An inverse finite element method for beam shape sensing: theoretical framework and experimental validation

Abstract

Shape sensing, i.e., reconstruction of the displacement field of a structure from surfacemeasured strains, has relevant implications for the monitoring, control and actuation of smart structures. The inverse finite element method (iFEM) is a shape-sensing methodology shown to be fast, accurate and robust. This paper aims to demonstrate that the recently presented iFEM for beam and frame structures is reliable when experimentally measured strains are used as input data. The theoretical framework of the methodology is first reviewed. Timoshenko beam theory is adopted, including stretching, bending, transverse shear and torsion deformation modes. The variational statement and its discretization with C 0-continuous inverse elements are briefly recalled. The three-dimensional displacement field of the beam structure is reconstructed under the condition that least-squares compatibility is guaranteed between the measured strains and those interpolated within the inverse elements. The experimental setup is then described. A thin-walled cantilevered beam is subjected to different static and dynamic loads. Measured surface strains are used as input data for shape sensing at first with a single inverse element. For the same test cases, convergence is also investigated using an increasing number of inverse elements. The iFEM-recovered deflections and twist rotations are then compared with those measured experimentally. The accuracy, convergence and robustness of the iFEM with respect to unavoidable measurement errors, due to strain sensor locations, measurement systems and geometry imperfections, are demonstrated for both static and dynamic loadings.

Optimal Sensor Placement for Inverse Finite Element Reconstruction of Three-Dimensional Frame Deformation

“…In the Timoshenko beam theory, the displacement field of an isotropic and straight beam with constant crosssection could be represented by Cartesian coordinates as follows [15,16]:…”

“…Firstly, the three different sensor placements were compared, two of which (C1 and C2) originated from the literature [16], while the third (C3) was the proposed optimal placement (Table 1). In lieu of the 5 International Journal of Aerospace Engineering experimentally measured surface strains on the cantilevered beam, high-fidelity direct finite element analyses (ANSYS 14.5) were carried out, whereas for the beam member based on Timoshenko theory accurate modeling, a beam of 188 elements was employed.…”

“…Due to the fact that only the displacement-strain relationship was used, this methodology could conduct deformation reconstruction without the prior knowledge of loads, materials, and inertial damping. Furthermore, these authors reproduced the structural deformation reconstruction of the single beam under loading case of the end-node force through iFEM [16]. The simulation and test results demonstrated that the scheme could accurately reconstruct the beam structure deformation under static load and force.…”

“…The simulation and test results demonstrated that the scheme could accurately reconstruct the beam structure deformation under static load and force. Moreover, as stated in [16], the authors proposed four schemes of strain sensor placement and discovered that the locations where the strain sensors were placed would affect the deformation reconstruction accuracy, but the location selection for the sensor placement to retain the accuracy of reconstruction was not mentioned. Consequently, it was necessary to discover a common strategy to optimize the placement of strain sensors to guarantee the accuracy and stability of structural deformation reconstruction in iFEM.…”

Strain‐based displacement field reconstruction method for thin rectangular plate through orthogonal deflection curves bridging

“…Because of the robustness, effectiveness, and efficiency of the algorithm, many researchers performed a further study of the method and applied it in different structures. [29][30][31][32][33][34][35][36][37][38][39] However, the method requires different strain components of a measuring point, which brings challenge to the measure technique and the distribution of strain sensors.…”