Shape sensing of variable cross-section beam using the inverse finite element method and isogeometric analysis

•This paper proposes a new iFEM method for reconstructing displacement field of variable cross-section beam.•Mechanical parameters are linearized, and the new constitutive equations are established.•This paper presents a new approach to approximate and instead of the original displacement field func...

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Veröffentlicht in:	Measurement : journal of the International Measurement Confederation Jg. 158; S. 107656
Hauptverfasser:	Zhao, Feifei, Xu, Libo, Bao, Hong, Du, Jingli
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	London Elsevier Ltd 01.07.2020 Elsevier Science Ltd
Schlagworte:	Concentrated loads Constitutive equations Constitutive relation Constitutive relationships Cross-sections Discrete element method Displacement Finite element analysis Finite element method Inverse finite element method Isogeometric analysis Mathematical analysis Mechanical properties Rigidity Shear strain Shear strength Smart structure Smart structures Strain Stress concentration Variable cross-section Isogeometric analysis Smart structure Variable cross-section Constitutive relation Inverse finite element method
ISSN:	0263-2241, 1873-412X
Online-Zugang:	Volltext
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Abstract	•This paper proposes a new iFEM method for reconstructing displacement field of variable cross-section beam.•Mechanical parameters are linearized, and the new constitutive equations are established.•This paper presents a new approach to approximate and instead of the original displacement field functions. The inverse finite element method (IFEM), which is used to reconstruct the displacement field from the discrete surface strain measurements, is of great significance to the management, control and driving of smart structures. However, the iFEM method based on constant cross-section beam elements proposed in previous works were no longer suitable for variable cross-section beam elements. To solve this problem, this paper proposes a new iFEM method for reconstructing the displacement field of variable cross-section beam based on isogeometric analysis. Firstly, the mechanical parameters of beam section are linearized, including section area, axial rigidity, shear rigidity, torsional rigidity and bending rigidity, and a new constitutive relations are established. Then, adhering to the constitutive equations and the small-strain hypothesis, the displacement equations of the theoretical deformation field are deduced. Nevertheless, considering that the deduced displacement equations can not be applied to the iFEM, this paper proposes a method for using isogeometric analysis instead of the original function, and the least-square method is used to establish the strain-displacement relation. Finally, to verify the validity and accuracy of the methodology, a concentrated load and a distributed load were applied to one airfoil in the experiment tests. The predicted displacements with previous iFEM and presented iFEM are compared with those experimentally measured values, respectively. The results show that the presented iFEM exhibited higher accuracy than the previous iFEM in the variable cross-section beam problem.
AbstractList	The inverse finite element method (IFEM), which is used to reconstruct the displacement field from the discrete surface strain measurements, is of great significance to the management, control and driving of smart structures. However, the iFEM method based on constant cross-section beam elements proposed in previous works were no longer suitable for variable cross-section beam elements. To solve this problem, this paper proposes a new iFEM method for reconstructing the displacement field of variable cross-section beam based on isogeometric analysis. Firstly, the mechanical parameters of beam section are linearized, including section area, axial rigidity, shear rigidity, torsional rigidity and bending rigidity, and a new constitutive relations are established. Then, adhering to the constitutive equations and the small-strain hypothesis, the displacement equations of the theoretical deformation field are deduced. Nevertheless, considering that the deduced displacement equations can not be applied to the iFEM, this paper proposes a method for using isogeometric analysis instead of the original function, and the least-square method is used to establish the strain-displacement relation. Finally, to verify the validity and accuracy of the methodology, a concentrated load and a distributed load were applied to one airfoil in the experiment tests. The predicted displacements with previous iFEM and presented iFEM are compared with those experimentally measured values, respectively. The results show that the presented iFEM exhibited higher accuracy than the previous iFEM in the variable cross-section beam problem. •This paper proposes a new iFEM method for reconstructing displacement field of variable cross-section beam.•Mechanical parameters are linearized, and the new constitutive equations are established.•This paper presents a new approach to approximate and instead of the original displacement field functions. The inverse finite element method (IFEM), which is used to reconstruct the displacement field from the discrete surface strain measurements, is of great significance to the management, control and driving of smart structures. However, the iFEM method based on constant cross-section beam elements proposed in previous works were no longer suitable for variable cross-section beam elements. To solve this problem, this paper proposes a new iFEM method for reconstructing the displacement field of variable cross-section beam based on isogeometric analysis. Firstly, the mechanical parameters of beam section are linearized, including section area, axial rigidity, shear rigidity, torsional rigidity and bending rigidity, and a new constitutive relations are established. Then, adhering to the constitutive equations and the small-strain hypothesis, the displacement equations of the theoretical deformation field are deduced. Nevertheless, considering that the deduced displacement equations can not be applied to the iFEM, this paper proposes a method for using isogeometric analysis instead of the original function, and the least-square method is used to establish the strain-displacement relation. Finally, to verify the validity and accuracy of the methodology, a concentrated load and a distributed load were applied to one airfoil in the experiment tests. The predicted displacements with previous iFEM and presented iFEM are compared with those experimentally measured values, respectively. The results show that the presented iFEM exhibited higher accuracy than the previous iFEM in the variable cross-section beam problem.
ArticleNumber	107656
Author	Bao, Hong Zhao, Feifei Xu, Libo Du, Jingli
Author_xml	– sequence: 1 givenname: Feifei orcidid: 0000-0002-7251-6802 surname: Zhao fullname: Zhao, Feifei email: ffzhao@stu.xidian.edu.cn organization: Key Laboratory of Electronic Equipment Structure Design of Ministry of Education, Xidian University, Xi’an, China – sequence: 2 givenname: Libo surname: Xu fullname: Xu, Libo organization: Shaanxi Key Laboratory of Space Solar Power Station System, Xidian University, Xi’an, China – sequence: 3 givenname: Hong surname: Bao fullname: Bao, Hong email: hbao@xidian.edu.cn organization: Key Laboratory of Electronic Equipment Structure Design of Ministry of Education, Xidian University, Xi’an, China – sequence: 4 givenname: Jingli surname: Du fullname: Du, Jingli email: jldu@mail.xidian.edu.cn organization: Key Laboratory of Electronic Equipment Structure Design of Ministry of Education, Xidian University, Xi’an, China
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Keywords	Isogeometric analysis Smart structure Variable cross-section Constitutive relation Inverse finite element method
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Snippet	•This paper proposes a new iFEM method for reconstructing displacement field of variable cross-section beam.•Mechanical parameters are linearized, and the new... The inverse finite element method (IFEM), which is used to reconstruct the displacement field from the discrete surface strain measurements, is of great...
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SubjectTerms	Concentrated loads Constitutive equations Constitutive relation Constitutive relationships Cross-sections Discrete element method Displacement Finite element analysis Finite element method Inverse finite element method Isogeometric analysis Mathematical analysis Mechanical properties Rigidity Shear strain Shear strength Smart structure Smart structures Strain Stress concentration Variable cross-section
Title	Shape sensing of variable cross-section beam using the inverse finite element method and isogeometric analysis
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