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

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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).

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Abbreviations

Φ :

Stacking sequence of all partitions

Φ tc :

Design domain satisfying manufacturing consideration

P k :

k-order control points of Bezier curve

α :

Reduction coefficient of overall pre-deformation structure’s thickness

g j :

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

σ i, τ ij :

Stress components

ε i, γ ij :

Strain components

Q ij :

The Q matrix coefficients in kth ply

F i, F ij :

Strength coefficients related to strength parameters

F. I.:

Failure index of the Tsai-Wu failure criterion

g 1 :

Failure function corresponding to constraints of strength

S z :

Shearing strength

g 2 :

Failure function for the sake of illustration

u 0, v 0, w 0 :

Displacements of the point in mid-plane

θ x, θ y :

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

C s :

Stiffness matrixes of shearing

ε 0 :

The vector of strains

κ :

The vector of bending curvature of mid-plane

w :

Deflection of the bay door

D ref :

The displacement constraint that the structure needs to satisfy

D max :

The maximum displacement caused by external forces

g 3 :

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

g j :

The overall structure failure constraints function of strength and stiffness

q(t i):

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

z i :

The global variables in each disciplinary

x i :

The local variables in each disciplinary

z 0 :

The global variables containing constants

x 0 :

The local variables containing constants

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Funding

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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Authors and Affiliations

  1. Institute of Solid Mechanics, School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, People’s Republic of China

    Xiaojun Wang, Yiru Cai & Xinyu Geng

  2. Beijing Aerospace Technology Institute, China Aerospace Science and Industry Aerodynamicsn Technology Academy, Beijing, 100074, People’s Republic of China

    Yiru Cai

  3. Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing, 100094, People’s Republic of China

    Xinyu Geng

Authors
  1. Xiaojun Wang
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  2. Yiru Cai
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  3. Xinyu Geng
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Correspondence to Xiaojun Wang.

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Wang, X., Cai, Y. & Geng, X. Integrated optimization of composite bay door with pre-deformation and variable thickness design. Struct Multidisc Optim 59, 1673–1684 (2019). https://doi.org/10.1007/s00158-018-2155-4

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