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

Gherlone, Marco; Cerracchio, Priscilla; Mattone, Manuela; Sciuva, Marco Di; Tessler, Alexander

doi:10.1016/j.ijsolstr.2012.06.009

Cited by 176 publications

(143 citation statements)

References 16 publications

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“…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).…”

Section: Ifem Algorithms For Beam Estimationmentioning

confidence: 99%

“…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.…”

Section: Minimum Number Of the Section Strain Location Selectionmentioning

confidence: 99%

“…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.…”

Section: Verificationmentioning

confidence: 99%

“…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).…”

Section: Verificationmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Zhao

Bao

Fang

2017

International Journal of Aerospace Engineering

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A frame deformation estimation algorithm is investigated for the purpose of real-time control and health monitoring of flexible lightweight aerospace structures. The inverse finite element method (iFEM) for beam deformation estimation was recently proposed by Gherlone and his collaborators. The methodology uses a least squares principle involving section strains of Timoshenko theory for stretching, torsion, bending, and transverse shearing. The proposed methodology is based on staindisplacement relations only, without invoking force equilibrium. Thus, the displacement fields can be reconstructed without the knowledge of structural mode shapes, material properties, and applied loading. In this paper, the number of the locations where the section strains are evaluated in the iFEM is discussed firstly, and the algorithm is subsequently investigated through a simple supplied beam and an experimental aluminum wing-like frame model in the loading case of end-node force. The estimation results from the iFEM are compared with reference displacements from optical measurement and computational analysis, and the accuracy of the algorithm estimation is quantified by the root-mean-square error and percentage difference error.

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Section: Ifem Algorithms For Beam Estimationmentioning

confidence: 99%

Section: Minimum Number Of the Section Strain Location Selectionmentioning

confidence: 99%

Section: Verificationmentioning

confidence: 99%

Section: Verificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Zhao

Bao

Fang

2017

International Journal of Aerospace Engineering

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

Luo

Gao

et al. 2019

Struct Control Health Monit

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Summary In the existing studies of strain‐based displacement field detection for thin rectangular plate, either the boundary conditions are too difficult to handle or the sensors layout and algorithm computing process are too complex to satisfy the requirement of rapid reconstruction of nonlinear vibration shape. In this paper, a strain‐displacement conversion method for reconstructing the deformed shape of rectangular plate with typical boundary conditions is presented. This method overcomes the above shortcomings for small deflection nonlinear vibration in linear elastic range. Strains measuring points are uniformly and regularly distributed in the middle area of the plate. Unmeasurable boundary strains will be estimated using the new derived formula according to quadratic interpolation of strains and boundary conditions. The principle of the proposed method is to bridge the orthogonal deflection curves by translating and rotating them. In this way, framework of displacement field can be formed. First, curvature integral method is employed to shape the orthogonal deflection curves of deformed plate. Then, the rotating angles and translating displacements are deduced according to boundary conditions. For some special boundary plates, it even needs to solve nonlinear optimization problem to get the rotating angles. The displacement field reconstructed by the proposed method shows great agreement with the finite element analyses results, which verifies the effectiveness of the methodology.

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Shape Sensing with Inverse Finite Element Method on a Composite Plate Under Compression Buckling

Oboe

Colombo

Sbarufatti

et al. 2021

Lecture Notes in Civil Engineering

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

Cited by 176 publications

References 16 publications

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

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

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

Shape Sensing with Inverse Finite Element Method on a Composite Plate Under Compression Buckling

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