Development of wing deflection assessment methods through experimental ground tests and finite element analysis

Gharibi, Ali; Ovesy, H.R.; Khaki, Reza

doi:10.1016/j.tws.2016.08.020

Cited by 6 publications

(15 citation statements)

References 18 publications

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“…Solving the integral (14) we got the equation (6). Rewriting the equation (6) for displaying the deflection we got the equation (7). Generating the deflection curve with step 0 01 x .…”

Section: Resultsmentioning

confidence: 99%

“…Many mathematical examples of differentiating under integral sign were published by [13] Explaining the visualization of Leibnitz rule was done by [6]. The deflection of machines parts applying the Castigliano's theorem was realized by [7,17].…”

Section: Introductionmentioning

confidence: 99%

“…The error function is depicted in theFigure 5. The similar numerical problem was investigated and evaluated by[7].…”

mentioning

confidence: 99%

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Differentiating under integral sign in Castigliano’s theorem

Rédl¹

2019

MERAA

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In this contribution we are dealing with application of differentiating of function defined with determined parametrical integral. The mathematical problem was analyzed form point of view of mechanics of materials. The mathematical model of loaded beam was created. Applying the cross section method we defined the exact function of bending moment. Additional properties of cantilever joint were neglected. We showed the derivation of modified Castigliano's theorem via Leibnitz rule of differentiating under integration sign. Appling the modified Castigliano's theorem we got the exact solution of the deflection of the beam. The exact solution of beam deflection was finished in PTC Mathcad Prime software (PTC-Parametric Technology). The numerical integration of the bending moment dataset and defined deflection function was done in program written in Microsoft Visual C# 2010. The Dormand-Prince numerical integration method was used for the numerical integration. Comparing the exact and numerical solution we got the error of numerical integration solution.

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“…Solving the integral (14) we got the equation (6). Rewriting the equation (6) for displaying the deflection we got the equation (7). Generating the deflection curve with step 0 01 x .…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Differentiating under integral sign in Castigliano’s theorem

Rédl¹

2019

MERAA

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“…Based on Castigliano's second theorem [40,41], for a linearly elastic structure under loads P 1 , P 2 , P 3 , . .…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…Based on Castigliano’s second theorem [ 40 , 41 ], for a linearly elastic structure under loads

at points

, the deflection

of point j can be calculated as follows:

where

is the deflection at point n due to a unit load applied at point m , normalized by the magnitude of the load. Based on this theorem, given loads at m points, one can calculate deflections at n points, as given in matrix form in Equation ( A2 ).…”

Section: Figure A1mentioning

confidence: 99%

Realtime Localization and Estimation of Loads on Aircraft Wings from Depth Images

Bilal

Ünel

Yıldız

et al. 2020

Sensors

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This paper deals with the development of a realtime structural health monitoring system for airframe structures to localize and estimate the magnitude of the loads causing deflections to the critical components, such as wings. To this end, a framework that is based on artificial neural networks is developed where features that are extracted from a depth camera are utilized. The localization of the load is treated as a multinomial logistic classification problem and the load magnitude estimation as a logistic regression problem. The neural networks trained for classification and regression are preceded with an autoencoder, through which maximum informative data at a much smaller scale are extracted from the depth features. The effectiveness of the proposed method is validated by an experimental study performed on a composite unmanned aerial vehicle (UAV) wing subject to concentrated and distributed loads, and the results obtained by the proposed method are superior when compared with a method based on Castigliano’s theorem.

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Deflection monitoring of thin-walled wing spar subjected to bending load using multi-element FBG sensors

Zhu

Sun

et al. 2018

Optik

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Development of wing deflection assessment methods through experimental ground tests and finite element analysis

Cited by 6 publications

References 18 publications

Differentiating under integral sign in Castigliano’s theorem

Differentiating under integral sign in Castigliano’s theorem

Realtime Localization and Estimation of Loads on Aircraft Wings from Depth Images

Deflection monitoring of thin-walled wing spar subjected to bending load using multi-element FBG sensors

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