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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.Maximum length scale requirement in a topology optimisation method based on NURBS hyper-surfaces
http://hdl.handle.net/10985/16375
Maximum length scale requirement in a topology optimisation method based on NURBS hyper-surfaces
COSTA, Giulio; MONTEMURRO, Marco; PAILHÈS, Jérôme; PERRY, Nicolas
This paper deals with a new method for handling manufacturing and geometrical requirements in the framework of a general Topology Optimisation (TO) strategy. In particular, the maximum length scale constraint (MLSC) implementation is addressed in order to obtain multiple load paths or to locally limit the size of the component. The classic formulation of the MLSC is revisited in the framework of a density-based TO algorithm wherein the pseudo-density field is represented through a NURBS hyper-surface. The NURBS hyper-surface properties are exploited to effectively formulate the MLSC. The effectiveness of the proposed approach is proven on a meaningful 3D benchmark.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/163752019-01-01T00:00:00ZCOSTA, GiulioMONTEMURRO, MarcoPAILHÈS, JérômePERRY, NicolasThis paper deals with a new method for handling manufacturing and geometrical requirements in the framework of a general Topology Optimisation (TO) strategy. In particular, the maximum length scale constraint (MLSC) implementation is addressed in order to obtain multiple load paths or to locally limit the size of the component. The classic formulation of the MLSC is revisited in the framework of a density-based TO algorithm wherein the pseudo-density field is represented through a NURBS hyper-surface. The NURBS hyper-surface properties are exploited to effectively formulate the MLSC. The effectiveness of the proposed approach is proven on a meaningful 3D benchmark.A general surface reconstruction method for post-processing of topology optimisation results
http://hdl.handle.net/10985/16996
A general surface reconstruction method for post-processing of topology optimisation results
BERTOLINO, Giulia; COSTA, Giulio; MONTEMURRO, Marco; PERRY, Nicolas; POURROY, Franck
In this work, a new semi-automatic surface reconstruction procedure is proposed. The main goal of the method is to reconstruct the boundary surface of a triangulation obtained as a result of a topology optimisation calculation. The reconstruction problem is articulated in two main phases: tessellation mapping and surface fitting. The first phase consists of retrieving a suitable map of the triangulation representing the boundary of the optimised topology. To this purpose, a segmentation of the original triangulation is performed and sub-domains (i.e. patches) are identified by means of a semi-automatic strategy. Then, a shape preserving parametrisation algorithm [1] is used on each patch in order to carry out the mapping and to preserve the real 3D shape of the boundary. The second phase deals with an original approach to the surface fitting problem: the problem is stated as a Constrained Non-Linear Programming Problem (CNLPP) by introducing a constraint on the maximum value of the Gaussian curvature of the boundary surface. In this study, the surface fitting problem is solved in the framework of Non-Uniform Rational Basis Splines (NURBS) surfaces. The main idea is to keep all the parameters defining the NURBS surface as design variables in order to state the surface fitting problem in the most general sense. Nevertheless, this fact implies two consequences of paramount importance, constituting just as many difficulties in solving the related CNLPP. Firstly, when the surface fitting problem is formulated by including the number of control points and the degrees of the basis functions among the unknowns, the overall number of design variables for the problem at hand is not fixed a-priori: hence, the resulting CNLPP is defined over a search space of variable dimension. Secondly, the numerical strategy chosen to face such a problem must be able to handle design variables of different nature and to optimise, at the same time, the dimension of the design domain as well as the value of each constitutive parameter of the NURBS surface. In order to overcome the two aforementioned issues, the surface fitting phase is composed of two optimisation steps. Firstly, the ERASMUS (EvolutionaRy Algorithm for optimiSation of ModUlar Systems) tool [2] optimises both the value and the number of design variables by means of a two-level Darwinian strategy, allowing the simultaneous evolution of individuals and species. Secondly, the optimum solution provided by ERASMUS constitutes the initial guess for the local gradient-based optimization, which aims at improving the accuracy of the fitting surface. The proposed method coupled with the NURBS based SIMP algorithm [3], represents a valid solution for the semi-automatic post-processing of complex 3D shapes resulting from topology optimisation.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/169962019-01-01T00:00:00ZBERTOLINO, GiuliaCOSTA, GiulioMONTEMURRO, MarcoPERRY, NicolasPOURROY, FranckIn this work, a new semi-automatic surface reconstruction procedure is proposed. The main goal of the method is to reconstruct the boundary surface of a triangulation obtained as a result of a topology optimisation calculation. The reconstruction problem is articulated in two main phases: tessellation mapping and surface fitting. The first phase consists of retrieving a suitable map of the triangulation representing the boundary of the optimised topology. To this purpose, a segmentation of the original triangulation is performed and sub-domains (i.e. patches) are identified by means of a semi-automatic strategy. Then, a shape preserving parametrisation algorithm [1] is used on each patch in order to carry out the mapping and to preserve the real 3D shape of the boundary. The second phase deals with an original approach to the surface fitting problem: the problem is stated as a Constrained Non-Linear Programming Problem (CNLPP) by introducing a constraint on the maximum value of the Gaussian curvature of the boundary surface. In this study, the surface fitting problem is solved in the framework of Non-Uniform Rational Basis Splines (NURBS) surfaces. The main idea is to keep all the parameters defining the NURBS surface as design variables in order to state the surface fitting problem in the most general sense. Nevertheless, this fact implies two consequences of paramount importance, constituting just as many difficulties in solving the related CNLPP. Firstly, when the surface fitting problem is formulated by including the number of control points and the degrees of the basis functions among the unknowns, the overall number of design variables for the problem at hand is not fixed a-priori: hence, the resulting CNLPP is defined over a search space of variable dimension. Secondly, the numerical strategy chosen to face such a problem must be able to handle design variables of different nature and to optimise, at the same time, the dimension of the design domain as well as the value of each constitutive parameter of the NURBS surface. In order to overcome the two aforementioned issues, the surface fitting phase is composed of two optimisation steps. Firstly, the ERASMUS (EvolutionaRy Algorithm for optimiSation of ModUlar Systems) tool [2] optimises both the value and the number of design variables by means of a two-level Darwinian strategy, allowing the simultaneous evolution of individuals and species. Secondly, the optimum solution provided by ERASMUS constitutes the initial guess for the local gradient-based optimization, which aims at improving the accuracy of the fitting surface. The proposed method coupled with the NURBS based SIMP algorithm [3], represents a valid solution for the semi-automatic post-processing of complex 3D shapes resulting from topology optimisation.A General Hybrid Optimization Strategy for Curve Fitting in the Non-uniform Rational Basis Spline Framework
http://hdl.handle.net/10985/17333
A General Hybrid Optimization Strategy for Curve Fitting in the Non-uniform Rational Basis Spline Framework
COSTA, Giulio; MONTEMURRO, Marco; PAILHES, Jérôme
In this paper, a general methodology to approximate sets of data points through Non-Uniform Rational Basis Spline curves is provided. The proposed approach aims at integrating and optimizing the full set of design variables (both integer and continuous) defining the shape of the Non-Uniform Rational Basis Spline curve. To this purpose, a new formulation of the curve fitting problem is required: it is stated in the form of a Constrained Non-Linear Programming Problem by introducing a suitable constraint on the curvature of the curve. In addition, the resulting optimization problem is defined over a domain having variable dimension, wherein both the number and the value of the design variables are optimized. To deal with this class of Constrained Non-Linear Programming Problems, a global optimization hybrid tool has been employed. The optimization procedure is split in two steps: firstly, an improved genetic algorithm optimizes both the value and the number of design variables by means of a two-level Darwinian strategy allowing the simultaneous evolution of individuals and species; secondly, the optimum solution provided by the genetic algorithm constitutes the initial guess for the subsequent gradient-based optimization, which aims at improving the accuracy of the fitting curve. The effectiveness of the proposed methodology is proven through some mathematical benchmarks as well as a real-world engineering problem.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/173332017-01-01T00:00:00ZCOSTA, GiulioMONTEMURRO, MarcoPAILHES, JérômeIn this paper, a general methodology to approximate sets of data points through Non-Uniform Rational Basis Spline curves is provided. The proposed approach aims at integrating and optimizing the full set of design variables (both integer and continuous) defining the shape of the Non-Uniform Rational Basis Spline curve. To this purpose, a new formulation of the curve fitting problem is required: it is stated in the form of a Constrained Non-Linear Programming Problem by introducing a suitable constraint on the curvature of the curve. In addition, the resulting optimization problem is defined over a domain having variable dimension, wherein both the number and the value of the design variables are optimized. To deal with this class of Constrained Non-Linear Programming Problems, a global optimization hybrid tool has been employed. The optimization procedure is split in two steps: firstly, an improved genetic algorithm optimizes both the value and the number of design variables by means of a two-level Darwinian strategy allowing the simultaneous evolution of individuals and species; secondly, the optimum solution provided by the genetic algorithm constitutes the initial guess for the subsequent gradient-based optimization, which aims at improving the accuracy of the fitting curve. The effectiveness of the proposed methodology is proven through some mathematical benchmarks as well as a real-world engineering problem.A 2D topology optimisation algorithm in NURBS framework with geometric constraints
http://hdl.handle.net/10985/17330
A 2D topology optimisation algorithm in NURBS framework with geometric constraints
COSTA, Giulio; MONTEMURRO, Marco; PAILHES, Jérôme
In this paper, the Solid Isotropic Material with Penalisation (SIMP) method for Topology Optimisation (TO) of 2D problems is reformulated in the Non-Uniform Rational BSpline (NURBS) framework. This choice implies several advantages, such as the definition of an implicit filter zone and the possibility for the designer to get a geometric entity at the end of the optimisation process. Therefore, important facilities are provided in CAD postprocessing phases in order to retrieve a consistent and well connected final topology. The effect of the main NURBS parameters (degrees, control points, weights and knot-vector components) on the final optimum topology is investigated. Classic geometric constraints, as the minimum and the maximum member size have been integrated and reformulated according to the NURBS formalism. Furthermore, a new constraint on the local curvature radius has been developed thanks to the NURBS formalism and properties. The effectiveness and the robustness of the proposed method are tested and proven through some benchmarks taken from literature and the results are compared with those provided by the classical SIMP approach.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/173302017-01-01T00:00:00ZCOSTA, GiulioMONTEMURRO, MarcoPAILHES, JérômeIn this paper, the Solid Isotropic Material with Penalisation (SIMP) method for Topology Optimisation (TO) of 2D problems is reformulated in the Non-Uniform Rational BSpline (NURBS) framework. This choice implies several advantages, such as the definition of an implicit filter zone and the possibility for the designer to get a geometric entity at the end of the optimisation process. Therefore, important facilities are provided in CAD postprocessing phases in order to retrieve a consistent and well connected final topology. The effect of the main NURBS parameters (degrees, control points, weights and knot-vector components) on the final optimum topology is investigated. Classic geometric constraints, as the minimum and the maximum member size have been integrated and reformulated according to the NURBS formalism. Furthermore, a new constraint on the local curvature radius has been developed thanks to the NURBS formalism and properties. The effectiveness and the robustness of the proposed method are tested and proven through some benchmarks taken from literature and the results are compared with those provided by the classical SIMP approach.