The Experts below are selected from a list of 1398 Experts worldwide ranked by ideXlab platform
Jérôme Pailhes - One of the best experts on this subject based on the ideXlab platform.
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A metamodel based on non-uniform rational basis spline hyper-surfaces for optimisation of composite structures
Composite Structures, 2020Co-Authors: Yohann Audoux, Marco Montemurro, Jérôme PailhesAbstract:This study presents a new strategy to generate a surrogate model used for design purposes. The metamodel is based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces and is able to fit non-convex sets of target points (TPs). The proposed method aims at determining all the parameters involved in the definition of the NURBS hyper-surface, i.e. control points (CPs) coordinates, weights, degrees, CPs number and Knot-Vector components. To this purpose, the problem of finding a suitable metamodel is formulated as a constrained non-linear programming problem (CNLPP) wherein the above variables are optimised in order to fit a set of TPs. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a variable dimension. This problem is solved by means of a special genetic algorithm able to determine simultaneously the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The NURBS-based metamodel is then used to emulate the first buckling load of a composite stiffened panel and it is used in the framework of a meaningful design problem.
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Non-uniform rational basis spline hyper-surfaces for metamodelling
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Yohann Audoux, Marco Montemurro, Jérôme PailhesAbstract:This study presents an original metamodelling technique based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces. The proposed approach is able to fit general non-convex sets of target points (TPs) by extending the NURBS formalism to the N-dimensional (N-D) case. The shape of such a hyper-surface is tuned by several parameters: the number of control points (CPs), their coordinates and the related weights, the degrees of the blending functions and the Knot-Vector components defined along each direction. The goal of the proposed strategy is to automatically determine (i.e. without the user’s intervention) the full set of parameters defining the NURBS hyper-surface approximating a given set of TPs, without considering simplifying hypotheses. To this purpose, the problem is formulated as a constrained nonlinear programming problem (CNLPP) wherein the optimization variables are all the parameters tuning the shape of the NURBS hyper-surface. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a changing dimension. This problem is solved by means of an original genetic algorithm able to determine, simultaneously, the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The effectiveness of the proposed approach is shown by means of two meaningful test cases. In addition, the proposed method has been applied to a benchmark taken from the literature and the results have been compared to those provided by the Proper Generalized Decomposition method.
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A surrogate model based on Non-Uniform Rational B-Splines hypersurfaces
Procedia CIRP, 2018Co-Authors: Yohann Audoux, Marco Montemurro, Jérôme PailhesAbstract:This study aims at providing an original metamodeling technique based on the Non-Uniform Rational B-Splines (NURBS) formalism. The proposed approach is able to fit general non-convex sets of target points (TPs) by extending the NURBS formalism to the N-dimensional (N-D) case, getting in this way a general NURBS hypersurface. The shape of such a hypersurface is tuned by several parameters: the number of control points (CPs), their coordinates and related weights, the degrees of the blending functions and the Knot-Vector components defined along each direction. The goal of the proposed strategy is to find the best NURBS hypersurface approximating a given set of TPs. To this purpose the problem is formulated as an unconstrained least-square distance problem wherein the optimisation variables are all the parameters tuning the shape of the NURBS hypersurface. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables the resulting problem is defined over a space having a variable dimension. To deal with this aspect, a special genetic algorithm, able to solve problems characterised by a variable number of design variables, is considered to determine automatically (i.e. without the user’s intervention) the optimum value of both the design space size (related to the integer variables of the NURBS hypersurface) and the NURBS hypersurface continuous parameters. The effectiveness of the proposed approach is proven by means of a meaningful benchmark.
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A 2D topology optimisation algorithm in NURBS framework with geometric constraints
International Journal of Mechanics and Materials in Design, 2017Co-Authors: Giulio Costa, Marco Montemurro, Jérôme PailhesAbstract: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.
Yohann Audoux - One of the best experts on this subject based on the ideXlab platform.
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A metamodel based on non-uniform rational basis spline hyper-surfaces for optimisation of composite structures
Composite Structures, 2020Co-Authors: Yohann Audoux, Marco Montemurro, Jérôme PailhesAbstract:This study presents a new strategy to generate a surrogate model used for design purposes. The metamodel is based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces and is able to fit non-convex sets of target points (TPs). The proposed method aims at determining all the parameters involved in the definition of the NURBS hyper-surface, i.e. control points (CPs) coordinates, weights, degrees, CPs number and Knot-Vector components. To this purpose, the problem of finding a suitable metamodel is formulated as a constrained non-linear programming problem (CNLPP) wherein the above variables are optimised in order to fit a set of TPs. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a variable dimension. This problem is solved by means of a special genetic algorithm able to determine simultaneously the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The NURBS-based metamodel is then used to emulate the first buckling load of a composite stiffened panel and it is used in the framework of a meaningful design problem.
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Non-uniform rational basis spline hyper-surfaces for metamodelling
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Yohann Audoux, Marco Montemurro, Jérôme PailhesAbstract:This study presents an original metamodelling technique based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces. The proposed approach is able to fit general non-convex sets of target points (TPs) by extending the NURBS formalism to the N-dimensional (N-D) case. The shape of such a hyper-surface is tuned by several parameters: the number of control points (CPs), their coordinates and the related weights, the degrees of the blending functions and the Knot-Vector components defined along each direction. The goal of the proposed strategy is to automatically determine (i.e. without the user’s intervention) the full set of parameters defining the NURBS hyper-surface approximating a given set of TPs, without considering simplifying hypotheses. To this purpose, the problem is formulated as a constrained nonlinear programming problem (CNLPP) wherein the optimization variables are all the parameters tuning the shape of the NURBS hyper-surface. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a changing dimension. This problem is solved by means of an original genetic algorithm able to determine, simultaneously, the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The effectiveness of the proposed approach is shown by means of two meaningful test cases. In addition, the proposed method has been applied to a benchmark taken from the literature and the results have been compared to those provided by the Proper Generalized Decomposition method.
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A surrogate model based on Non-Uniform Rational B-Splines hypersurfaces
Procedia CIRP, 2018Co-Authors: Yohann Audoux, Marco Montemurro, Jérôme PailhesAbstract:This study aims at providing an original metamodeling technique based on the Non-Uniform Rational B-Splines (NURBS) formalism. The proposed approach is able to fit general non-convex sets of target points (TPs) by extending the NURBS formalism to the N-dimensional (N-D) case, getting in this way a general NURBS hypersurface. The shape of such a hypersurface is tuned by several parameters: the number of control points (CPs), their coordinates and related weights, the degrees of the blending functions and the Knot-Vector components defined along each direction. The goal of the proposed strategy is to find the best NURBS hypersurface approximating a given set of TPs. To this purpose the problem is formulated as an unconstrained least-square distance problem wherein the optimisation variables are all the parameters tuning the shape of the NURBS hypersurface. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables the resulting problem is defined over a space having a variable dimension. To deal with this aspect, a special genetic algorithm, able to solve problems characterised by a variable number of design variables, is considered to determine automatically (i.e. without the user’s intervention) the optimum value of both the design space size (related to the integer variables of the NURBS hypersurface) and the NURBS hypersurface continuous parameters. The effectiveness of the proposed approach is proven by means of a meaningful benchmark.
Marco Montemurro - One of the best experts on this subject based on the ideXlab platform.
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A metamodel based on non-uniform rational basis spline hyper-surfaces for optimisation of composite structures
Composite Structures, 2020Co-Authors: Yohann Audoux, Marco Montemurro, Jérôme PailhesAbstract:This study presents a new strategy to generate a surrogate model used for design purposes. The metamodel is based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces and is able to fit non-convex sets of target points (TPs). The proposed method aims at determining all the parameters involved in the definition of the NURBS hyper-surface, i.e. control points (CPs) coordinates, weights, degrees, CPs number and Knot-Vector components. To this purpose, the problem of finding a suitable metamodel is formulated as a constrained non-linear programming problem (CNLPP) wherein the above variables are optimised in order to fit a set of TPs. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a variable dimension. This problem is solved by means of a special genetic algorithm able to determine simultaneously the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The NURBS-based metamodel is then used to emulate the first buckling load of a composite stiffened panel and it is used in the framework of a meaningful design problem.
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Non-uniform rational basis spline hyper-surfaces for metamodelling
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Yohann Audoux, Marco Montemurro, Jérôme PailhesAbstract:This study presents an original metamodelling technique based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces. The proposed approach is able to fit general non-convex sets of target points (TPs) by extending the NURBS formalism to the N-dimensional (N-D) case. The shape of such a hyper-surface is tuned by several parameters: the number of control points (CPs), their coordinates and the related weights, the degrees of the blending functions and the Knot-Vector components defined along each direction. The goal of the proposed strategy is to automatically determine (i.e. without the user’s intervention) the full set of parameters defining the NURBS hyper-surface approximating a given set of TPs, without considering simplifying hypotheses. To this purpose, the problem is formulated as a constrained nonlinear programming problem (CNLPP) wherein the optimization variables are all the parameters tuning the shape of the NURBS hyper-surface. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a changing dimension. This problem is solved by means of an original genetic algorithm able to determine, simultaneously, the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The effectiveness of the proposed approach is shown by means of two meaningful test cases. In addition, the proposed method has been applied to a benchmark taken from the literature and the results have been compared to those provided by the Proper Generalized Decomposition method.
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A surrogate model based on Non-Uniform Rational B-Splines hypersurfaces
Procedia CIRP, 2018Co-Authors: Yohann Audoux, Marco Montemurro, Jérôme PailhesAbstract:This study aims at providing an original metamodeling technique based on the Non-Uniform Rational B-Splines (NURBS) formalism. The proposed approach is able to fit general non-convex sets of target points (TPs) by extending the NURBS formalism to the N-dimensional (N-D) case, getting in this way a general NURBS hypersurface. The shape of such a hypersurface is tuned by several parameters: the number of control points (CPs), their coordinates and related weights, the degrees of the blending functions and the Knot-Vector components defined along each direction. The goal of the proposed strategy is to find the best NURBS hypersurface approximating a given set of TPs. To this purpose the problem is formulated as an unconstrained least-square distance problem wherein the optimisation variables are all the parameters tuning the shape of the NURBS hypersurface. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables the resulting problem is defined over a space having a variable dimension. To deal with this aspect, a special genetic algorithm, able to solve problems characterised by a variable number of design variables, is considered to determine automatically (i.e. without the user’s intervention) the optimum value of both the design space size (related to the integer variables of the NURBS hypersurface) and the NURBS hypersurface continuous parameters. The effectiveness of the proposed approach is proven by means of a meaningful benchmark.
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A 2D topology optimisation algorithm in NURBS framework with geometric constraints
International Journal of Mechanics and Materials in Design, 2017Co-Authors: Giulio Costa, Marco Montemurro, Jérôme PailhesAbstract: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.
Xuli Han - One of the best experts on this subject based on the ideXlab platform.
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A class of general quartic spline curves with shape parameters
Computer Aided Geometric Design, 2011Co-Authors: Xuli HanAbstract:With a support on four consecutive subintervals, a class of general quartic splines are presented for a non-uniform Knot Vector. The splines have C^2 continuity at simple Knots and include the cubic non-uniform B-spline as a special case. Based on the given splines, piecewise quartic spline curves with three local shape parameters are given. The given spline curves can be C^[email protected]?G^3 continuous by fixing some values of the [email protected]?s parameters. Without solving a linear system, the spline curves can also be used to interpolate sets of points with C^2 continuity. The effects of varying the three shape parameters on the shape of the quartic spline curves are determined and illustrated.
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CAD/Graphics - Quadratic Trigonometric Spline Curves with Multiple Shape Parameters
2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics, 2007Co-Authors: Xuli Han, Shanmin LuoAbstract:Quadratic trigonometric spline curves with multiple shape parameters are presented in this paper. Analogous to the cubic B-spline curves, each trigonometric spline curve segment is generated by four consecutive control points. The trigonometric spline curves with a non-uniform Knot Vector are C1 continuous. With a uniform Knot Vector, the trigonometric spline curves are C continuous when all shape parameter lambdai =1. Taking different values of the shape parameters, one can globally or locally adjust the shapes of the curves, so that the trigonometric spline curves can be close to the cubic B-spline curves or closer to the given control polygon than the cubic B-spline curves. The trigonometric spline curves also can represent ellipse and generate a family of ellipse with the same control points. A quadratic trigonometric Bezier curves are also introduced as a special case of the given trigonometric spline curves.
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quadratic trigonometric polynomial curves concerning local control
Applied Numerical Mathematics, 2006Co-Authors: Xuli HanAbstract:With a non-uniform Knot Vector and two local shape parameters, a kind of piecewise quadratic trigonometric polynomial curves is presented in this paper. The given curves have similar construction and the same continuity as the quadratic non-uniform B-spline curves. Two local parameters serve to local control tension and local control bias respectively in the curves. The changes of a local shape parameter will only affect two curve segments. The given curves can approximate the quadratic non-uniform rational B-spline curves and the quadratic rational Bezier curves well for which the relations of the local shape parameters and the weight numbers of the rational curves are described. The trigonometric polynomial curves can yield tight envelopes for the quadratic rational Bezier curves. The given curve also can be decreased to linear trigonometric polynomial curve which is equal to a quadratic rational Bezier curve and represents ellipse curve.
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c2 quadratic trigonometric polynomial curves with local bias
Journal of Computational and Applied Mathematics, 2005Co-Authors: Xuli HanAbstract:Quadratic trigonometric polynomial curves with local bias are presented in this paper. The quadratic trigonometric polynomial curves have C^2 continuity with a non-uniform Knot Vector and any value of the bias, while the quadratic B-spline curves have C^1 continuity. The changes of a local bias parameter will only affect two curve segments. With the bias parameters, the quadratic trigonometric polynomial curves can move locally toward or against a control vertex. A quadratic trigonometric Bezier curve is also introduced as special case of the given trigonometric polynomial curves.
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Cubic trigonometric polynomial curves with a shape parameter
Computer Aided Geometric Design, 2004Co-Authors: Xuli HanAbstract:Cubic trigonometric polynomial curves with a shape parameter are presented in this paper. The trigonometric polynomial curves are C2 continuous and G3 continuous with a non-uniform Knot Vector. With a uniform Knot Vector, the trigonometric polynomial curves are C3 continuous for the shape parameter λ ≠ 1 and C5 continuous for λ = 1. With the shape parameter, the trigonometric polynomial curves can be close to the cubic B-spline curves or closer to the given control polygon than the cubic B-spline curves. The trigonometric polynomial curves also can be decreased to quadratic trigonometric polynomial curves which can represent ellipses. The trigonometric Bezier curve and trigonometric polynomial interpolation are also discussed.
Jianmin Zheng - One of the best experts on this subject based on the ideXlab platform.
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Surface skinning using periodic T -spline in semi-NURBS form
Journal of Computational and Applied Mathematics, 2015Co-Authors: Wenyu Chen, Yiyu Cai, Ahmad H. Nasri, Jianmin ZhengAbstract:NURBS skinning is a powerful and effective process in Computer Aided Geometric Design (CAGD). It constructs a surface by interpolating a set of cross sectional NURBS curves. These curves however may not be compatible, i.e., they have different Knot Vectors. This incompatibility is conventionally solved by Knot refinement bringing all curves to share the same Knot Vector, which leads to an explosion in the number of control points defining the skinned surface. Another disadvantage of NURBS skinning is the difficulty of local modification: adjusting one cross section may result in a global change of the surface. In this paper, periodic T -spline in semi-NURBS form is discussed. Surface skinning using such T -splines is able to handle closed cross sections, to support local modifications and to control smoothness along the cross sectional curves. We provide explicit formulae for constructing such T -spline skinned surfaces, which avoid solving a large system of equations. Experimental results and theoretical analysis confirm that our approach is better than NURBS skinning as it generates surfaces with fewer control points.
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CAD/Graphics - TV-L1 Optimization for B-Spline Surface Reconstruction with Sharp Features
2013 International Conference on Computer-Aided Design and Computer Graphics, 2013Co-Authors: Yiyu Cai, Jianmin ZhengAbstract:The placement of Knot Vector and the determination of control points are two fundamental issues in B-spline surface reconstruction. This paper presents a variational approach to construct B-spline surfaces from a set of data points. The approach finds the optimal placement of Knots and control points simultaneously while most previous methods determine the Knots heuristically or in a separate step. Moreover, different from most previous methods using least squares metric, our approach adapts L_1-norm with total variation (TV) as regularization in the fitting procedure, which enables the approach to handle both Gaussian noise and outliers in the same manner and is able to automatically optimize the placement of Knot Vector to faithfully reconstruct the sharp features. A numerical solver based on the augmented Lagrangian method is also proposed in the paper to efficiently solve the TV-L_1 optimization. Experimental results demonstrate the effectiveness and efficiency of the proposed variational B-spline surface reconstruction.
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Blind watermarking of NURBS curves and surfaces
Computer-Aided Design, 2013Co-Authors: Jianjiang Pan, Jianmin Zheng, Gang ZhaoAbstract:This paper presents two watermarking methods for NURBS curves and surfaces. Both methods are blind, shape-preserving and data amount-preserving. These features are often required in watermarking of CAD models. The first method is based on the replacement of exterior Knots of NURBS. Watermarks are embedded into the cross-ratio of four Knots in the Knot Vector(s) and the method is robust to affine transformation, Mobius reparameterization, and interior Knot insertion and removal operations. The second method is based on reparameterization using Mobius transformation. Watermarks are embedded into the ratio of two Knot intervals selected from the Knot Vector(s) and the method is robust to affine transformation and linear reparameterization. The capacity of the first method is m-1 for a degree m NURBS curve and m+n-2 for a degree mxn NURBS surface, and the capacity of the second method is 1 for a curve and 2 for a surface. Experiments have been conducted to demonstrate the shape-preserving, data amount-preserving properties and robustness.
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Approximate T-spline surface skinning
Computer-Aided Design, 2012Co-Authors: Xunnian Yang, Jianmin ZhengAbstract:This paper considers the problem of constructing a smooth surface to fit rows of data points. A special class of T-spline surfaces is examined, which is characterized to have a global Knot Vector in one parameter direction and individual Knot Vectors from row to row in the other parameter direction. These T-spline surfaces are suitable for lofted surface interpolation or approximation. A skinning algorithm using these T-spline surfaces is proposed, which does not require the Knot compatibility of sectional curves. The algorithm consists of three main steps: generating sectional curves by interpolating data points of each row by a B-spline curve; computing the control curves of a skinning surface that interpolates the sectional curves; and approximating each control curve by a B-spline curve with fewer Knots, which results in a T-spline surface. Compared with conventional B-spline surface skinning, the proposed T-spline surface skinning has two advantages. First, the sectional curves and the control curves of a T-spline surface can be constructed independently. Second, the generated T-spline skinning surface usually has much fewer control points than a lofted B-spline surface that fits the data points with the same error bound. Experimental examples have demonstrated the effectiveness of the proposed algorithm.
