Shape reconstruction of plane beam with finite deformation based on absolute nodal coordinate formulation

被引：0
|
作者：
Wu M. [1 ]
Tan S. [1 ,2 ]
Gao F. [1 ]
机构：
[1] State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian
[2] Key Laboratory of Advanced Technology for Aerospace Vehicles of Liaoning Province, Dalian University of Technology, Dalian
来源：
Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics | 2021年 / 53卷 / 10期
关键词：
Absolute nodal coordinate formulation (ANCF); Finite deformation; Inverse finite element method; Plane beam; Shape reconstruction;
D O I：
10.6052/0459-1879-21-338
中图分类号：
学科分类号：
摘要：
Most of the existing researches on deformation reconstruction of flexible structures with finite deformation are only based on the geometric relationship between curvature and strain, which ignores the longitudinal deformation and the coupling effect of the longitudinal deformation and the bending deformation. In order to construct a more accurate deformation reconstruction method which can be extended with the help of existing mechanical tools, this paper takes the plane beam as the object, partially inherits inverse finite element method developed by Tessler A, and regards the deformation reconstruction problem of plane beam as a kind of numerical optimization problem. Firstly, by introducing the absolute nodal coordinate formulation (ANCF) into the description of mapping relationship between strain and displacement, an inverse gradient reduced ANCF plane beam element is derived. Secondly, the inverse ANCF element is modified to simplify the degree of freedom of nodes and ensure the C2 continuity at nodes by introducing the penalty function, which not only ensures the problem is well-posed, but also improves the accuracy of the final result. Finally, based on the inverse ANCF element, the Newton method is used to develop two types of algorithms for deformation reconstruction under different working conditions, one is the element-by-element algorithm and the other is the multi-element algorithm. The numerical simulation results show that the reconstruction relative error of this method is less than 1% under the condition of large deformation, and it still maintains high accuracy under the condition of few measuring points. The convergence and computational efficiency of the method are verified by numerical simulation example. © 2021, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.
引用
收藏
页码：2776 / 2789
页数：13
相关论文
共 36 条
  • [11] Gherlone M, Cerracchio P, Mattone M, Et al., An inverse finite element method for beam shape sensing: theoretical framework and experimental validation, Smart Materials&Structures, 23, 4, (2014)
  • [12] Groh R, Tessler A., Computationally efficient beam elements for accurate stresses in sandwich laminates and laminated composites with delaminations, Computer Methods in Applied Mechanics&Engineering, 320, pp. 369-395, (2017)
  • [13] Roy R, Tessler A, Surace C, Et al., Shape sensing of plate structures using the inverse finite element method: investigation of efficient strain-sensor patterns, Sensors, 20, 24, (2020)
  • [14] Kefal A, Tessler A, Oterkus E., An enhanced inverse finite element method for displacement and stress monitoring of multilayered composite and sandwich structures, Composite Structures, 179, pp. 514-540, (2017)
  • [15] Kefal A, Tabrizi IE, Yildiz M, Et al., A smoothed iFEM approach for efficient shape-sensing applications: Numerical and experimental validation on composite structures, Mechanical Systems and Signal Processing, 152, (2020)
  • [16] Oboe D, Colombo L, Sbarufatti C, Et al., Shape sensing of a complex aeronautical structure with inverse finite element method, Sensors, 21, 4, (2021)
  • [17] Li T, Cao M, Li J, Et al., Structural damage identification based on integrated utilization of inverse finite element method and pseudo-excitation approach, Sensors, 21, 2, (2021)
  • [18] Ko WL, Richards WL, Tran VT., Displacement theories for in-flight deformed shape predictions of aerospace structures, (2007)
  • [19] Yi JC, Zhu XJ, Zhang HS, Et al., Spatial shape reconstruction using orthogonal fiber Bragg grating sensor array, Mechatronics, 22, 6, pp. 679-687, (2012)
  • [20] Roesthuis RJ, Kemp M, Dobbelsteen JJ, Et al., Three-dimensional needle shape reconstruction using an array of fiber bragg grating sensors, IEEE/ASME Transactions on Mechatronics, 19, 4, pp. 1115-1126, (2014)
1234