Counting and generating manufacturable composite stacking sequences efficiently
Counting and Sampling Manufacturable Stacking Sequences
Discrete MathematicsComputational Engineering, Finance, and ScienceFormal Languages and Automata Theory
Summary
Creating the order and orientation of layers in composite materials is tricky because of strict manufacturing rules and performance guidelines. The paper’s authors explain a precise way to represent all allowed layer sequences using a mathematical model called an automaton. This lets them count and pick valid sequences quickly without testing each one by trial and error. They also show how to check partial designs early to avoid impossible paths, improving design efficiency.
What this means in practice
- •For composite material designers: Efficiently generate and count valid stacking sequences obeying manufacturing constraints to reduce design iterations in composite parts.
- •For aerospace engineers: Optimize composite laminate designs by quickly eliminating layer sequences that can never meet production rules, saving simulation time.
- •For automated manufacturing software developers: Incorporate exact admissibility checks into composite design tools to ensure generated sequences are manufacturable by construction.$Commercial implications: Enables development of design software that guarantees manufacturable stacking sequences, adding value for aerospace and automotive composite manufacturers.
Authors
Alessio Langiu, Felice Rubino, Giacomo Canale
Abstract
Designing the stacking sequence of a composite laminate is a discrete optimisation problem: each ply takes one of a few orientations, each evaluation may cost a finite-element solve, and the design must obey manufacturing rules and design guidelines, which optimisers enforce by penalty, repair or rejection. We describe the admissible set exactly. The two manufacturing rules forbid a finite set of factors, so the sequences they admit form a regular language, recognised by an automaton that tracks the last orientation and the length of its run; balance and the ten per cent rule constrain the Parikh vector and are carried by a dynamic program over automaton state and counters. One table, polynomial in N, counts the admissible sequences without producing them, draws them uniformly, and tells whether a partial sequence can still be completed. We give pseudocode, exact counts for three orientation sets, closed-form ceilings on the composition, and four of the five single-rule entries a published table left uncomputed. At 48 plies, 99.8% of the nodes of a layer-wise search tree checking the rules locally have no admissible completion on eight orientations; the completion test removes them. A one-point crossover that cuts two admissible parents only where they share an automaton state and their child closes the counters returns admissible children by construction.