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Structural and Multidisciplinary Optimization

, Volume 59, Issue 5, pp 1673–1684 | Cite as

Integrated optimization of composite bay door with pre-deformation and variable thickness design

  • Xiaojun WangEmail author
  • Yiru Cai
  • Xinyu Geng
Research Paper
  • 152 Downloads

Abstract

The paper presents an integrated design approach of composite bay door with pre-deformation and variable thickness optimization. Firstly, design and optimization of functional composite curved surface are discussed. To avoid adopting locking mechanism, a design of pre-deformation is used in aircraft bay door to keep the door closed. In this paper, the curve of composite bay door is considered as part of design variables. By means of the internal forces caused by the deformation of curve, the aircraft bay door could be able to fix in target position firmly and stably. The pre-deformation of bay door is controlled by particular parametric Bezier curve, which provides abundant changing range to meet the needs. Secondly, the variable thickness optimization of composite laminates is introduced. To take full advantage of designability of composites, variable thickness design is actualized through partitioning in bay door, not only considering the weight reduction of the structure, but also ensuring the enough strength and stiffness in the critical load positions where the strength and stiffness requirements are harsh. Furthermore, the integrated optimization is carried out based on the method of concurrent subspace optimization (CSSO).

Keywords

Composite laminate optimization Pre-deformation Variable thickness Aircraft bay door CSSO 

Nomenclature

Φ

Stacking sequence of all partitions

Φtc

Design domain satisfying manufacturing consideration

Pk

k-order control points of Bezier curve

α

Reduction coefficient of overall pre-deformation structure’s thickness

gj

Overall structure failure function corresponding to constraints of strength and stiffness

S

Compliance coefficients

ε

Vectors of strain in laminated composite

σ

Vectors of stress in laminated composite

σi, τij

Stress components

εi, γij

Strain components

Qij

The Q matrix coefficients in kth ply

Fi, Fij

Strength coefficients related to strength parameters

F. I.

Failure index of the Tsai-Wu failure criterion

g1

Failure function corresponding to constraints of strength

Sz

Shearing strength

g2

Failure function for the sake of illustration

u0, v0, w0

Displacements of the point in mid-plane

θx, θy

Angles of normal line of the mid-plane relative to x- and y-axes

N

Matrixes of in-plane force, moment, and shearing force in mid-plane

A

Stiffness matrixes of tensile

B

Stiffness matrixes of coupling

D

Stiffness matrixes of bending

Cs

Stiffness matrixes of shearing

ε0

The vector of strains

κ

The vector of bending curvature of mid-plane

w

Deflection of the bay door

Dref

The displacement constraint that the structure needs to satisfy

Dmax

The maximum displacement caused by external forces

g3

Failure function corresponding to constraints of stiffness

W

Structural weight

\( {t}_0^i,{t}_{90}^i,{t}_{\pm 45}^i \)

The thicknesses of super layers

gj

The overall structure failure constraints function of strength and stiffness

q(ti)

Interpolation corresponding to point ti

m

The order of the Bezier curve

\( f\left(z,x,\overset{\sim }{y}\right) \)

Objective function of system-level

\( g\left(z,x,\overset{\sim }{y}\right) \)

Constrain function in system-level

z

The global variables

x

The local variables

\( f\left({z}_i,{z}_0,\cdots, \overset{\sim }{y_j}\right) \)

Objective function of disciplinary-level

\( g\left({z}_i,{z}_0,\cdots, \overset{\sim }{y_j}\right) \)

Constrain function in disciplinary-level

zi

The global variables in each disciplinary

xi

The local variables in each disciplinary

z0

The global variables containing constants

x0

The local variables containing constants

Notes

Funding information

The work is supported by the National Key Research and Development Program (No. 2016YFB0200700), the National Nature Science Foundation of the P.R. China (No. 11872089, No. 11572024, No. 11432002), and the Defense Industrial Technology Development Program (No. JCKY2017601B001, No. JCKY2016601B001) for the financial supports.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Solid Mechanics, School of Aeronautic Science and EngineeringBeihang UniversityBeijingPeople’s Republic of China
  2. 2.Beijing Aerospace Technology InstituteChina Aerospace Science and Industry Aerodynamicsn Technology AcademyBeijingPeople’s Republic of China
  3. 3.Qian Xuesen Laboratory of Space TechnologyChina Academy of Space TechnologyBeijingPeople’s Republic of China

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