References of "International Journal for Numerical Methods in Engineering"
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See detailOn the equivalent static load method for flexible multibody systems described with a nonlinear finite element formalism
Tromme, Emmanuel ULg; Sonneville, Valentin ULg; Bruls, Olivier ULg et al

in International Journal for Numerical Methods in Engineering (2016)

The equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response ... [more ▼]

The equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response optimization under multiple load cases. The ESL cases are defined based on the transient analysis response whereupon all the standard techniques of static response optimization can be used. In the last decade, the ESL method has been applied to perform the structural optimization of flexible components of mechanical systems modeled as multibody systems (MBS). The ESL evaluation strongly depends on the adopted formulation to describe the MBS and has been initially derived based on a floating frame of reference formulation. In this paper, we propose a method to derive the ESL adapted to a nonlinear finite element approach based on a Lie group formalism for two main reasons. Firstly, the finite element approach is completely general to analyze complex MBS and is suitable to perform more advanced optimization problems like topology optimization. Secondly, the selected Lie group formalism leads to a formulation of the equations of motion in the local frame, that turns out to be a strong practical advantage for the ESL evaluation. Examples are provided to validate the proposed method. [less ▲]

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See detailA ‘nodeless’ dual superelement formulation for structural and multibody dynamics application to reduction of contact problems
Géradin, Michel ULg; Rixen, Daniel

in International Journal for Numerical Methods in Engineering (2015)

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See detailEfficient 3D transfer operators based on numerical integration
Bussetta, Philippe ULg; Boman, Romain ULg; Ponthot, Jean-Philippe ULg

in International Journal for Numerical Methods in Engineering (2015), 102(3-4), 892-929

This paper deals with data transfer between two meshes as it happens in a finite element context when a remeshing has to be performed. We propose a finite-volume-based data transfer method for an ... [more ▼]

This paper deals with data transfer between two meshes as it happens in a finite element context when a remeshing has to be performed. We propose a finite-volume-based data transfer method for an efficient remeshing of three-dimensional solid mechanics problems. The originality of this transfer method stems from a linear reconstruction of the fields to be transferred on an auxiliary finite volume mesh, a fast computation of the transfer operator and the application to the complete remeshing of 3D problems. This procedure is applicable to both nodal values and discrete fields defined at quadrature points. In addition, a data transfer method using mortar elements is presented. The main improvement made to this second method comes from a fast computation of mortar elements. These two data transfer methods are compared with the simplest transfer method, which consists of a classical interpolation. After some academic examples, we present 2D forging and 3D friction stir welding applications. [less ▲]

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See detailAnalytical sensitivity analysis using the extended finite element method in shape optimization of bimaterial structures
Noël, Lise ULg; Van Miegroet, Laurent; Duysinx, Pierre ULg

in International Journal for Numerical Methods in Engineering (2015)

The present work investigates the shape optimization of bimaterial structures. The problem is formulated using a level set description of the geometry and the extended finite element method (XFEM) to ... [more ▼]

The present work investigates the shape optimization of bimaterial structures. The problem is formulated using a level set description of the geometry and the extended finite element method (XFEM) to enable an easy treatment of complex geometries. A key issue comes from the sensitivity analysis of the structural responses with respect to the design parameters ruling the boundaries. Even if the approach does not imply any mesh modification, the study shows that shape modifications lead to difficulties when the perturbation of the level sets modifies the set of extended finite elements. To circumvent the problem, an analytical sensitivity analysis of the structural system is developed. Differences between the sensitivity analysis using FEM or XFEM are put in evidence. To conduct the sensitivity analysis, an efficient approach to evaluate the so-called velocity field is developed within the XFEM domain. The proposed approach determines a continuous velocity field in a boundary layer around the zero level set using a local finite element approximation. The analytical sensitivity analysis is validated against the finite differences and a semi- analytical approach. Finally our shape optimization tool for bimaterial structures is illustrated by revisiting the classical problem of the shape of soft and stiff inclusions in plates. [less ▲]

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See detailOptimizing Perfectly Matched Layers in Discrete Contexts
Modave, Axel ULg; Delhez, Eric ULg; Geuzaine, Christophe ULg

in International Journal for Numerical Methods in Engineering (2014), 99(6), 410437

Perfectly Matched Layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both the time-dependent and the time-harmonic ... [more ▼]

Perfectly Matched Layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both the time-dependent and the time-harmonic cases, their performance critically depends on the so-called absorption function. This paper deals with the choice of this function when classical numerical methods are used (based on finite differences, finite volumes, continuous finite elements and discontinuous finite elements). After reviewing the properties of the PMLs at the continuous level, we analyse how they are altered by the different spatial discretizations. In the light of these results, different shapes of absorption function are optimized and compared by means of both one- and two-dimensional representative time-dependent cases. This study highlights the advantages of the so-called shifted hyperbolic function, which is efficient in all cases and does not require the tuning of a free parameter, by contrast with the widely used polynomial functions. [less ▲]

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See detailReduced chaos expansions with random coefficients in reduced-dimensional stochastic modeling of coupled problems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

in International Journal for Numerical Methods in Engineering (2014), 97

We address the curse of dimensionality in methods for solving stochastic coupled problems with an emphasis on stochastic expansion methods such as those involving polynomial chaos expansions. The proposed ... [more ▼]

We address the curse of dimensionality in methods for solving stochastic coupled problems with an emphasis on stochastic expansion methods such as those involving polynomial chaos expansions. The proposed method entails a partitioned iterative solution algorithm that relies on a reduced-dimensional representation of information exchanged between subproblems to allow each subproblem to be solved within its own stochastic dimension while interacting with a reduced projection of the other subproblems. The proposed method extends previous work by the authors by introducing a reduced chaos expansion with random coefficients. The representation of the exchanged information by using this reduced chaos expansion with random coefficients enables an expeditious construction of doubly stochastic polynomial chaos expansions that separate the effect of uncertainty local to a subproblem from the effect of statistically independent uncertainty coming from other subproblems through the coupling. After laying out the theoretical framework, we apply the proposed method to a multiphysics problem from nuclear engineering. [less ▲]

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See detailAccuracy of one-step integration schemes for damped/forced linear structural dynamics
Depouhon, Alexandre ULg; Detournay, Emmanuel; Denoël, Vincent ULg

in International Journal for Numerical Methods in Engineering (2014)

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See detailA nonsmooth generalized-alpha scheme for flexible multibody systems with unilateral constraints
Chen, Qiong-zhong; Acary, Vincent; Virlez, Geoffrey ULg et al

in International Journal for Numerical Methods in Engineering (2013), 96(8), 487-511

Mechanical systems are usually subjected not only to bilateral constraints but also to unilateral constraints. Inspired by the generalized-alpha time integration method for smooth flexible multibody ... [more ▼]

Mechanical systems are usually subjected not only to bilateral constraints but also to unilateral constraints. Inspired by the generalized-alpha time integration method for smooth flexible multibody dynamics, this paper presents a nonsmooth generalized-alpha method, which allows a consistent treatment of the nonsmooth phenomena induced by unilateral constraints and an accurate description of the structural vibrations during free motions. Both the algorithm and the implementation are illustrated in detail. Numerical example tests are given in the scope of both rigid and flexible body models, taking account for both linear and nonlinear systems, and comprising both unilateral and bilateral constraints. The extended nonsmooth generalized-alpha method is verified through comparison to the traditional Moreau-Jean method and the fully implicit Newmark method. Results show that the nonsmooth generalized-alpha method benefits from the accuracy and stability property of the classical generalized-alpha method with controllable numerical damping. In particular, when it comes to the analysis of flexible systems, the nonsmooth generalized-alpha method shows much better accuracy property than the other two methods. [less ▲]

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See detailTransient Fokker-Planck-Kolmogorov equation solved with smoothed particle hydrodynamics method
Canor, Thomas ULg; Denoël, Vincent ULg

in International Journal for Numerical Methods in Engineering (2013), 94(6), 535553

Probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function (pdf). The time ... [more ▼]

Probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function (pdf). The time evolution of the pdf of the response of a randomly excited deterministic system is commonly described with the transient Fokker-Planck-Kolmogorov equation (FPK). The FPK equation is a conservation equation of a hypothetical or abstract fluid, which models the transport of probability. This paper presents a generalized formalism for the resolution of the transient FPK equation using the well-known mesh-free Lagrangian method, Smoothed Particle Hydrodynamics (SPH). Numerical implementation shows notable advantages of this method in an unbounded state space: (i) the conservation of total probability in the state space is explicitly written, (ii) no artifact is required to manage far- eld boundary conditions , (iii) the positivity of the pdf is ensured and (iv) the extension to higher dimensions is straightforward. Furthermore, thanks to the moving particles, this method is adapted for a large kind of initial conditions, even slightly dispersed distributions. The FPK equation is solved without any a priori knowledge of the stationary distribution; just a precise representation of the initial distribution is required. [less ▲]

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See detailA full-discontinuous Galerkin formulation of non-linear Kirchhoff-Love shells: elasto-plastic finite deformations, parallel computation & fracture applications
Becker, Gauthier ULg; Noels, Ludovic ULg

in International Journal for Numerical Methods in Engineering (2013), 93(1), 80-117

Due to its ability to take into account discontinuities, the discontinuous Galerkin (DG) method presents some advantages for modeling crack initiations and propagations. This concept has been recently ... [more ▼]

Due to its ability to take into account discontinuities, the discontinuous Galerkin (DG) method presents some advantages for modeling crack initiations and propagations. This concept has been recently applied to 3D simulations and to elastic thin bodies. In this last case, the assumption of small elastic deformations before crack initiations or propagations reduces drastically the applicability of the framework to a reduced number of materials. To remove this limitation, a full-DG formulation of non-linear Kirchhoff-Love shells is presented and is used in combination with an elasto-plastic finite deformations model. The results obtained by this new formulation are in agreement with other continuum elasto-plastic shell formulations. Then this full-DG formulation of Kirchhoff-Love shells is coupled with the cohesive zone model to perform thin body fracture simulations. As this method allows considering elasto-plastic constitutive laws in combination with the cohesive model, accurate results compared to the experiments are found. In particular, the crack path and propagation rate of a blasted cylinder are shown to match experimental results. One of the main advantages of this framework is its ability to run in parallel with a high speed-up factor, allowing the simulation of ultra fine meshes. [less ▲]

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See detailA Frontal Delaunay Quad Mesh Generator Using the L ∞  Norm
Remacle, J.-F.; Henrotte, F.; Carrier-Baudouin, T. et al

in International Journal for Numerical Methods in Engineering (2013), 94(5), 494-512

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See detailAn efficient 3D implicit approach for the thermomechanical simulation of elastic–viscoplastic materials submitted to high strain rate and damage
Jeunechamps, Pierre-Paul; Ponthot, Jean-Philippe ULg

in International Journal for Numerical Methods in Engineering (2013), 94

This paper aims at presenting a general consistent numerical formulation able to take into account, in a coupled way, strain rate, thermal and damage effects on the behavior of materials submitted to ... [more ▼]

This paper aims at presenting a general consistent numerical formulation able to take into account, in a coupled way, strain rate, thermal and damage effects on the behavior of materials submitted to quasistatic or dynamic loading conditions in a large deformation context. The main features of this algorithmic treatment are as follows: -A unified treatment for the analysis and implicit time integration of thermo-elasto-viscoplastic constitutive equations including damage that depends on the strain rate for dynamic loading conditions. This formalism enables us to use dynamic thermomechanically coupled damage laws in an implicit framework. -An implicit framework developed for time integration of the equations of motion. An efficient staggered solution procedure has been elaborated and implemented so that the inertia and heat conduction effects can be properly treated. - An operator split-based implementation, accompanied by a unified method to analytically evaluate the consistent tangent operator for the (implicit) coupled damage–thermo-elasto-viscoplastic problem. -The possibility to couple any hardening law, including rate-dependent models, with any damage model that fits into the present framework. All the developments have been considered in the framework of an implicit finite element code adapted to large strain problems. The numerical model will be illustrated by several applications issued from the impact andmetal-forming domains. All these physical phenomena have been included into an oriented object finite element code (implemented at LTAS-MN2L, University of Liège, Belgium) named Metafor. [less ▲]

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See detailEfficient ALE mesh management for 3D quasi-Eulerian problems
Boman, Romain ULg; Ponthot, Jean-Philippe ULg

in International Journal for Numerical Methods in Engineering (2012), 92(10), 857-890

In computational solid mechanics, the ALE formalism can be very useful to reduce the size of finite element models of continuous forming operations such as roll forming. The mesh of these ALE models is ... [more ▼]

In computational solid mechanics, the ALE formalism can be very useful to reduce the size of finite element models of continuous forming operations such as roll forming. The mesh of these ALE models is said to be quasi-Eulerian because the nodes remain almost fixed—or almost Eulerian—in the main process direction, although they are required to move in the orthogonal plane in order to follow the lateral displacements of the solid. This paper extensively presents a complete node relocation procedure dedicated to such ALE models. The discussion focusses on quadrangular and hexahedral meshes with local refinements. The main concern of this work is the preservation of the geometrical features and the shape of the free boundaries of the mesh. With this aim in view, each type of nodes (corner, edge, surface and volume) is treated sequentially with dedicated algorithms. A special care is given to highly curved 3D surfaces for which a CPU-efficient smoothing technique is proposed. This new method relies on a spline surface reconstruction, on a very fast weighted Laplacian smoother with original weights and on a robust reprojection algorithm. The overall consistency of this mesh management procedure is finally demonstrated in two numerical applications. The first one is a 2D ALE simulation of a drawbead, which provides similar results to an equivalent Lagrangian model yet is much faster. The second application is a 3D industrial ALE model of a 16-stand roll forming line. In this case, all attempts to perform the same simulation by using the Lagrangian formalism have been unsuccessful. [less ▲]

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See detailMeasure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

in International Journal for Numerical Methods in Engineering (2012), 92

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of ... [more ▼]

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower-dimensional space than the sources themselves. In this work, we thus propose to use a dimension reduction technique for obtaining the representation of the exchanged information, and we propose a measure transformation technique that allows subproblem implementations to exploit this dimension reduction to achieve computational gains. The effectiveness of the proposed dimension reduction and measure transformation methodology is demonstrated through a multiphysics problem relevant to nuclear engineering. [less ▲]

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See detailDimension reduction in stochastic modeling of coupled problems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

in International Journal for Numerical Methods in Engineering (2012), 92

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of ... [more ▼]

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower dimensional space than the sources themselves. This work thus presents an investigation into the characterization of the exchanged information by a reduced-dimensional representation and in particular by an adaptation of the Karhunen-Loève decomposition. The effectiveness of the proposed dimension–reduction methodology is analyzed and demonstrated through a multiphysics problem relevant to nuclear engineering. [less ▲]

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See detailA bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate
Gao, Tong ULg; ZHANG, Weihong; Duysinx, Pierre ULg

in International Journal for Numerical Methods in Engineering (2012), 91(1), 98-114

The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by continuous topology optimization method. In this work, a new bi-value coding ... [more ▼]

The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by continuous topology optimization method. In this work, a new bi-value coding parameterization (BCP) scheme is proposed to this aim. The idea of the BCP scheme is to “code” each material phase using integer values of +1 and -1. Each available material phase has one unique “code” consisting of +1 and/or -1 assigned to design variables. Theoretical and numerical comparisons between the proposed BCP scheme and existing schemes show that the BCP has the advantage of an evident reduction of the number of design variables in logarithmic form. This is very beneficial when the number of candidate materials becomes important. Numerical tests with up to 36 candidate material orientations are illustrated for the first time to indicate the reliability and efficiency of the proposed scheme in solving this kind of problem. It proves that the BCP is an interesting and potential scheme to achieve the optimal orientations for large-scale design problems. [less ▲]

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See detailA mixed solid-shell element for the analysis of laminated composites
Rah, Kamran; Paepegem, Wim; Habraken, Anne ULg et al

in International Journal for numerical methods in engineering (2012), 89(7), 805-828

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See detailBlossom-Quad: a non-uniform quadrilateral mesh generator using a minimum cost perfect matching algorithm
Remacle, Jean-François; Lambrechts, Jonathan; Seny, Bruno et al

in International Journal for Numerical Methods in Engineering (2012), 89(9), 1102-1119

A new indirect way of producing all-quad meshes is presented. The method takes advantage of a well-known algorithm of the graph theory, namely the Blossom algorithm, that computes the minimum-cost perfect ... [more ▼]

A new indirect way of producing all-quad meshes is presented. The method takes advantage of a well-known algorithm of the graph theory, namely the Blossom algorithm, that computes the minimum-cost perfect matching in a graph in polynomial time. The new Blossom-Quad algorithm is compared with standard indirect procedures. Meshes produced by the new approach are better both in terms of element shape and in terms of size field efficiency. [less ▲]

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See detailHigh Quality Surface Remeshing Using Harmonic Maps. Part II: Surfaces with High Genus and of Large Aspect Ratio
Marchandise, E.; Carton de Wiart, C.; Vos, W. et al

in International Journal for Numerical Methods in Engineering (2011), 86(11), 1303-1321

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See detailElectrostatic Simulation using XFEM for Conductor and Dielectric Interfaces
Rochus, Véronique ULg; Rixen, Daniel; Van Miegroet, Laurent ULg et al

in International Journal for Numerical Methods in Engineering (2011), 85(10), 12071226

ManyMicro-Electro-Mechanical Systems (e.g. RF-switches, micro-resonators and micro-rotors) involve mechanical structures moving in an electrostatic field. For this type of problems, it is required to ... [more ▼]

ManyMicro-Electro-Mechanical Systems (e.g. RF-switches, micro-resonators and micro-rotors) involve mechanical structures moving in an electrostatic field. For this type of problems, it is required to evaluate accurately the electrostatic forces acting on the devices. Extended Finite Element (X-FEM) approaches can easily handle moving boundaries and interfaces in the electrostatic domain and seem therefore very suitable to model Micro-Electro-Mechanical Systems. In this study we investigate different X-FEM techniques to solve the electrostatic problem when the electrostatic domain is bounded by a conducting material. Preliminary studies in one-dimension have shown that one can obtain good results in the computation of electrostatic potential using X-FEM. In this paper the extension of these preliminary studies to 2D problem is presented. In particular a new type of enrichment functions is proposed in order to treat accurately Dirichlet boundary conditions on the interface. [less ▲]

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