# A novel technique for the design of hybrid composite laminates based on dynamic programming and dynamic tree trimming

## Abstract

This paper proposes a novel technique for the design of hybrid composite laminates. The method explores design space with several implicit decision trees in order to obtain the Pareto front, applying a number of manufacturing and structural considerations. The research is carried out using a parallelized breadth first search algorithm aided by dynamic programming and dynamic tree trimming; as a consequence the searching process is significantly accelerated. This novel procedure is applied to a well-known design case, where it identifies the best carbon-epoxy and glass-epoxy laminate combinations in terms of weight versus cost, and finds the Pareto front with less computational effort than alternative methods used in the past to solve the same problem. Since a full set of feasible solutions is produced with this new methodology, some important conclusions are obtained regarding hybrid laminate design criteria.

## Keywords

Discrete multi-objective optimization Hybrid laminate design Dynamic programming Pareto front Optimum laminate stacking sequence Decision trees Graph theory## Abbreviations

- BB
Building block

- BFS
Breadth-first search

- CFRP
Carbon fiber reinforced plastic

- COV
Covariance operator

- CLT
Classical laminate theory

- DTT
Dynamic tree trimming

- FSD
Fully stressed design

- GA
Genetic algorithm

- GFRP
Glass fiber reinforced plastic

- OT
Order tree

- OOP
Object oriented programming

- NSGA
Non-sorted dominated GA

- PDP
Parallel dynamic programming

- RHS
Right-hand side

- SF
Structural safety factor

- VAR
Variance operator

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