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Peer Reviewed
See detailGeneralized multipole technique with directive beam expansions
Landesa, Luis; V Sabariego, Ruth ULg; Jose Manuel, Taboada

(1999, September)

Detailed reference viewed: 11 (2 ULg)
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See detailGeneralized multistage mechanical model for nonlinear metallic materials
Hradil, Petr; Talja, Asko; Real, Esther et al

in Thin-Walled Structures (2013), 63

Metallic alloys have a significant role in thin-walled engineering structures due to their unique properties such as corrosion resistance, low density or durability. Their mechanical behaviour is usually ... [more ▼]

Metallic alloys have a significant role in thin-walled engineering structures due to their unique properties such as corrosion resistance, low density or durability. Their mechanical behaviour is usually nonlinear, and this nonlinearity can be further increased during the work-hardening process. In such cases, designers have to take the proper stress-strain relationship into account to obtain reliable prediction of deformations or internal forces. In this paper, a theoretical model is proposed to match different kinds of measured data or already existing stress-strain models. It is flexible to accommodate any number of measured or recommended material parameters, and therefore makes design rules independent on testing standards. It is particularly suitable for computer code implementation. The approximate inversion of the multistage model is also included in the presented study. The general formula is applied on the set of parameters typically available for structural stainless steels in Europe (0.2% and 1.0% proof strength and ultimate strength) and compared to the existing models by curve-fitting of analytical equations to measured stresses and strains of austenitic, duplex and ferritic stainless steels. The comparisons clearly showed that this three-stage application of the generalized multistage model yields more accurate results compared to the existing material models both in direct and inverse form. [less ▲]

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See detailGeneralized Pareto fit to the Society of Actuaries large claims database
Cebrian, Ana; Denuit, Michel; Lambert, Philippe ULg

in North American Actuarial Journal (2003), 7

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See detailGeneralized parton distributions of the pion
Bissey, F.; Cudell, Jean-René ULg; Cugnon, Joseph ULg et al

in Nuclear Physics B-Proceedings Supplements (2004, July), 133

Off-forward structure functions of the pion are investigated in twist-two and twist-three approximation. A simple model is used for the pion, which allows to introduce finite size effects, while ... [more ▼]

Off-forward structure functions of the pion are investigated in twist-two and twist-three approximation. A simple model is used for the pion, which allows to introduce finite size effects, while preserving gauge invariance. Results for the imaginary parts of the gamma*pi --> gamma*pi off-forward amplitude and of the structure functions are presented. Generalized Callan-Gross relations are obtained. [less ▲]

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See detailGeneralized Pascal triangle for binomial coefficients of finite words
Stipulanti, Manon ULg

Poster (2016, April 05)

Abstract. We introduce a generalization of Pascal triangle based on bino- mial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite ... [more ▼]

Abstract. We introduce a generalization of Pascal triangle based on bino- mial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpinski gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p. [less ▲]

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See detailGeneralized Pascal triangle for binomial coefficients of words
Leroy, Julien ULg; Rigo, Michel ULg; Stipulanti, Manon ULg

in Advances in Applied Mathematics (2016), 80

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word ... [more ▼]

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpiński gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p. [less ▲]

Detailed reference viewed: 107 (56 ULg)
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See detailGeneralized Pascal triangle for binomial coefficients of words : an overview
Stipulanti, Manon ULg

Conference (2016, September 07)

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a finite word appears as a subsequence of another finite word ... [more ▼]

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a finite word appears as a subsequence of another finite word. Similarly to the Sierpiński gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p. Then we create a new sequence from this extended Pascal triangle that counts, on each row of this triangle, the number of positive binomial coefficients. We study some properties of this sequences. To be precise, we investigate some properties regarding the regularity of the sequence. To extend our work, we construct a Pascal triangle using the Fibonacci representations of all the nonnegative integers and we define the corresponding sequence of which we study the regularity. This regularity is an extension of the classical k-regularity of sequences. [less ▲]

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See detailGeneralized Pascal triangles and binomial coefficients of words
Stipulanti, Manon ULg

Poster (2016, December 01)

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word ... [more ▼]

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpinski gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p. From the extended Pascal triangle obtained when p is equal to 2, we derive a sequence of which we study the regularity and the asymptotic behavior of the summatory function. Inspired from this regularity, we extend our results to another famous numeration systems, namely the Zeckendorff numeration system. [less ▲]

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See detailGeneralized Pascal triangles for binomial coefficients of words: a short introduction
Stipulanti, Manon ULg

Conference (2017, January 09)

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a finite word appears as a subsequence of another finite word ... [more ▼]

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a finite word appears as a subsequence of another finite word. Similarly to the Sierpiński gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p. [less ▲]

Detailed reference viewed: 18 (2 ULg)
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See detailGeneralized Pointwise Hölder Spaces
Nicolay, Samuel ULg; Kreit, Damien

Conference (2013, October 31)

In [8,7], the properties of generalized uniform Hölder spaces have been investigated. The idea underlying the definition is to replace the exponent α of the usual spaces Λ^α(R^d) (see e.g. [6]) with a ... [more ▼]

In [8,7], the properties of generalized uniform Hölder spaces have been investigated. The idea underlying the definition is to replace the exponent α of the usual spaces Λ^α(R^d) (see e.g. [6]) with a sequence σ satisfying some conditions. The so-obtained spaces Λ^σ(R^d) generalize the spaces Λ^α(R^d); the spaces Λ^σ(R^d) are actually the spaces B^{1/σ_{∞,∞}(R^d), but they present specific properties (induced by L^∞-norms) when compared to the more general spaces B^{1/σ}_{p,q}(R^d) studied in [2,4,1,5,9,10] for example. Indeed it is shown in [8,7] that most of the usual properties holding for the spaces Λ^α(R^d) can be transposed to the spaces Λ^σ(R^d). Here, we introduce the pointwise version of these spaces: the spaces Λ^{σ,M}(x_0), with x_0∈R^d. Let us recall that a function f∈L^∞_loc(R^d) belongs to the usual pointwise Hölder space Λ^α(x_0) (α>0) if and only if there exist C,J>0 and a polynomial P of degree at most α such that sup_{|h|≤2^{−j}} |f(x_0+h)−P(h)|≤C2^{−jα}. As in [8,7], the idea is again to replace the sequence (2^{−jα})_j appearing in this inequality with a positive sequence (σ_j)j such that σ_{j+1}/σ_j is bounded (for any j); the number M stands for the maximal degree of the polynomial (this degree can not be induced by a sequence σ). By doing so, one tries to get a better characterization of the regularity of the studied function f. Generalizations of the pointwise Hölder spaces have already been proposed (see e.g. [3]), but, to our knowledge, the definition we give here is the most general version and leads to the sharpest results. [1] Alexandre Almeida. Wavelet bases in generalized Besov spaces. J. Math. Anal. Appl., 304(1):198–211, 2005. [2] António M. Caetano and Susana D. Moura. Local growth envelopes of spaces of generalized smoothness: the critical case. Math. Inequal. Appl., 7(4):573–606, 2004. [3] Marianne Clausel. Quelques notions d'irrégularité uniforme et ponctuelle : le point de vue ondelettes. PhD thesis, University of Paris XII, 2008. [4] Walter Farkas. Function spaces of generalised smoothness and pseudo-differential operators associated to a continuous negative definite function. Habilitation Thesis, 2002. [5] Walter Farkas and Hans-Gerd Leopold. Characterisations of function spaces of generalised smoothness. Ann. Mat. Pura Appl., IV. Ser., 185(1):1–62, 2006. [6] Steven G. Krantz. Lipschitz spaces, smoothness of functions, and approximation theory. Exposition. Math., 1(3):193–260, 1983. [7] Damien Kreit and Samuel Nicolay. Characterizations of the elements of generalized Hölder-Zygmund spaces by means of their representation. J. Approx. Theory, to appear, 10.1016/j.jat.2013.04.003. [8] Damien Kreit and Samuel Nicolay. Some characterizations of generalized Hölder spaces. Math. Nachr., 285(17-18):2157–2172, 2012. [9] Thomas Kühn, Hans-Gerd Leopold, Winfried Sickel, and Leszek Skrzypczak. Entropy numbers of embeddings of weighted Besov spaces II. Proceedings of the Edinburgh Mathematical Society (Series 2), 49(02):331–359, 2006. [10] Susana D. Moura. On some characterizations of Besov spaces of generalized smoothness. Math. Nachr., 280(9-10):1190–1199, 2007. [less ▲]

Detailed reference viewed: 57 (12 ULg)
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Peer Reviewed
See detailGeneralized power method for sparse principal component analysis
Nesterov, Yurii; Richtarik, Peter; Journee, Michel ULg et al

in Journal of Machine Learning Research (2010), 11

Detailed reference viewed: 123 (34 ULg)
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See detailGeneralized Shape And Topology Optimization: Recent Developments And Application Perspectives To Automotive Structures
Duysinx, Pierre ULg; Van Miegroet, Laurent ULg; Remouchamps, Alain et al

in New Advances in Body Engineering - Lightweight design, passive safety, pedestrian protection, and numerical optimization (2006, December)

More than 15 years after the seminal work by Bendsøe and Kikuchi, topology optimization of structures has taken advantage of my research efforts and has now become a commercial available tool (e.g ... [more ▼]

More than 15 years after the seminal work by Bendsøe and Kikuchi, topology optimization of structures has taken advantage of my research efforts and has now become a commercial available tool (e.g. OptiStruct by Altair, Topol by Samtech, etc.). These software tools are daily used in automotive industry and provide engineers with a rational tool for preliminary design of efficient structural components. This paper presents the status of available topology optimization tools and introduces the recent developments that extend their capabilities in order to handle stress constraints, manufacturing constraints, etc. The communication also presents a novel approach of generalized shape optimization that has been introduced to circumvent the difficulties of parametric shape optimization and to complement topology optimization. The approach is based on the eXtended Finite Element Method (XFEM) and the Level Set Description of the geometry. The Level Set description introduces smooth curve descriptions and allows modifying the connectivity of the wholes. The XFEM works with a fixed mesh as in topology optimization, which makes the method very convenient for engineers. Thus the novel approach is likely to bring the next future evolution of structural optimization. Impressive capabilities of this new generation approach will be demonstrated. Application examples from automotive and aerospace engineering will illustrate the different possibilities offered by two approaches. [less ▲]

Detailed reference viewed: 120 (5 ULg)
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See detailGeneralized Shape optimization based on the Level Set method
Van Miegroet, Laurent ULg; Moës, Nicolas; Fleury, Claude ULg et al

in Herskowitz, José (Ed.) Proceedings of the 6th World Congress of Structural and Multidisciplinary Optimization (WCSMO6) (2005, May)

This paper describes a first step work devoted to applying XFEM and Level Sets methods in optimization of structures. This first step work is based on integrating an existing XFEM code within a general ... [more ▼]

This paper describes a first step work devoted to applying XFEM and Level Sets methods in optimization of structures. This first step work is based on integrating an existing XFEM code within a general open optimization tool, SAMCEF BOSS QUATTRO. Unlike most of the existing works, this approach is more shape optimization oriented. A library of pre-formatted basic geometric entities (such as ellipses, squares, triangles, etc.) described by Level Sets functions are used. These basic Level Set features can be combined to represent many kinds of interfaces and holes. The construction parameters of the basic Level Sets are considered as the design variables. In order to evaluate the sensitivities, a finite difference scheme over the design variables is used in this first work. Different mechanical responses (energy, weight, displacement, . . .) can be considered as objective functions or constraints in the problem formulation. Several academic 2D test cases of shape and topology optimization are presented within the XFEM and Level Set approach. In addition, a work by Missoum et al. [11], in which the shape and topology optimization of the structure is carried out by an optimal selection of holes characteristics with a genetic algorithm is presented. [less ▲]

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See detailGeneralized shape optimization using X-FEM and Level Set methods
Duysinx, Pierre ULg; Van Miegroet, Laurent ULg; Jacobs, Thibaut et al

in Bendsoe, M.-P.; Olhoff, N.; Sigmund, O. (Eds.) IUTAM Sumposium on Topological Design Optimization of Structures, Machines, and Materials. Status and Perspectives (2006)

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended ... [more ▼]

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using X-FEM and of the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit the classical elliptical hole benchmark from shape optimization. [less ▲]

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See detailGeneralized Shape Optimization using XFEM and Level Set Description
Van Miegroet, Laurent ULg

Doctoral thesis (2012)

CAD based shape optimization aims at finding the shapes of internal and external boundaries of a structural components. The method is able to improve the design of structures against var- ious criteria ... [more ▼]

CAD based shape optimization aims at finding the shapes of internal and external boundaries of a structural components. The method is able to improve the design of structures against var- ious criteria such as restricted displacements, stress criteria, eigenfrequencies, etc. However, this technique has been quite unsuccessful in industrial applications because of the mesh management problems coming from the large shape modifications. The main technical problems stems from the sensitivity analysis requiring the calculation of the so-called velocity field related to mesh modifications. If 2D problems are quite well mastered, 3D solid and shell problems are difficult to handle in the most general way. It turns out that shape optimization remains generally quite fragile and delicate to use in industrial context. To circumvent the technical difficulties of the moving mesh problems, a couple of methods have been proposed such as the fictitious domain approach, the fixed grid finite elements and the projection methods. The present work relies on the application of the extended finite element method (X-FEM) to handle parametric shape optimization. The X-FEM method is naturally associated with the Level Set description of the geometry to provide an efficient and flexible treatment of problems involving moving boundaries or discontinuities. On the one hand, the method proposed benefits from the fixed mesh approach using X-FEM to prevent from mesh management difficulties. On the other hand, the Level Set description provides a smooth curves representation while being able to treat topology modifications naturally. In this thesis, we focus on the material-void and bi-material X-FEM elements for mechanical structures. The representation of the geometry is realized with a Level Set description. Basic shapes can be modeled from simple Level Set such as plane, circle, ... NURBS curves and surfaces that can be combined together using a Constructive Solid Geometry approach to represent com- plex geometries. The design variables of the optimization problem are the parameters of basic Level Set features or the NURBS control points. Classical global (compliance, eigenfrequencies, volume) and local responses (such as stress constraint) can be considered in the optimization problem that is solved using a mathematical programming approach with the CONLIN optimizer. The problem of the computation of the shape sensitivity analysis with X-FEM is carefully ad- dressed and investigated using several original methods based on semi-analytical and analytical approaches that are developed. Academic examples are first considered to illustrate that the proposed method is able to tackle accurately shape optimization problems. Then, real life struc- tures including 2D and 3D complex geometries illustrate the advantages and the drawbacks of using X-FEM and Level Set description for generalized shape optimization. [less ▲]

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See detailGeneralized shape optimization using XFEM and Level Set method
Duysinx, Pierre ULg; Van Miegroet, Laurent ULg; Jacobs, Thierry

Conference (2006, November)

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended ... [more ▼]

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using XFEM and of the smooth curves description of the Level Set method. Design variables are shape parameters of basic geometric features like circles, triangles etc. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced by the programme. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit some classical (academic) benchmarks from shape and topology optimization. [less ▲]

Detailed reference viewed: 155 (7 ULg)
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Peer Reviewed
See detailGeneralized shape optimization using XFEM and Level Set methods
Duysinx, Pierre ULg; Van Miegroet, Laurent ULg; jacobs, Thibaut et al

in Bendsoe, M.-P.; Olhoff, N.; Sigmund, O. (Eds.) Proceedings of Topopt SYMP2005, IUTAM Symposium. Topological Design Optimization of Structures, Machines and Materials. Status and Perspectives (2005, October)

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended ... [more ▼]

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using X-FEM and of the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit the classical elliptical hole benchmark from shape optimization. [less ▲]

Detailed reference viewed: 100 (3 ULg)
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See detailA Generalized Simulation Model of Chillers and Heat Pumps to be Calibrated on Published Manufacturer's Data
Lemort, Vincent ULg; Bertagnolio, Stéphane ULg

(2010, August 07)

This paper shows how semi-empirical models of chillers and heat pumps can be calibrated on the basis of manufacturer’s published data, which is most of the time the only available source of information. A ... [more ▼]

This paper shows how semi-empirical models of chillers and heat pumps can be calibrated on the basis of manufacturer’s published data, which is most of the time the only available source of information. A calibration methodology is proposed and illustrated for different technologies of vapor-compression machines, pointing out tips and tricks. Whatever the size and technology (e.g. scroll, screw or reciprocating compressors), the semi-empirical model is found to predict both full load and part load performance with a very good accuracy. This is partially due to the tailor-made formalism of the model, which allows describing the main features of the machine. [less ▲]

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See detailA Generalized Source Magnetic Field Calculation Method for Inductors of any Shape
Dular, Patrick ULg; Henrotte, François; Robert, Frédéric et al

in IEEE Transactions on Magnetics (1997), 33(2), 1398-1401

A general method to compute source fields in magnetostatics or magnetodynamics is presented for inductors of any shape. That source field is not the physical one because the zero divergence condition is ... [more ▼]

A general method to compute source fields in magnetostatics or magnetodynamics is presented for inductors of any shape. That source field is not the physical one because the zero divergence condition is not satisfied. However, the freedom so obtained is exploited to minimize its support as well as to reduce the CPU time. The use of edge finite elements enables its rigorous construction. A test problem illustrates the method. [less ▲]

Detailed reference viewed: 24 (2 ULg)