Natural Element Method for the Simulation of Structures and Processes

Chinesta, Francisco; Cescotto, Serge; Lorong, Philippe

doi:10.1002/9781118616901

Cited by 21 publications

(21 citation statements)

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“…In the same way that the finite element method, the CNEM approximates a field by using a variational/weak formulation and uses an interpolation function built thanks to a Vorono diagram like the Sibson function ( [37] and [8]). This method allows to work in Lagrangian description but with no mesh distortion problem.…”

Section: Numerical Implementation Space Discretization Using Constraimentioning

confidence: 99%

“…However, the NEM uses the Natural Neighbor Interpolation inside the variational/weak formulation. The Natural Neighbor Interpolation is built thanks to a Vorono diagram like the Sibson function ( [37] and [8]). This kind of interpolation allows working in updated Lagrangian descriptions but with no mesh distortion problem [7].…”

Section: Numerical Implementation Space Discretization Using Constraimentioning

confidence: 99%

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Modeling laser drilling in percussion regime using constraint natural element method

et al. 2015

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Abstract The laser drilling process is the main process used in machining procedures on aeronautic engines, especially in the cooling parts. The industrial problematic is to reduce geometrical deviations of the holes and defects during manufacturing. The interaction between a laser beam and an absorbent metallic matter in the laser drilling regime involves thermal and hydrodynamical phenomenon. Their role on the drilling is not yet completely understood and a realistic simulation of the process could contribute to a better understanding of these phenomenon. The simulation of such process induces strong numerical difficulties. This work presents a physical model combined with the use of the original Constraint Natural Element Method to simulate the laser drilling. The physical model includes solid/liquid and liquid/vapor phase transformations, the liquid ejection and the convective and conductive thermal exchanges. It is the first time that all these phenomena are included in a modelling and numerically solved in a 2D axisymmmetric problem. Simulations results predict most of measurements (hole geometry, velocity of the liquid ejection and laser drilling velocity) without adjusting any parameters.

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Section: Numerical Implementation Space Discretization Using Constraimentioning

confidence: 99%

Section: Numerical Implementation Space Discretization Using Constraimentioning

confidence: 99%

Modeling laser drilling in percussion regime using constraint natural element method

et al. 2015

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“…In this area, the Discrete Element Method [4] is a good alternative to the FEM to locally solve problems related to material fracture [5], multibody system coupling [6] or dry sliding contact with a third body presence [7], among others. A long term solution consists of solving the contact area with the DEM and solving the piece and tool far from the contact with continuous approaches, such as the FEM or the NEM [8], and then coupling these methods (figure 1). Figure 1: Simplified example of a milling process.…”

Section: Introductionmentioning

confidence: 99%

Simulation of continuum heat conduction using DEM domains

Terreros

Iordanoff

Charles

2013

Computational Materials Science

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Currently, almost all material manufacturing processes are simulated using methods based on continuum approaches such as the Finite Element Method (FEM). These methods, though widely studied, face difficulties with multibody, contact, high-strain and high-displacement problems, which are usually found in manufacturing processes. In some cases, the Discrete Element Method (DEM) is used to overcome these problems, but it is not yet able to simulate some of the physics of a continuum material, such as 3D heat transfer.To carry out a realistic simulation of a process, its thermal field must be properly predicted. This work describes a fast and efficient method to simulate heat conduction through a 3D continuum material using the Discrete Element Method. The material is modelled with spherical discrete elements of different sizes to obtain a compact and isotropic domain adequate for carrying out mechanical simulations to obtain straightforward thermal and mechanical coupling.Thermal simulations carried out with the proposed Discrete Element Method are compared to both the analytical and FEM results. This comparison shows excellent agreement and validates the proposed method.

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“…Each method is distinguished by its capability to spatially discretize the studied model. Among them, the constrained natural element method CNEM [26][27][28], which is an extension of the natural element method (NEM) [29] to nonconvex domains, is chosen in this study. This method has practically all of the advantages of the FEM approach, and it circumvents the major drawbacks related to the meshing.…”

Section: Spatial Discretization and Integration Issuesmentioning

confidence: 99%

“…Therefore, the continuum subdomain in X C is discretized with the CNEM approach. Consequently, X C is approximated by a set of nodes in which connectivity is not necessary [26].…”

Section: Spatial Discretization and Integration Issuesmentioning

confidence: 99%

3D coupling approach between discrete and continuum models for dynamic simulations (DEM–CNEM)

Jebahi

Charles

Dau

et al. 2013

Computer Methods in Applied Mechanics and Engineering

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. a b s t r a c tThe coupling between two dissimilar numerical methods presents a major challenge, especially in case of discrete-continuum coupling. The Arlequin approach provides a flexible framework and presents several advantages in comparison to alternative approaches. Many studies have analyzed, in statics, the ingredients of this approach in 1D configurations under several particular conditions. The present study extends the Arlequin parameter studies to incorporate a dynamic behavior using 3D models. Based on these studies, a new 3D coupling method adapted for dynamic simulations is developed. This method couples two 3D codes: DEM-based code and CNEM-based code. The 3D coupling method was applied to several reference dynamics tests. Good results are obtained using this method, compared with the analytical and numerical results of both DEM and CNEM.

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Natural Element Method for the Simulation of Structures and Processes

Cited by 21 publications

References 0 publications

Modeling laser drilling in percussion regime using constraint natural element method

Modeling laser drilling in percussion regime using constraint natural element method

Simulation of continuum heat conduction using DEM domains

3D coupling approach between discrete and continuum models for dynamic simulations (DEM–CNEM)

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