A Generalized Approach for Reconstructing the Three-Dimensional Shape of Slender Structures Including the Effects of Curvature, Shear, Torsion, and Elongation

Abstract

This paper extends the approach for determining the three-dimensional global displaced shape of slender structures from a limited set of scalar surface strain measurements. It is an exhaustive approach that captures the effect of curvature, shear, torsion, and elongation. The theory developed provides both a determination of the uniaxial strain (in a given direction) anywhere in the structure and the deformed shape, given a set of strain values. The approach utilizes Cosserat rod theory and exploits a localized linearization approach that helps to obtain a local basis function set for the displacement solution in the Cosserat frame. For the assumed deformed shape (both the midcurve and the crosssectional orientation), the uniaxial value of strain in any given direction is obtained analytically, and this strain model is the basis used to predict the shape via an approximate local linearized solution strategy. Error analysis due to noise in measured strain values and in uncertainty in the proximal boundary condition is performed showing uniform convergence with increased sensor count.

3D small strain large deflection beam shape sensing including poisson effect

“…The shearing deformation can be taken into account by assuming that the cross sections still remain rigid but are no longer perpendicular to the neutral axis, such as formulated in the Timoshenko beam theory. It is then possible to reconstruct the beam shape by taking into account this additional deformation type such as in Chadha et al [6].…”

Strain Gauges Based 3D Shape Monitoring of Beam Structures Using Finite Width Gauge Model

“…The topic of using strain measures for beam shape monitoring has been widely covered in the litterature on both theoretical [10,11,12,13,14] and applied aspects, such as needles deflections during medical intervention [4,5,15] or bridge deformation over time [16]. The strain measures are acquired through technologies such as strain gauges [10,13,17], or fiber Bragg gratings [16,18,19,20,21] and are used to obtain deformations of the beam.…”

“…The strain measures are acquired through technologies such as strain gauges [10,13,17], or fiber Bragg gratings [16,18,19,20,21] and are used to obtain deformations of the beam. Depending on the orientations of the sensors these measures can be used to recover the different deformations of the beam such as bending [12], torsion [22] and shearing and elongation [14]. The strain measures are thus used as inputs in a reconstruction method to obtain the structure deformed shape.…”

“…The strain measures are thus used as inputs in a reconstruction method to obtain the structure deformed shape. The reconstruction methods proposed in the literature are either two dimensional [10,11,16,17,18,23] or three dimensional [12,14,19,20,21] depending on the deformation hypothesis made.…”

Nonlinear Vibration of Orthotropic Rectangular Membrane Structures Including Modal Coupling

“…Applications utilizing membrane structures are prevalent, ranging from traditional areas in mechanical engineering, civil engineering, space and aeronautics, etc. [1,2] to more modern areas such as robotics, biological devices, and musical instruments [3,4]. This is mainly because this type of structure is both relatively lightweight and highly flexible, which are often requirements for this diverse range of applications.…”