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2018 Vol.31, Issue 4 Preview Page
Cross-sectional Optimization of a Human-Powered Aircraft Main Spar using SQP and Geometrically Exact Beam Model

기하학적 정밀 보 이론 및 SQP 기법에 의한 인간동력항공기 Main Spar 단면 설계 최적화 연구

Seung-Hoon Kang1
,
Byeong-Uk Im1
,
Hae-Seong Cho2
,
Sang-Joon Shin1†
강 승 훈1
,
임 병 욱1
,
조 해 성2
,
신 상 준1†
1Department of Mechanical and Aerospace Engineering, Seoul Nat’l Univ., Seoul, 08826, Korea
2Institute of Advanced Machines and Design, Seoul Nat’l Univ, Seoul, 08826, Korea
1서울대학교 기계항공공학부
2서울대학교 정밀기계설계공동연구소
†Corresponding author: Tel: +82-2-880-1608; E-mail: ssjoon@snu.ac.kr
2018. pp. 183-190
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Abstract

This paper presents optimization of the main spar of Human-Powered Aircraft (HPA) wing. Mass minimization was attempted, while considering large torsional deformation of the beam. Sequential Quadratic Programming (SQP) method was adopted as a relevant tool to conduct structural optimization algorithm. An inner diameter and ply thicknesses of the main spar were selected as the design variables. The objective function includes factors such as mass minimization, constant tip bending displacement, and constant tip twist of the beam. For estimation of bending and torsional deformation, the geometrically exact beam model, which is appropriate for large deflection, was adopted. Properties of the cross sectional area which the geometrically exact beam model requires were obtained by Variational Asymptotic Beam Sectional Analysis (VABS), which is a cross sectional analysis program. As a result, maintaining tip bending displacement and tip twist within 1.45%, optimal design that accomplished 7.88% of the mass reduction was acquired. By the stress and strain recovery, structural integrity of the optimal design and validity of the present optimization procedure were authenticated.

Keywords
human-powered aircraft
structural optimization
sequential quadratic programming
geometrically exact beam model
VABS
stress/strain recovery

본 논문에서는 보의 대변형 및 비틀림 변형을 고려한 인간동력항공기 주익 main spar 질량 최적화 과정을 소개한다. 순차 적 이차 프로그래밍 기법(sequential quadratic programming)을 최적화 기법으로 선정해 구조 최적설계에 적절한 최적화 알 고리즘을 수행하였다. Main spar 내부 직경, 적층 두께 등을 설계변수로 설정하였다. 목적함수에는 질량 최소화, 굽힘 변형 변위 일정, 그리고 비틀림 변형 각도 일정 등의 요소를 포함하였다. 굽힘과 비틀림 변형 계산엔 대변형 해석에 적합한 기하 학적 정밀 보 모델을 도입하였으며, 기하학적 정밀 보 모델에 필요한 단면 물성은 Variational Asymptotic Beam Sectional Analysis(VABS) 단면 해석프로그램를 통해 계산하였다. 그 결과 main spar의 굽힘 변형 및 비틀림 변형을 최대 1.45% 이 내로 유지한 채로 7.88%의 질량 감소를 이루는 최적설계를 도출하였다, 이후 응력복원 및 변형률 복원을 통해 최적설계의 구조적 안정성과 최적화 과정의 타당성을 검증하였다.

키워드
인간동력항공기
구조 최적화
순차적 이차 프로그래밍
기하학적 정밀 보 모델
VABS
응력/변형률 복원
References
1
Ahn, S.H. (2016) A Study on Stress Recovery Analysis of Dimensionally Reducible Composite Beam Structure with High Aspect Ratio using VABS, J. Comput. Struct. Eng. Inst. Korea, 29(5), pp.405∼411.
10.7734/COSEIK.2016.29.5.405
2
Berdichevskii, V. (1981) On the Energy of an Elastic Rod, J. Appl. Math. &Mech., 45(4), pp.518∼529.
10.1016/0021-8928(81)90097-6
3
Cheng, T. (2002) Structural Dynamics Modeling of Helicopter Blades for Computational Aeroelasticity, M.S. Thesis, Massachusetts Institute of Technology, p.180.
4
Danielson, D.A., Hodges, D.H. (1988) A Beam Theory for Large Global Rotation, Moderate Local Rotation, and Small Strain, J. Appl. Mech., 55(1), pp.179∼ 184.
10.1115/1.3173625
5
Hodges, D.H. (1990) A Mixed Variational Formulations Based on Exact Intrinsic Equations for Dynamics of Moving Beams, Int. J. Solids &Struct., 25(11), pp.1253~1273. 10.1016/0020-7683(90)90060-90020-7683
10.1016/0020-7683(90)90060-9
6
Crossref reports the volume should be "26", not "25". (Ref. "Hodges, 1990")
7
Jang. J.H., Koo. H.M., Ahn. S.H. (2017) Computation of Energy Release Rates for Slender Beam through Recovery Analysis and Virtual Crack Closure Technique, J. Comput. Struct. Eng. Inst. Korea, 30(1), pp.31∼37.
10.7734/COSEIK.2017.30.1.31
8
Kogiso, N., Tsushima, T., Murotsu, Y. (2000) Wing Planform Optimization of Human Powered Aircraft in Low Reynolds Number Range, AIAA-2000-4739, AIAA, USA, p.10.
10.2514/6.2000-4739
9
Lee, C.R., Park, J.W., Go, E.S., Choi, J.S., Kim, I.G., Kim, B.S. (2013) HPA Structure Design and Power Measurement, Aerosp. Eng. &Technol., 12(2), pp.209~220.
10
Nocedal, J., Wright, S.J. (2006) Numerical Optimization, Springer-Verlag, New York, p.664.
11
Vanderhoydonck, B., Santo, G., Vierendeels, J., Degroote, J. (2016) Optimization of a Human-Powered Aircraft Using Fluid-Structure Interaction Simulations, Aerosp., 3(3), pp.1~25. 10.3390/aerospace3030026
10.3390/aerospace3030026
12
Schittkowski, K., Zillober, C., Zotemantel, R. (1994) Numerical Comparison of Nonlinear Programming Algorithms for Structural Optimization, Struct. Optim., 7(1), pp.1∼28.
10.1007/BF01742498
13
Yu, W., Volovoi, V.V., Hodges, D.H., Hong, X. (2002) Validation of the Variational Asymptotic Beam Sectional Analysis(VABS), AIAA J., 40(10), pp.2105∼2133.
10.2514/2.1545
14
Yu, W. (2011) VABS Manual for Users, http://analyswift.com/wp-content/uploads/2012/10/VABS-Manual.pdf (accessed May., 6, 2018)
Information
  • Publisher :Computational Structural Engineering Institute of Korea
  • Publisher(Ko) :한국전산구조공학회
  • Journal Title :Journal of the Computational Structural Engineering Institute of Korea
  • Journal Title(Ko) :한국전산구조공학회 논문집
  • Volume : 31
  • No :4
  • Pages :183-190
  • Received Date : 2018-05-21
  • Revised Date : 2018-06-20
  • Accepted Date : 2018-06-21
  • DOI :https://doi.org/10.7734/COSEIK.2018.31.4.183
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