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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 11 Dec 2019 21:11:12 GMT2019-12-11T21:11:12ZA multi-scale approach for the simultaneous shape and material optimisation of sandwich panels with cellular core
http://hdl.handle.net/10985/10674
A multi-scale approach for the simultaneous shape and material optimisation of sandwich panels with cellular core
MONTEMURRO, Marco; CATAPANO, Anita; DOROSZEWSKI, Dominique
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.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/106742016-01-01T00:00:00ZMONTEMURRO, MarcoCATAPANO, AnitaDOROSZEWSKI, DominiqueThis 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.The polar analysis of the Third-order Shear Deformation Theory of laminates
http://hdl.handle.net/10985/9921
The polar analysis of the Third-order Shear Deformation Theory of laminates
MONTEMURRO, Marco
In this paper the Verchery's polar method is extended to the conceptual framework of the Reddy's Third-order Shear Deformation Theory (TSDT) of laminates. In particular, a mathematical representation based upon tensor invariants is derived for all the laminate stiffness matrices (basic and higher-order stiffness terms). The major analytical results of the application of the polar formalism to the TSDT of laminates are the generalisation of the concept of a \textit{quasi-homogeneous} laminate as well as the definition of some new classes of laminates. Moreover, it is proved that the elastic symmetries of the laminate shear stiffness matrices (basic and higher-order terms) depend upon those of their in-plane counterparts. As a consequence of these results a unified formulation for the problem of designing the laminate elastic symmetries in the context of the TSDT is proposed. The optimum solutions are found within the framework of the polar-genetic approach, since the objective function is written in terms of the laminate polar parameters, while a genetic algorithm is used as a numerical tool for the solution search. In order to support the theoretical results, and also to prove the effectiveness of the proposed approach, some new and meaningful numerical examples are discussed in the paper.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/99212015-01-01T00:00:00ZMONTEMURRO, MarcoIn this paper the Verchery's polar method is extended to the conceptual framework of the Reddy's Third-order Shear Deformation Theory (TSDT) of laminates. In particular, a mathematical representation based upon tensor invariants is derived for all the laminate stiffness matrices (basic and higher-order stiffness terms). The major analytical results of the application of the polar formalism to the TSDT of laminates are the generalisation of the concept of a \textit{quasi-homogeneous} laminate as well as the definition of some new classes of laminates. Moreover, it is proved that the elastic symmetries of the laminate shear stiffness matrices (basic and higher-order terms) depend upon those of their in-plane counterparts. As a consequence of these results a unified formulation for the problem of designing the laminate elastic symmetries in the context of the TSDT is proposed. The optimum solutions are found within the framework of the polar-genetic approach, since the objective function is written in terms of the laminate polar parameters, while a genetic algorithm is used as a numerical tool for the solution search. In order to support the theoretical results, and also to prove the effectiveness of the proposed approach, some new and meaningful numerical examples are discussed in the paper.On the effective integration of manufacturability constraints within the multi-scale methodology for designing variable angle-tow laminates
http://hdl.handle.net/10985/11438
On the effective integration of manufacturability constraints within the multi-scale methodology for designing variable angle-tow laminates
MONTEMURRO, Marco; CATAPANO, Anita
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.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/114382017-01-01T00:00:00ZMONTEMURRO, MarcoCATAPANO, AnitaIn 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
http://hdl.handle.net/10985/11437
A general multi-scale design strategy for the optimisation of variable stiffness composites
MONTEMURRO, Marco; CATAPANO, Anita
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.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/114372016-01-01T00:00:00ZMONTEMURRO, MarcoCATAPANO, AnitaThe 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.Low-velocity impact tests on carbon/epoxy composite laminates: A benchmark study
http://hdl.handle.net/10985/11386
Low-velocity impact tests on carbon/epoxy composite laminates: A benchmark study
PANETTIERI, Enrico; FANTERIA, Daniele; MONTEMURRO, Marco; FROUSTEY, Catherine
Low-velocity impacts (LVI) on composite laminates pose significant safety issues since they are able to generate extended damage within the structure, mostly delaminations and matrix cracking, while being hardly detectable in visual inspections. The role of LVI tests at the coupon level is to evaluate quantities that can be useful both in the design process, such as the delamination threshold load, and in dealing with safety issues, that is correlating the internal damage with the indentation depth. This paper aims at providing a benchmark of LVIs on quasi-isotropic carbon/epoxy laminates; 2 laminates are tested, 16 and 24 plies and a total of 8 impact energies have been selected ranging from very low energy impacts up to around 30 J. Delamination threshold loads, shape and extension of délaminations as well as post-impact 3D measurements of the impacted surface have been carried out in order to characterize the behavior of the considered material system in LVIs. The analysis of test results relevant to the lowest energies pointed out that large contact force fluctuations, typically associated to delamination onset, occurred but ultrasonic scans did not reveal any significant internal damage. Due to these unexpected results, such tests were further investigated through a detailed FE model. The results of this investigation highlights the detrimental effects of the dissipative mechanisms of the impactor. A combined numericale-experimental approach is thus proposed to evaluate the effective impact energies.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/113862016-01-01T00:00:00ZPANETTIERI, EnricoFANTERIA, DanieleMONTEMURRO, MarcoFROUSTEY, CatherineLow-velocity impacts (LVI) on composite laminates pose significant safety issues since they are able to generate extended damage within the structure, mostly delaminations and matrix cracking, while being hardly detectable in visual inspections. The role of LVI tests at the coupon level is to evaluate quantities that can be useful both in the design process, such as the delamination threshold load, and in dealing with safety issues, that is correlating the internal damage with the indentation depth. This paper aims at providing a benchmark of LVIs on quasi-isotropic carbon/epoxy laminates; 2 laminates are tested, 16 and 24 plies and a total of 8 impact energies have been selected ranging from very low energy impacts up to around 30 J. Delamination threshold loads, shape and extension of délaminations as well as post-impact 3D measurements of the impacted surface have been carried out in order to characterize the behavior of the considered material system in LVIs. The analysis of test results relevant to the lowest energies pointed out that large contact force fluctuations, typically associated to delamination onset, occurred but ultrasonic scans did not reveal any significant internal damage. Due to these unexpected results, such tests were further investigated through a detailed FE model. The results of this investigation highlights the detrimental effects of the dissipative mechanisms of the impactor. A combined numericale-experimental approach is thus proposed to evaluate the effective impact energies.Multi-scale identification of elastic properties for anisotropic media through a global hybrid evolutionary-based inverse approach
http://hdl.handle.net/10985/12937
Multi-scale identification of elastic properties for anisotropic media through a global hybrid evolutionary-based inverse approach
CAPPELLI, Lorenzo; MONTEMURRO, Marco; DAU, Frédéric; GUILLAUMAT, Laurent
One of the main issues of composite materials is related to the difficulty of characterising the full set of material properties at both mesoscopic and microscopic scales. Indeed, classical mechanical tests (traction/compression, 3 or 4 points bending tests, etc.) are not able to provide the full set of 3D material properties of composites. Furthermore, these tests can provide only the in-plane elastic properties of the constitutive lamina (i.e at. the laminate mesoscopic scale). Therefore, in order to go beyond the main restrictions imposed by standard destructive tests, this work deals with the problem of characterising the material properties of a composite plate made of unidirectional fibre-reinforced laminae (at each characteristic scale), through a single non-destructive modal test performed at the macroscale, i.e. that of the specimen (the laminate). To face such a problem a general multi-scale identification strategy (MSIS) is proposed. The MSIS aims at identifying the constitutive properties at both micro and meso scales by exploiting the information restrained in the macroscopic dynamical response of the laminate (e.g. in terms of its eigenfrequencies). The MSIS relies on the one hand on the strain energy homogenisation technique of periodic media (for determining the effective elastic properties of the lamina as a function of the geometrical and material properties of the microscopic constitutive phases) and on the other hand on a special hybrid algorithm (genetic algorithm + gradient-based algorithm) in order to perform the solution search for the considered problem. The identification problem is stated as a constrained inverse problem (a least-square constrained problem), where the objective function depends upon both the measured and evaluated (from finite element analysis) natural frequencies of the laminated plate. In this background, the optimisation variables are both geometrical and material properties of the constitutive phases composing the representative volume element (RVE) of the composite. The effectiveness of the proposed approach will be proven through a campaign of experimental/numerical tests conducted on standard laminates made of unidirectional plies.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/129372017-01-01T00:00:00ZCAPPELLI, LorenzoMONTEMURRO, MarcoDAU, FrédéricGUILLAUMAT, LaurentOne of the main issues of composite materials is related to the difficulty of characterising the full set of material properties at both mesoscopic and microscopic scales. Indeed, classical mechanical tests (traction/compression, 3 or 4 points bending tests, etc.) are not able to provide the full set of 3D material properties of composites. Furthermore, these tests can provide only the in-plane elastic properties of the constitutive lamina (i.e at. the laminate mesoscopic scale). Therefore, in order to go beyond the main restrictions imposed by standard destructive tests, this work deals with the problem of characterising the material properties of a composite plate made of unidirectional fibre-reinforced laminae (at each characteristic scale), through a single non-destructive modal test performed at the macroscale, i.e. that of the specimen (the laminate). To face such a problem a general multi-scale identification strategy (MSIS) is proposed. The MSIS aims at identifying the constitutive properties at both micro and meso scales by exploiting the information restrained in the macroscopic dynamical response of the laminate (e.g. in terms of its eigenfrequencies). The MSIS relies on the one hand on the strain energy homogenisation technique of periodic media (for determining the effective elastic properties of the lamina as a function of the geometrical and material properties of the microscopic constitutive phases) and on the other hand on a special hybrid algorithm (genetic algorithm + gradient-based algorithm) in order to perform the solution search for the considered problem. The identification problem is stated as a constrained inverse problem (a least-square constrained problem), where the objective function depends upon both the measured and evaluated (from finite element analysis) natural frequencies of the laminated plate. In this background, the optimisation variables are both geometrical and material properties of the constitutive phases composing the representative volume element (RVE) of the composite. The effectiveness of the proposed approach will be proven through a campaign of experimental/numerical tests conducted on standard laminates made of unidirectional plies.On the integration of additive manufacturing constraints in the framework of a NURBS-based topology optimisation method
http://hdl.handle.net/10985/12538
On the integration of additive manufacturing constraints in the framework of a NURBS-based topology optimisation method; Intégration des contraintes de l'ALM dans le cadre de la méthode d'optimisation topologique basée sur les NURBS
COSTA, Giulio; MONTEMURRO, Marco; PAILHES, Jérôme
This work focuses on the topology optimization (TO) of 2D structures: the Solid Isotropic Material with Penalisation (SIMP) method is revisited and reformulated within the mathematical framework of Non-Uniform Rational BSpline (NURBS) functions. Several advantages arise from such a choice: firstly, a NURBS surface allows for exploiting an implicitly defined filter zone; secondly, the number of optimisation variables (i.e. the parameters defining the NURBS surface) is relatively small when compared to the classical SIMP approach. Finally, the TO can be carried out by including non-conventional manufacturing constraints, as those related to the Additive Manufacturing (AM) technology.The proposed TO method is applied to a standard benchmark problem in this paper.; Ce travail se focalise sur l’optimisation topologique des structures 2D : la méthode Solid Isotropic Material with Penalisation (SIMP) est révisée et reformulée dans le cadre mathématique des fonctions NURBS (Non-Uniform Rational BSpline). Ce choix comporte plusieurs avantages : a)une surface NURBS est caractérisée par une zone de filtre définie de façon implicite ; b) le nombre de variables d’optimisation (à savoir les paramètres qui définissent la surface NURBS) est réduit vis-à-vis de l’approche SIMP classique ;c) les contraintes non-conventionnelles liées au procédé de Fabrication Additive peuvent être facilement intégrées dans le processus d’optimisation topologique grâce au formalisme NURBS .L’efficacité de la méthode d’optimisation topologique proposée sera prouvée via un benchmark classique.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/125382017-01-01T00:00:00ZCOSTA, GiulioMONTEMURRO, MarcoPAILHES, JérômeThis work focuses on the topology optimization (TO) of 2D structures: the Solid Isotropic Material with Penalisation (SIMP) method is revisited and reformulated within the mathematical framework of Non-Uniform Rational BSpline (NURBS) functions. Several advantages arise from such a choice: firstly, a NURBS surface allows for exploiting an implicitly defined filter zone; secondly, the number of optimisation variables (i.e. the parameters defining the NURBS surface) is relatively small when compared to the classical SIMP approach. Finally, the TO can be carried out by including non-conventional manufacturing constraints, as those related to the Additive Manufacturing (AM) technology.The proposed TO method is applied to a standard benchmark problem in this paper.
Ce travail se focalise sur l’optimisation topologique des structures 2D : la méthode Solid Isotropic Material with Penalisation (SIMP) est révisée et reformulée dans le cadre mathématique des fonctions NURBS (Non-Uniform Rational BSpline). Ce choix comporte plusieurs avantages : a)une surface NURBS est caractérisée par une zone de filtre définie de façon implicite ; b) le nombre de variables d’optimisation (à savoir les paramètres qui définissent la surface NURBS) est réduit vis-à-vis de l’approche SIMP classique ;c) les contraintes non-conventionnelles liées au procédé de Fabrication Additive peuvent être facilement intégrées dans le processus d’optimisation topologique grâce au formalisme NURBS .L’efficacité de la méthode d’optimisation topologique proposée sera prouvée via un benchmark classique.A NURBS-BASED TOPOLOGY OPTIMIZATION METHOD INCLUDING ADDITIVE MANUFACTURING CONSTRAINTS
http://hdl.handle.net/10985/12539
A NURBS-BASED TOPOLOGY OPTIMIZATION METHOD INCLUDING ADDITIVE MANUFACTURING CONSTRAINTS
COSTA, Giulio; MONTEMURRO, Marco; PAILHES, Jérôme
In this work, the Solid Isotropic Material with Penalization (SIMP) topology optimization (TO) method is revisited and reformulated within the mathematical framework of NURBS functions. This implies several advantages: firstly, a NURBS surface allows exploiting an implicitly defined filter zone; secondly, the number of optimization variables (i.e. the parameters defining the NURBS surface) is relatively small when compared to the classical SIMP approach. Finally the TO can be carried out by including non-linearity (either geometric or material) or non-conventional manufacturing constraints, as those related to the Additive Manufacturing (AM) technology. In this work the TO is applied to a standard benchmark.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/125392017-01-01T00:00:00ZCOSTA, GiulioMONTEMURRO, MarcoPAILHES, JérômeIn this work, the Solid Isotropic Material with Penalization (SIMP) topology optimization (TO) method is revisited and reformulated within the mathematical framework of NURBS functions. This implies several advantages: firstly, a NURBS surface allows exploiting an implicitly defined filter zone; secondly, the number of optimization variables (i.e. the parameters defining the NURBS surface) is relatively small when compared to the classical SIMP approach. Finally the TO can be carried out by including non-linearity (either geometric or material) or non-conventional manufacturing constraints, as those related to the Additive Manufacturing (AM) technology. In this work the TO is applied to a standard benchmark.ON THE FORMULATION OF A TENSORIAL LAMINATE-LEVEL FAILURE CRITERION THROUGH INVARIANTS
http://hdl.handle.net/10985/12559
ON THE FORMULATION OF A TENSORIAL LAMINATE-LEVEL FAILURE CRITERION THROUGH INVARIANTS
CATAPANO, Anita; MONTEMURRO, Marco
Anisotropic materials, such as fibre-reinforced composite materials, are extensively used in many industrial fields thanks to their mechanical performances. The main characteristic of an anisotropic material is the dependency of physical properties upon the direction. Anisotropy influences strongly also the mechanical strength of a material, usually described by a failure criterion. We can separate the failure criteria into two distinct classes: the phenomenological/polynomial ones and the physically-based ones. The polynomial failure criteria are called in this way because the occurrence of the failure is checked through the computation of a scalar indicator, i.e. the failure index. In this framework, a unique scalar condition has to be verified, regardless the nature of the failure mechanism that is activated. It is noteworthy that all polynomial failure criteria are “ply-level failure criteria", thus, when utilised to analyse the failure of laminated structures, they are applied to each ply composing the structure in order to check the so-called first-ply-failure. However, this approach is not compatible with the methodologies often used for the preliminary design of composite structures. Indeed in this background, the number of design variables is economised by representing each laminate (composing the structure) as an equivalent homogeneous anisotropic plate characterised by a few number of parameters describing its overall mechanical response regardless to the nature of the stacking sequence. In order to include the failure mechanisms within the mathematical framework of preliminary design of composite structure an alternative approach is needed. To this purpose, a method to generalise the ply-level failure criterion of Tsai-Wu to the laminate-level (with the aim of introducing strength requirements at the macroscopic scale within the optimisation process of a composite structures) is proposed in this work.The Tsai-Wu criterion is formulated in the framework of the First-order Shear Deformation Theory (FSDT) in order to take into account the out-of-plane shear stress and strain components. Then, through the use of the polar method, the criterion is firstly formulated in terms of invariants. Finally it is extended, via a through-the-thickness homogenisation step, to the laminate-level in order to evaluate the strength of the entire laminate. The laminate-level failure criterion is thus expressed for a laminated plate modelled as an equivalent single layer having the same thickness of the laminate. Thanks to the polar representation a physical meaning of each tensor appearing in the laminate-level criterion is also given. The resulting criterion is then used in the framework of a strength optimisation problem in order to show the effectiveness of the proposed method. The multi-scale two-level optimisation strategy is used to firstly optimise the polar parameters of the tensors of the laminate-level criterion (macro-scale optimisation step) and then the lay-up design is carried out to find at least one stacking sequence satisfying the strength polar parameters provided by the first-step of the strategy (meso-scale optimisation step)
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/125592017-01-01T00:00:00ZCATAPANO, AnitaMONTEMURRO, MarcoAnisotropic materials, such as fibre-reinforced composite materials, are extensively used in many industrial fields thanks to their mechanical performances. The main characteristic of an anisotropic material is the dependency of physical properties upon the direction. Anisotropy influences strongly also the mechanical strength of a material, usually described by a failure criterion. We can separate the failure criteria into two distinct classes: the phenomenological/polynomial ones and the physically-based ones. The polynomial failure criteria are called in this way because the occurrence of the failure is checked through the computation of a scalar indicator, i.e. the failure index. In this framework, a unique scalar condition has to be verified, regardless the nature of the failure mechanism that is activated. It is noteworthy that all polynomial failure criteria are “ply-level failure criteria", thus, when utilised to analyse the failure of laminated structures, they are applied to each ply composing the structure in order to check the so-called first-ply-failure. However, this approach is not compatible with the methodologies often used for the preliminary design of composite structures. Indeed in this background, the number of design variables is economised by representing each laminate (composing the structure) as an equivalent homogeneous anisotropic plate characterised by a few number of parameters describing its overall mechanical response regardless to the nature of the stacking sequence. In order to include the failure mechanisms within the mathematical framework of preliminary design of composite structure an alternative approach is needed. To this purpose, a method to generalise the ply-level failure criterion of Tsai-Wu to the laminate-level (with the aim of introducing strength requirements at the macroscopic scale within the optimisation process of a composite structures) is proposed in this work.The Tsai-Wu criterion is formulated in the framework of the First-order Shear Deformation Theory (FSDT) in order to take into account the out-of-plane shear stress and strain components. Then, through the use of the polar method, the criterion is firstly formulated in terms of invariants. Finally it is extended, via a through-the-thickness homogenisation step, to the laminate-level in order to evaluate the strength of the entire laminate. The laminate-level failure criterion is thus expressed for a laminated plate modelled as an equivalent single layer having the same thickness of the laminate. Thanks to the polar representation a physical meaning of each tensor appearing in the laminate-level criterion is also given. The resulting criterion is then used in the framework of a strength optimisation problem in order to show the effectiveness of the proposed method. The multi-scale two-level optimisation strategy is used to firstly optimise the polar parameters of the tensors of the laminate-level criterion (macro-scale optimisation step) and then the lay-up design is carried out to find at least one stacking sequence satisfying the strength polar parameters provided by the first-step of the strategy (meso-scale optimisation step)A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties
http://hdl.handle.net/10985/8498
A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties
CATAPANO, Anita; MONTEMURRO, Marco
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.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/84982014-01-01T00:00:00ZCATAPANO, AnitaMONTEMURRO, MarcoThis 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.