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

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 new multi-scale optimisation strategy for designing variable angle tow composites by integrating manufacturing constraints

In this work a multi-scale two-level (MS2L) optimisation strategy for optimising variable angle tow (VAT) composites is presented. In the framework of the MS2L methodology [1], [2], [3] 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 design strategy is characterised on the one hand by the refusal of simplifying hypotheses and classical rules usually employed in the framework of the design process of laminates, and on the other hand by a proper and complete mathematical formalisation of the optimum design problem at each characteristic scale (meso-macro). The MS2L strategy relies on the use of the polar formalism (extended to the case of higher-order theories [4], [5]) for the description of the anisotropic behaviour of the composite. The real advantage in using the Verchery's polar method is in the fact that the elastic response of the structure at the macro-scale is described in terms of tensor invariants, the so-called polar parameters, having a precise physical meaning (which is linked to the elastic symmetries of the material) [4]. On the other hand the MS2L strategy relies on the use of a particular genetic algorithm (GA) able to deal with a special class of huge-size optimisation problems (from hundreds to thousands of design variables) defined over a domain of variable dimension, i.e. optimisation problems involving a variable number of design variables [6]. The MS2L strategy has been improved in order to integrate all types of requirements (mechanical, manufacturability, geometric, etc.) within the first-level problem [3]. Several modifications have been introduced in the theoretical and numerical framework of the MS2L design procedure at both first and second levels [2], [3]. At the first level (laminate macroscopic scale) of the procedure, where the VAT laminate is modelled as an equivalent homogeneous anisotropic plate whose mechanical behaviour is described in terms of polar parameters (which vary locally over the structure), the major modifications focus on: 1) the utilisation of higher-order theories (First-order Shear Deformation Theory (FSDT) framework [4], [5] for taking into account the influence of the transverse shear stiffness on the overall mechanical response of VAT composites; 2) the utilisation of B-spline surfaces for obtaining a continuous point-wise variation of the laminate polar parameters; 3) a proper mathematical formalisation of the manufacturability constraints linked to the AFP process in the framework of the B-spline representation and in terms of laminate polar parameters. Regarding the second-level problem (laminate mesoscopic scale, i.e. the ply level) the main modifications is the utilisation of B-spline surfaces for obtaining a continuous point-wise variation of the fibres-path within each ply. Accordingly, the second-level problem (the lay-up design) can now be formulated as an unconstrained minimisation problem as all the requirements (geometrical, technological, mechanical, etc.) are satisfied since the first step of the MS2L strategy. All of these modifications imply several advantages for the resolution of the related optimisation problems (both at first and second level of the strategy) as detailed in [3]. 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

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

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

Corrigendum to "An extension of the polar method to the First-order Shear Deformation Theory of laminates" [Compos. Struct. 127 (2015) 328-339]

This is a Corrigendum to a previous publication entitled: "An extension of the polar method to the First-order Shear Deformation Theory of laminates"Corrigendum to "An extension of the polar method to the First-order Shear Deformation Theory of laminates" [Compos. Struct. 127 (2015) 328-339

A new multi-scale optimisation strategy for designing variable angle tow composites by integrating manufacturing constraints

In this work a multi-scale two-level (MS2L) optimisation strategy for optimising variable angle tow (VAT) composites is presented. In the framework of the MS2L methodology [1], [2], [3] 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 design strategy is characterised on the one hand by the refusal of simplifying hypotheses and classical rules usually employed in the framework of the design process of laminates, and on the other hand by a proper and complete mathematical formalisation of the optimum design problem at each characteristic scale (meso-macro). The MS2L strategy relies on the use of the polar formalism (extended to the case of higher-order theories [4], [5]) for the description of the anisotropic behaviour of the composite. The real advantage in using the Verchery's polar method is in the fact that the elastic response of the structure at the macro-scale is described in terms of tensor invariants, the so-called polar parameters, having a precise physical meaning (which is linked to the elastic symmetries of the material) [4]. On the other hand the MS2L strategy relies on the use of a particular genetic algorithm (GA) able to deal with a special class of huge-size optimisation problems (from hundreds to thousands of design variables) defined over a domain of variable dimension, i.e. optimisation problems involving a variable number of design variables [6]. The MS2L strategy has been improved in order to integrate all types of requirements (mechanical, manufacturability, geometric, etc.) within the first-level problem [3]. Several modifications have been introduced in the theoretical and numerical framework of the MS2L design procedure at both first and second levels [2], [3]. At the first level (laminate macroscopic scale) of the procedure, where the VAT laminate is modelled as an equivalent homogeneous anisotropic plate whose mechanical behaviour is described in terms of polar parameters (which vary locally over the structure), the major modifications focus on: 1) the utilisation of higher-order theories (First-order Shear Deformation Theory (FSDT) framework [4], [5] for taking into account the influence of the transverse shear stiffness on the overall mechanical response of VAT composites; 2) the utilisation of B-spline surfaces for obtaining a continuous point-wise variation of the laminate polar parameters; 3) a proper mathematical formalisation of the manufacturability constraints linked to the AFP process in the framework of the B-spline representation and in terms of laminate polar parameters. Regarding the second-level problem (laminate mesoscopic scale, i.e. the ply level) the main modifications is the utilisation of B-spline surfaces for obtaining a continuous point-wise variation of the fibres-path within each ply. Accordingly, the second-level problem (the lay-up design) can now be formulated as an unconstrained minimisation problem as all the requirements (geometrical, technological, mechanical, etc.) are satisfied since the first step of the MS2L strategy. All of these modifications imply several advantages for the resolution of the related optimisation problems (both at first and second level of the strategy) as detailed in [3]. 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

Recent Advances in the Use of Sourdough Biotechnology in Pasta Making

The growing consumers' request for foods with well-balanced nutritional profile and functional properties promotes research on innovation in pasta making. As a staple food and a common component of diet, pasta can be considered as a vector of dietary fiber, vegetable proteins, vitamins, minerals, and functional compounds. The conventional process for pasta production does not include a fermentation step. However, novel recipes including sourdough-fermented ingredients have been recently proposed, aiming at enhancing the nutritional and functional properties of this product and at enriching commercial offerings with products with new sensorial profiles. The use of sourdough for pasta fortification has been investigated under several aspects, including fortification in vitamin B, the reduction of starch digestibility, and gluten content. Sourdough fermentation has also been successfully applied to non-conventional flours, (e.g., from pseudocereals and legumes), in which an overall increase of the nutritional value and health-promoting compounds, such as a significant decrease of antinutritional factors, were observed. Fermented non-conventional flours, obtained through spontaneous fermentation or using selected starters, have been proposed as pasta ingredients. As the result of wheat replacement, modification in textural properties of pasta may occur. Nonetheless, fermentation represents an efficient tool in improving, besides nutritional and functional profile, the sensory and technological features of fortified pasta.Peer reviewe

Design of a "Clean-Label" Gluten-Free Bread to Meet Consumers Demand

The market of gluten-free (GF) products has been steadily increasing in last few years. Due to the technological importance of gluten, the GF food production is still a challenge for the industry. Indeed, large quantities of fat, sugars, structuring agents, and flavor enhancers are added to GF formulations to make textural and sensorial characteristics comparable to conventional products, leading to nutritional and caloric intake imbalances. The formulation of the novel "clean-label" GF bread included a commonly used mixture of maize and rice flour (ratio 1:1) fortified with selected protein-rich flours. Naturally hydrocolloids-containing flours (psyllium, flaxseed, chia) were included in the bread formulation as structuring agents. A type-II sourdough was obtained by using a selected Weissella cibaria P9 and a GF sucrose-containing flour as substrate for fermentation to promote the exo-polysaccharides synthesis by the starter lactic acid bacterium. A two-step protocol for bread-making was set-up: first, the GF sourdough was fermented (24 h at 30 degrees C); then, it was mixed with the other ingredients (30% of the final dough) and leavened with baker's yeast before baking. Overall, the novel GF bread was characterized by good textural properties, high protein content (8.9% of dry matter) and in vitro protein digestibility (76.9%), low sugar (1.0% of dry matter) and fat (3.1% of dry matter) content, and an in vitro predicted glycemic index of 85