Structural and Multidisciplinary Optimization

, Volume 59, Issue 2, pp 539–575 | Cite as

Constrained-manufacturable stacking sequence design optimization using an improved global shared-layer blending method and its 98-line Matlab code

  • Zhao JingEmail author
  • Jianqiao Chen
  • Qin Sun


An improved global shared-layer blending method (GSLB) is suggested to address the constrained-manufacturable stacking sequence design optimization problem of tapered composite structures. First, the mathematical model for tapered composite structures design problem is constructed and the effect of blending constraint on the design space is analyzed. By introducing the set theory, the original GSLB method is improved by aggregating a shape prediction algorithm and a thickness evaluation procedure. The shape prediction algorithm takes advantage of the set computation procedure, which simplifies the process for detecting the shared layers’ boundaries. The maximum blending shared layers are evaluated by the improved GSLB in terms of the thickness distribution of multiple ply orientations. Subsequently, the obtained shared-layers are served as integrated variables for stacking sequence design, in which complex manufacturing constraints are involved. Three multi-panel structures and a wing box structure are adopted to verify the improved GSLB method and stacking sequence design strategy, and perfectly blended solutions are found without violation of manufacturing constraints and mechanical requirements. Finally, the 98 line Matlab code of the improved GSLB method is provided for the convenience of engineering application. This research has two purposes: providing a technique for tailoring design of tapered composite structures and giving reference solutions for constrained-manufacturable stacking sequence design optimization problem.


Global shared-layer blending method Tapered composite structures Stacking sequence Shared layers Manufacturing constraints 



A set to denote the appeared panels


number of subregions corresponding to a specific ply drop matrix G


A set to denote the checked panels


The ith manufacturing constraint


Number of contiguity ply drops


A region set with panels whose ply number is bigger than 1


Total design space


Design space within the domain of all panels


Design space with maximum blending constraint


Bending stiffness coefficients of the optimal stacking sequence (i, j = 1, 2, 6)

\( {D}_{ij}^{\ast } \)

Bending stiffness coefficients of the initial superply bundles (i, j = 1, 2, 6)


Vector to denote a shared layer dropped at panel j

FP × P

Matrix to denote a shared layer dropped at some panels


Vector to denote a shared layer drops or covers panel j

GP × P

Ply drop matrix


Ply drop matrix of the kth shared layer


Ply thickness


Stacking position k = 1,2,...,Q


Total weight of the structure


Total number of candidate ply orientations


Total ply number of panel i

\( {n}_j^{\theta_r} \)

Ply number of ply orientation θr in panel j (r = 1,2,...,M and j = 1,2,...,P)


Total number of panels


Total number of shared layers


Ratio of perfectly blending design space to total design space


jth subregion


Region matrix


The set to record the thickness distribution of jth subregion


Number of subregions with corresponding ply drop matrix Gt


Thickness distribution vector of ply orientation θr

TM × P

Thickness distribution matrix


number of stacking positions in a panel


Element 0 or 1 to denote the adjacent relationship of panel i and j


Adjacent matrix of a shared layer


Structural adjacent matrix


A set to denote unchecked panels


A set to denote the connect panels


Vector to denote panel j is covered by a shared layer

ZP × P

Matrix to denote all panels are covered by a shared layer


A ply orientation


The rth candidate ply orientation

\( {\theta}_{r_k} \)

The ply orientation of the kth shared layer (k = 1,2,...,Q)

θM × P

Ply orientation matrix


Stacking sequence of panel i


The elements of same shape shared-layer-matrix \( \overline{\omega} \)


Vector to denote the a same shape shared-layer with ply orientation θr

\( {\omega}_{r_k}^k \)

The kth (k = 1,2,...,Q) shared layer with ply orientation \( {\theta}_{r_k} \)

\( \overline{\omega} \)M × P

Same shape shared-layer-matrix

Ω, j

Column vector to denote stacking sequence of panel j with ply drops


Row vector to the ith shared layer


Stacking sequence matrix


Critical buckling load factor





This work is supported by the National Natural Science Foundation of China (Nos. 11572134, 51375386) and the Project funded by China Postdoctoral Science Foundation (No. 2017M612443). Thanks to the anonymous reviewers for their efforts and constructive advice to improve the study.


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Copyright information

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

Authors and Affiliations

  1. 1.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.School of AeronauticsNorthwestern Polytechnical UniversityXi’anChina

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