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


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).


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



Stacking sequence of all partitions


Design domain satisfying manufacturing consideration


k-order control points of Bezier curve


Reduction coefficient of overall pre-deformation structure’s thickness


Overall structure failure function corresponding to constraints of strength and stiffness


Compliance coefficients


Vectors of strain in laminated composite


Vectors of stress in laminated composite

σi, τij

Stress components

εi, γij

Strain components


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


Failure function corresponding to constraints of strength


Shearing strength


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


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


Stiffness matrixes of tensile


Stiffness matrixes of coupling


Stiffness matrixes of bending


Stiffness matrixes of shearing


The vector of strains


The vector of bending curvature of mid-plane


Deflection of the bay door


The displacement constraint that the structure needs to satisfy


The maximum displacement caused by external forces


Failure function corresponding to constraints of stiffness


Structural weight

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

The thicknesses of super layers


The overall structure failure constraints function of strength and stiffness


Interpolation corresponding to point ti


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


The global variables


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


The global variables in each disciplinary


The local variables in each disciplinary


The global variables containing constants


The local variables containing constants


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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