Ottimizzazione di pannelli a rigidezza variabile attraverso il metodo PSO

The present work studies optimization of aeronautic panels characterized by in-plane variable stiffness. Specifically are considered two different structural solutions: variable stiffness composite panels called VSP, and the panels with curvilinear stiffeners. The developed optimization's code is based on the particle swarm technique (PSO), an heuristic and adaptive algorithm suitable for multimodal problem's optimization. The algorithm is based on the swarm intelligence to look for the optimum of a function expressed in the explicit form. It has been defined also a specific methodology for the management of constraints on the function's internal values. This method speeds up the whole optimization process and allows to establish how the constraints implementation could affect the solution. The optimization code, developed in Matlab, must be coupled with a second code used to analize the finite element of the structure. This code has to generate, analyze and read the results of the FEM model of panels in relation to the input variables. To contrive the FEM analysis of variable stiffness composites panels are defined different fiber's directions for each finite element. The analysis made have covered different buckling solutions in term of fiber's direction in relation to the different kind of loads, constraints and lamina stacking. Various configurations have been studied showing how the stiffness is distributes the prebuckling loads to the boundaries of the panels. For the developed PSO method was also created an environment for the topological definition of stiffeners on panels subjected to buckling analysis. To do so, an automated generator of curvilinear stiffened panels was developed. This generator creates the models, the mesh, manages the buckling analysis and reads the response. With these tools were studied stiffened panels with different geometric definition of the stiffeners subjected to different loads and constraints, analyzing their stiffness distribution.The present work studies optimization of aeronautic panels characterized by in-plane variable stiffness. Specifically are considered two different structural solutions: variable stiffness composite panels called VSP, and the panels with curvilinear stiffeners. The developed optimization's code is based on the particle swarm technique (PSO), an heuristic and adaptive algorithm suitable for multimodal problem's optimization. The algorithm is based on the swarm intelligence to look for the optimum of a function expressed in the explicit form. It has been defined also a specific methodology for the management of constraints on the function's internal values. This method speeds up the whole optimization process and allows to establish how the constraints implementation could affect the solution. The optimization code, developed in Matlab, must be coupled with a second code used to analize the finite element of the structure. This code has to generate, analyze and read the results of the FEM model of panels in relation to the input variables. To contrive the FEM analysis of variable stiffness composites panels are defined different fiber's directions for each finite element. The analysis made have covered different buckling solutions in term of fiber's direction in relation to the different kind of loads, constraints and lamina stacking. Various configurations have been studied showing how the stiffness is distributes the prebuckling loads to the boundaries of the panels. For the developed PSO method was also created an environment for the topological definition of stiffeners on panels subjected to buckling analysis. To do so, an automated generator of curvilinear stiffened panels was developed. This generator creates the models, the mesh, manages the buckling analysis and reads the response. With these tools were studied stiffened panels with different geometric definition of the stiffeners subjected to different loads and constraints, analyzing their stiffness distribution.The present work studies optimization of aeronautic panels characterized by in-plane variable stiffness. Specifically are considered two different structural solutions: variable stiffness composite panels called VSP, and the panels with curvilinear stiffeners. The developed optimization's code is based on the particle swarm technique (PSO), an heuristic and adaptive algorithm suitable for multimodal problem's optimization. The algorithm is based on the swarm intelligence to look for the optimum of a function expressed in the explicit form. It has been defined also a specific methodology for the management of constraints on the function's internal values. This method speeds up the whole optimization process and allows to establish how the constraints implementation could affect the solution. The optimization code, developed in Matlab, must be coupled with a second code used to analize the finite element of the structure. This code has to generate, analyze and read the results of the FEM model of panels in relation to the input variables. To contrive the FEM analysis of variable stiffness composites panels are defined different fiber's directions for each finite element. The analysis made have covered different buckling solutions in term of fiber's direction in relation to the different kind of loads, constraints and lamina stacking. Various configurations have been studied showing how the stiffness is distributes the prebuckling loads to the boundaries of the panels. For the developed PSO method was also created an environment for the topological definition of stiffeners on panels subjected to buckling analysis. To do so, an automated generator of curvilinear stiffened panels was developed. This generator creates the models, the mesh, manages the buckling analysis and reads the response. With these tools were studied stiffened panels with different geometric definition of the stiffeners subjected to different loads and constraints, analyzing their stiffness distribution.

Il presente lavoro tratta l’ottimizzazione di pannelli aeronautici caratterizzati da una rigidezza variabile nel piano. Nello specifico si considerano due configurazioni: pannelli in materiale composito a fibre curvilinee, detti variable stiffness panels (VSP), e pannelli con irrigidimenti curvilinei. Il codice di ottimizzazione sviluppato si basa su metodo particle swarm (PSO), algoritmo di tipo euristico ed evolutivo, idoneo all’ottimizzazione di problemi multimodali. L’algoritmo è ispirato al comportamento degli sciami, il cui movimento è utilizzato come strategia per identificare la soluzione ottima. É stata definita inoltre una metodologia particolare nella gestione dell’ottimizzazione vincolata tramite una variazione dei parametri che regolano l’imposizione dei vincoli. Tale metodo di gestione dell’ottimizzazione si è dimostrato interessante sia perché permette di comprendere l’influenza dei vincoli sul risultato, sia perchè garantisce un significativo aumento di velocità di indagine del minimo. L’ottimizzatore, sviluppato in ambiente Matlab, è interfacciato con un secondo codice, adibito all’analisi ad elementi finiti della struttura. Quest’ultimo ha il compito di generare il modello FEM in relazione alle variabili in ingresso, di effettuare l’analisi e di leggerne i risultati. I modelli FEM dei pannelli a rigidezza variabile sono realizzati assegnando diverse orientazioni del materiale ai vari elementi. Con questo metodo è dunque possibile ottimizzare la direzione delle fibre di materiale composito nelle diverse lamine che compongono il pannello. Le analisi condotte prevedono l’applicazione di diverse condizioni di carico e l’imposizione di vincoli sulla rigidezza. É così possibile studiare la disposizione delle fibre in relazione al carico, mostrando come la rigidezza ottenuta tenda a distribuire il precarico sui bordi del pannello per massimizzarne la risposta a instabilità. La generazione dei modelli FEM di pannelli con correnti curvilinei è gestita invece con una fase di pre-processing che permette la generazione in ambiente Python di un modello con la geometria, i vincoli e i carichi voluti. Di questa geometria è effettuata in seguito la discretizzazione ad elementi finiti e la relativa analisi. In questo modo è possibile studiare diverse configurazioni di pannelli con correnti curvilinei, per diversi tipi di carico e definizioni dei correnti. Lo strumento di analisi e ottimizzazione realizzato rappresenta un primo passo verso la più dettagliata comprensione dei potenziali vantaggi offerti dai correnti curvilinei. Limitatamente ad alcuni casi preliminari, si è dimostrata la possibilità di ottenere dei benefici in termini di carico critico. Grazie alla robustezza del codice generato, in futuro esso potrà essere utilizzato per estendere lo studio a condizioni di carico più realistiche. Con quanto fatto si è quindi dimostrata anche la possibilità di gestire l’ottimizzazione topologica di pannelli irrigiditi con vincoli sulla massa tramite generazione automatica del modello.