrically applied static load conditions.