Benefiting from the ability of providing reference information for deformation-control system, shape sensing technology is considered as an important way to guarantee the safety and improve the operational performance of self-adaptive morphing structures. However, the conventional optical imaging based shape sensing technologies are unable to meet the need of real-time shape sensing of self-adaptive morphing structures. In this paper, a shape sensing technology based on the inverse Finite Element Method (iFEM) and the idea of superposing segmented displacement is proposed to reconstruct the deformation of morphing wing’s major load-bearing structure of fishbone. Firstly, a four-node quadrilateral inverse-shell element is developed based on Mindlin deformation theory for the major load-bearing structure of the morphing wing. Secondly, strain sensors are used to obtain strain distribution of the structure surface as the input of the proposed method. Then the transfer function between the strain field and the displacement field can be obtained by adopting the least square variational equation. Finally, the corresponding displacement of the major load-bearing structure is reconstructed, based on which the reconstruction of wing deformation can be realized. The proposed method is verified through experiments performed on the major load-bearing structure of a morphing wing. The results show that under the deflection angles of 5°, 10°, and 15° of the morphing wing, the reconstructive displacements have a strong consistency with measured displacements, which verifies the feasibility and accuracy of the proposed method.
ZHANG Ke
,
YUAN Shenfang
,
REN Yuanqiang
,
XU Yuesheng
. Shape reconstruction of self-adaptive morphing wings’ fishbone based on inverse finite element method[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020
, 41(8)
: 223617
-223617
.
DOI: 10.7527/S1000-6893.2019.23617
[1] CHOPRA I. Review of state of art of smart structures and integrated systems[J]. AIAA Journal, 2012, 40(11):2145-2187.
[2] YIN W, FU T, LIU J, et al. Structural shape sensing for variable camber wing using FBG sensors[J]. Journal of Mechanics of Materials and Structures, 2010, 5(2):341-367.
[3] 陆宇平, 何真. 变体飞行器控制系统综述[J]. 航空学报, 2009,30(10):1906-1911. LU Y P, HE Z. A survey of morphing aircraft control systems[J]. Acta Aeronautica et Astronautica Sinica, 2009,30(10):1906-1911(in Chinese).
[4] YI J, ZHU X, ZHANG H, et al. Spatial shape reconstruction using orthogonal fiber Bragg grating sensor array[J]. Mechatronics, 2012, 22(6):679-687.
[5] 冷劲松, 孙健, 刘彦菊. 智能材料和结构在变体飞行器上的应用现状与前景展望[J]. 航空学报, 2013, 35(1):29-45. LENG J S, SUN J, LIU Y J. Application status and future prospect of smart materials and structures in morphing aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2013, 35(1):29-45(in Chinese).
[6] 袁慎芳, 闫美佳, 张巾巾,等. 一种适用于梁式机翼的变形重构方法[J]. 南京航空航天大学学报, 2014, 46(6):825-830. YUAN S F, YAN M J, ZHANG J J, et al. Shape reconstruction method of spar wing structure[J]. Journal of Nanjing University of Aeronautics and Astronautics, 2014, 46(6):825-830(in Chinese).
[7] KO W L, JACKSON R H. Multilayer theory for delamination analysis of a composite curved bar subjected to end forces and end moments[J]. Composite Structures, 1989, 19:173-198.
[8] WANG Z, WANG J, SUI Q, et al. Deformation reconstruction of a smart Geogrid embedded with fiber Bragg grating sensors[J]. Measurement Science and Technology, 2015, 26(12):125202.
[9] FOSS G C, HAUGSE E D. Using modal test results to develop strain to displacement transformations[J]. Aerospace Science and Technology, 2007, 10:16-29.
[10] TESSLER A, SPANGLER J. An inverse finite element method for application to structural health monitoring[J] Journal of Composite Materials, 2009, 43(9):1051-1081.
[11] KEFAL A, OTERKUS E. Displacement and stress monitoring of a Panamax containership using inverse finite element method[J]. Ocean Engineering, 2016, 119:16-29.
[12] KEFAL A, OTERKUS E. Displacement and stress monitoring of a chemical tanker based on inverse finite element method[J]. Ocean Engineering, 2016, 112:33-46.
[13] GHERLONE M, CERRACCHIO P, MATTONE M, et al. Shape sensing of 3D frame structures using an inverse finite element method[J]. International Journal of Solids and Structures, 2012, 49(22):3100-3112.
[14] ALBANESI A, BRE F, FACHINOTTI V, et al. Simultaneous ply-order, ply-number and ply-drop optimization of laminate wind turbine blades using the inverse finite element method[J]. Composite Structures, 2018, 184:894-903.
[15] KEFAL A, YILDIZ M. Modeling of sensor placement strategy for shape sensing and structural health monitoring of a wing-shaped sandwich panel using inverse finite element method[J]. Sensors, 2017, 17(12):2775.
[16] PAPA U, RUSSO S, LAMBOGLIA A, et al. Health structure monitoring for the design of an innovative UAS fixed wing through inverse Finite Element Method (iFEM)[J]. Aerospace Science and Technology, 2017, 69:439-448.
[17] KIM H, HAN J, BANG H. Real-time deformed shape estimation of a wind turbine blade using distributed fiber Bragg grating sensors[J]. Wind Energy, 2014, 17(9):1455-1467.
[18] KEFAL A, OTERKUS E. Displacement and stress monitoring of a chemical tanker based on inverse finite element method[J]. Ocean Engineering, 2016, 112:33-46.
[19] KEFAL A, YILDIZ M. Modeling of sensor placement strategy for shape sensing and structural health monitoring of a wing-shaped sandwich panel using inverse finite element method[J]. Sensors, 2017, 17(12):2775-2786.
[20] LIU M, WANG L, YUN K, et al. Study on the deformation measurement and reconstruction of heavy-duty machine column based on FBG sensor[J]. Smart Structures and Materials, 2013, 10(2):88-100.
[21] GHERLONE M, CERRACCHIO P, MATTONE M. Shape sensing methods:Review and experimental comparison on a wing-shaped plate[J]. Progress in Aerospace Sciences, 2018, 99:56-63.
[22] LI L, ZHONG B S, LI W Q, et al. Structural shape reconstruction of fiber Bragg grating flexible plate based on strain modes using finite element method[J]. Journal of Intelligent Material Systems and Structures, 2017, 5(12):104-125.
[23] MIELOSZYK M, SKARBEK L, KRAWCZUK M, et al. Application of fibre Bragg grating sensors for structural health monitoring of an adaptive wing[J]. Smart Materials & Structures, 2011, 20(12):125-144.