A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties

This work deals with the problem of the optimum design of a sandwich panel. The design process is based on a general two-level optimisation strategy involving different scales: the meso-scale for both the unit cell of the core and the constitutive layer of the laminated skins and the macro-scale for the whole panel. Concerning the meso-scale of the honeycomb core, an appropriate model of the unit cell able to properly provide its effective elastic properties (to be used at the macro-scale) must be conceived. To this purpose, in this first paper, we present the numerical homogenisation technique as well as the related finite element model of the unit cell which makes use of solid elements instead of the usual shell ones. A numerical study to determine the effective properties of the honeycomb along with a comparison with existing models and a sensitive analysis in terms of the geometric parameters of the unit cell have been conducted. Numerical results show that shell-based models are no longer adapted to evaluate the core properties, mostly in the context of an optimisation procedure where the parameters of the unit cell can get values that go beyond the limits imposed by a 2D model

Optimal design of sandwich plates with honeycomb core

This work deals with the problem of the optimum design of a sandwich structure composed of two laminated skins and a honeycomb core. The goal is to propose a numerical optimisation procedure that does not make any simplifying hypothesis in order to obtain a true global optimal solution for the considered problem. In order to face the design of the sandwich structure at both meso and macro scales, we use a two-level optimisation strategy. At the first level, we determine the optimum geometry of the unit cell together with the material and geometric parameters of the laminated skins, while at the second level we determine the optimal skins lay-up giving the geometrical and material parameters issued from the first level. We will illustrate the application of our strategy to the least-weight design of a sandwich plate submitted to several constraints: on the first buckling load, on the positive-definiteness of the stiffness tensor of the core, on the ratio between skins and core thickness and on the admissible moduli for the laminated skins

A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part II: the optimisation strategy

This work deals with the problem of the optimum design of a sandwich panel. The design strategy that we propose is a numerical optimisation procedure that does not make any simplifying assumption to obtain a true global optimum configuration of the system. To face the design of the sandwich structure at both meso and macro scales, we use a two-level optimisation strategy: at the first level we determine the optimal geometry of the unit cell of the core together with the material and geometric parameters of the laminated skins, while at the second level we determine the optimal skins lay-up giving the geometrical and material parameters issued from the first level. The two-level strategy relies both on the use of the polar formalism for the description of the anisotropic behaviour of the laminates and on the use of a genetic algorithm as optimisation tool to perform the solution search. To prove its effectiveness, we apply our strategy to the least-weight design of a sandwich plate, satisfying several constraints: on the first buckling load, on the positive-definiteness of the stiffness tensor of the core, on the ratio between skins and core thickness and on the admissible moduli for the laminated skins

Simultaneous shape and material optimization of sandwich panels with honeycomb core for additive manufacturing

This works deals with the problem of the optimum design of a sandwich plate composed of CFRP faces and Al honeycomb core. The proposed design strategy is a multi-scale numerical optimization procedure that does not make use of any simplifying assumption to find a global optimum configuration of the system. The goal of such a procedure consists in simultaneously optimizing the shape of the unit cell of the honeycomb core (meso-scale) and the geometrical as well as the material parameters of the CFRP laminated skins (meso and macro scales). To prove its effectiveness, the multi-scale optimization strategy is applied to the problem of the least-weight design of a sandwich panel subject to constraints of different nature: on the positive-definiteness of the stiffness tensor of the core, on the admissible material properties of the laminated faces, on the local buckling load of the unit cell of the core, on the global buckling load of the panel and geometrical as well as manufacturability constraints linked to the fabrication process of the honeycomb core

Dimensionamento preliminare di una sezione di fusoliera di un velivolo da oltre 1000 passeggeri

Il presente lavoro di tesi riguarda lo studio preliminare della fusoliera di un velivolo Prandtl Plane di grandi dimensioni. Lo scopo è verificare se, grazie al sistema portante di tipo Prandtl Plane, è possibile superare le barriere imposte dalle configurazioni convenzionali dei velivoli commerciali per creare un velivolo capace di trasportare un numero di passeggeri superiore a quello dell’A380 rispettando le massime dimensioni in pianta di 80x80 mq compatibili con gli spazi aeroportuali. Nella prima parte del lavoro è stata generata, mediante il codice ASD, la geometria esterna della fusoliera considerando aspetti strutturali e aerodinamici. Successivamente, mediante il programma di modellazione Catia è stata determinata la configurazione della cabina passeggeri e piloti. Al termine di questa fase, quindi, è stato ottenuto un layout della fusoliera che permette di ospitare circa 1500 passeggeri. Nella seconda fase è stata effettuata una valutazione di prima approssimazione del peso massimo al decollo e della superficie portante necessaria. Nell’ultima fase è stata eseguita un’analisi agli elementi finiti di un tronco di fusoliera, compreso tra l’ala anteriore e quella posteriore, per condurre un primo dimensionamento di una sezione tipica di fusoliera soggetta a carichi di manovra con e di pressurizzazione, al solo scopo di confrontare il peso a vuoto per passeggero con quello di configurazioni esistenti

Simultaneous shape and material optimization of sandwich panels with honeycomb core for additive manufacturing

This works deals with the problem of the optimum design of a sandwich plate composed of CFRP faces and Al honeycomb core. The proposed design strategy is a multi-scale numerical optimization procedure that does not make use of any simplifying assumption to find a global optimum configuration of the system. The goal of such a procedure consists in simultaneously optimizing the shape of the unit cell of the honeycomb core (meso-scale) and the geometrical as well as the material parameters of the CFRP laminated skins (meso and macro scales). To prove its effectiveness, the multi-scale optimization strategy is applied to the problem of the least-weight design of a sandwich panel subject to constraints of different nature: on the positive-definiteness of the stiffness tensor of the core, on the admissible material properties of the laminated faces, on the local buckling load of the unit cell of the core, on the global buckling load of the panel and geometrical as well as manufacturability constraints linked to the fabrication process of the honeycomb core

A mean-field homogenisation scheme with CZM-based interfaces describing progressive inclusions debonding

The objective of the present study is to describe the progressive debonding of inclusions in particle or fibre reinforced composites. To do so, the mean-field homogenisation scheme of Mori-Tanaka is enriched to take into account imperfect interfaces. The interfaces are modelled by a bilinear Cohesive Zone Model (CZM) taking into account normal and tangential effects. Results obtained with this new mean-field homogenisation scheme are compared to 2D FE-based numerical simulations that are used as reference results. The effects of inclusions volume fraction and size are also observed

On the effective integration of manufacturability constraints within the multi-scale methodology for designing variable angle-tow laminates

In this work a multi-scale two-level (MS2L) optimisation strategy for optimising VAT composites is presented. In the framework of the MS2L methodology, the design problem is split and solved into two steps. At the first step the goal is to determine the optimum distribution of the laminate stiffness properties over the structure (macroscopic scale), while the second step aims at retrieving the optimum fibres-path in each layer meeting all the requirements provided by the problem at hand (mesoscopic scale). The MS2L strategy has been improved in order to integrate all types of requirements (mechanical, manufacturability, geometric, etc.) within the first-level problem.The proposed approach relies on: a) the polar formalism for describing the behaviour of the VAT laminate, b) the iso-geometric surfaces for describing the spatial variation of both the laminate stiffness properties (macro-scale) and the layers fibres-path (meso-scale) and c) an hybrid optimisation tool (genetic and gradient-based algorithms) to perform the solution search. The effectiveness of the MS2L strategy is proven through a numerical example on the maximisation of the first buckling factor of a VAT plate subject to both mechanical and manufacturability constraints

A general multi-scale design strategy for the optimisation of variable stiffness composites

The present paper focuses on the development of a multi-scale design strategy for the optimisation of variable angle stiffness laminates. The main goal consists in proving that it is possible to design structures having complex shapes made of variable stiffness composites by taking into account, from the early stages of the design process, the constraints linked to the manufacturing process

A multi-scale approach for the simultaneous shape and material optimisation of sandwich panels with cellular core

This work deals with the problem of the optimum design of a sandwich panel made of carbon-epoxy skins and a metallic cellular core. The proposed design strategy is a multi-scale numerical optimisation procedure that does not make use of any simplifying hypothesis to obtain a true global optimum configuration of the system. To face the design of the sandwich structure at both meso and macro scales, a two-level optimisation strategy is employed: at the first level the goal is the determination of the optimum shape of the unit cell of the core (meso-scale) together with the material and geometric parameters of the laminated skins (macro-scale), while at the second level the objective is the design of the skins stacking sequence (skin meso-scale) meeting the geometrical and material parameters provided by the first-level problem. The two-level strategy is founded on the polar formalism for the description of the anisotropic behaviour of the laminates, on the NURBS basis functions for representing the shape of the unit cell and on the use of a genetic algorithm as optimisation tool to perform the solution search. To prove its effectiveness, the multi-scale strategy is applied to the least-weight design of a sandwich plate subject to constraints of different nature: on the positive-definiteness of the stiffness tensor of the core, on the admissible material properties of the laminated faces, on the local buckling load of the unit cell, on the global buckling load of the panel and geometrical as well as manufacturability constraints related to the fabrication process of the cellular core