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A constraint satisfaction problem algorithm for large-scale multi-panel composite structures

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Abstract

This paper proposes a constraint satisfaction problem algorithm based on implicit decision trees and dynamic programming for the design of multiple composite panels subjected to a set of blending rules and external forces. This decision tree is built incrementally on the ‘fly’, adding plies from a particular set, and does not require any guiding laminate or stacking sequence table for blending purposes. The upper bound algorithm complexity is provided in this work. The technique is applied to the design of a well-known composite multi-panel problem addressed in previous studies; the novel procedure exhibits high-quality solutions (in terms of structure weight) and low computational cost (in terms of laminate evaluations). The novel algorithm scalability is also checked showing that the node tree expansion is independent of the number of panels to be designed. This algorithm could therefore be a suitable choice for large-scale multi-panel design problems.

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Abbreviations

BB:

Building block

BFS:

Breadth-first search

λ:

Lambda Buckling scaling load

CFRP:

Carbon fiber reinforced plastic

CLT:

Classical laminate theory

FSD:

Fully stressed design

FEM:

Finite element method

GA:

Genetic algorithm

RHS:

Right-hand side

P:

Polynomial complexity

NP:

Non-polynomial complexity

SST:

Stacking sequence table

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  1. Meletea Engineering Solutions S.L.U, Calle Estella 10, 1° Izda, 31002, Pamplona, Navarra, Spain

    Javier Sanz-Corretge

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  1. Javier Sanz-Corretge
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Correspondence to Javier Sanz-Corretge.

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In this appendix A, all laminate stacking sequences obtained in Sect. 4.1 are shown using different tables. Tables 4, 5, 6, and 7 are linked to the solutions depicted in Figs. 4, 5, 6, and 7, respectively

In this appendix A, all laminate stacking sequences obtained in Sect. 4.1 are shown using different tables. Tables 4, 5, 6, and 7 are linked to the solutions depicted in Figs. 4, 5, 6, and 7, respectively

The number of plies, minimum λ, number of tree expansions, and the panel labels (according to the identification numbers indicated in Fig. 3) solved are included in these tables.

Table 4 Laminate stacking sequences for 4 BBs
Full size table
Table 5 Laminate stacking sequences for 5 BBs
Full size table
Table 6 Laminate stacking sequences for 6 BBs
Full size table
Table 7 Laminate stacking sequences for 7 BBs
Full size table

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Sanz-Corretge, J. A constraint satisfaction problem algorithm for large-scale multi-panel composite structures. Struct Multidisc Optim 60, 2035–2051 (2019). https://doi.org/10.1007/s00158-019-02309-4

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