Shape sensing of 3D frame structures using an inverse Finite Element Method

The Application Research of Inverse Finite Element Method for Frame Deformation Estimation

“…A beam deflection estimation algorithm was developed by Gherlone and his collaborators [20]. In the algorithm, the Timoshenko beam theory is first used to analyze the expression of the displacement field in a straight beam element ( Figure 1).…”

“…Although the displacement shape function and the number of surface strain measurements in different loading cases have been discussed in [20,21], n, the number of the sections where the section strains are distributed in, is not shown clearly. In (11), once the problem-dependent displacement boundary conditions are determined, the nonsingularity of the equation will depend on the selection of n. In our investigation, it is found that n can be determined by a specific loading case.…”

“…The frame was composed of three solid beams and middle plates; the span of each beam L = 640 mm and the radius R = 10 mm (see Figure 5). For the solid circular cross section, the shear correction factors are k 2 y = k 2 z = 0 887 [21]. In our verification, every whole solid beam is regarded as one beam element.…”

“…For the end-node static loads, the displacement field of the whole beam element is interpolated by C 0 continuous shape function and the number of required strain sensors is 6 (see [21]). As the radius of the beam element is small (R = 10 mm) and the grid length of every fiber grating sensor is 10 mm, it is difficult to stick the six strain gauges on one section; six fiber optic strain gauges are placed on two different sections along the beam (Table 1).…”

“…The beam-deformed displacement and cross-sectional torsion were reconstructed by Gherlone et al who employed the inverse finite element formulation to achieve high reconstruction accuracy of deformed displacement [20][21]. The authors first used the Timoshenko beam theory to model the beam kinematic accurately, then used the C 0 or C 1 inverse frame elements and least squares formulation to establish the relationship between the measured strain and the arbitrary node displacement field of the beam element with no prior knowledge of the finite element model and loads.…”