Finite element mesh generation

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Subject Specific Finite Element Mesh Generation of the Pelvis from Biplanar X-ray Images: Application to 120 clinical cases

Subject Specific Finite Element Mesh Generation of the Pelvis from Biplanar X-ray Images: Application to 120 clinical cases

Several Finite Element (FE) models of the pelvis have been developed to comprehensively assess the onset of pathologies and for clinical and industrial applications. However, because of the difficulties associated with the creation of subject-specific FE mesh from CT scan and MR images, most of the existing models rely on the data of one given individual. Moreover, although several fast and robust methods have been developed for automatically generating tetrahedral meshes of arbitrary geometries, hexahedral meshes are still preferred today because of their distinct advantages but their generation remains an open challenge. Recently, approaches have been proposed for fast 3D reconstruction of bones based on X-ray imaging. In this study, we adapted such an approach for the fast and automatic generation of all-hexahedral subject-specific FE models of the pelvis based on the elastic registration of a generic mesh to the subject-specific target in conjunction with element regularity and quality correction. The technique was successfully tested on a database of 120 3D reconstructions of pelvises from biplanar X-ray images. For each patient, a full hexahedral subject-specific FE mesh was generated with an accurate surface representation.
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Subject specific hexahedral Finite Element mesh generation of the pelvis from bi-Planar X-ray images

Subject specific hexahedral Finite Element mesh generation of the pelvis from bi-Planar X-ray images

Finite Element models are generally built from patient medical image data, such as computed tomography (CT) or magnetic resonance imaging (MRI) (Linder-Ganz et al. 2008). However, image segmentation and finite element mesh design are long and tedious processes that represent major bottlenecks for the fast generation of patient-specific Finite Element Meshes. Many attempts have been made in the literature to circumvent this problem and today several fast and robust methods have been developed for automatically generating tetrahedral meshes of arbitrary geometries. However, for a wide range of applications, hexahedral-based meshes are preferred: First, to achieve the same solution, accuracy for a given analysis requires far more tetrahedral elements than hexahedral elements, and this leads to higher computational costs (both time and memory). Second, it is well known that for incompressible and/or nearly incompressible materials, 4-noded tetrahedra with linear shape functions tend to lock and become overly stiff, generally producing acceptable displacement results but relatively inaccurate results for stresses.
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Subject Specific Finite Element Mesh Generation of the Pelvis from Biplanar X-ray Images: Application to 120 clinical cases

Subject Specific Finite Element Mesh Generation of the Pelvis from Biplanar X-ray Images: Application to 120 clinical cases

Several Finite Element (FE) models of the pelvis have been developed to comprehensively assess the onset of pathologies and for clinical and industrial applications. However, because of the difficulties associated with the creation of subject-specific FE mesh from CT scan and MR images, most of the existing models rely on the data of one given individual. Moreover, although several fast and robust methods have been developed for automatically generating tetrahedral meshes of arbitrary geometries, hexahedral meshes are still preferred today because of their distinct advantages but their generation remains an open challenge. Recently, approaches have been proposed for fast 3D reconstruction of bones based on X-ray imaging. In this study, we adapted such an approach for the fast and automatic generation of all-hexahedral subject-specific FE models of the pelvis based on the elastic registration of a generic mesh to the subject-specific target in conjunction with element regularity and quality correction. The technique was successfully tested on a database of 120 3D reconstructions of pelvises from biplanar X-ray images. For each patient, a full hexahedral subject-specific FE mesh was generated with an accurate surface representation.
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Fast Subject Specific Finite Element Mesh Generation of Knee Joint from Biplanar X-ray Images

Fast Subject Specific Finite Element Mesh Generation of Knee Joint from Biplanar X-ray Images

2.1 Mesh generation of bony structures First, biplanar radiographic images of bony structures (femur, tibia and patella) for one of the cadaveric specimens (named as generic) as well as all the 11 specimens of interest were acquired using EOS low dose imaging device (EOS ® , EOS-imaging, France). Then from the radiographic images, 3D digital models of all specimens were obtained using 3D reconstruction algorithm validated by previous studies with reconstruction time of 10 min for each specimen [9, 21, 22]. As a reminder, 3D reconstruction process begins with identification and labelling of various anatomical regions and landmarks on the biplanar images. Next, based on statistical inferences a simplified personalized parametric model (SPPM) is generated. After that, the morpho-realistic 3D generic model is deformed towards the SPPM to obtain morpho-realistic personalized parametric model (MPPM) using moving least square and kriging interpolation [23]. Finally, this MPPM is manually adjusted till the best estimate of the respective subject specific model (Fig. 2).
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Atlas-Based Automatic Generation of Subject-Specific Finite Element Tongue Meshes

Atlas-Based Automatic Generation of Subject-Specific Finite Element Tongue Meshes

Abstract Generation of subject-specific 3D Finite Element (FE) models requires the processing of numerous medical images that inform about subject-specific anatomy, and this processing still remains extremely challenging. To overcome these issues, this paper presents an automatic atlas-based methodology for the generation of subject-specific FE meshes via a 3D registration guided by MR images, which does not require any typical-information extraction about the target organ. The method extracts a 3D transformation by registering the atlas volume image to the subject’s one, and estab- lishes a one-to-one correspondence between the two volumes. The obtained 3D transformation field deforms the atlas- mesh to generate the subject-specific FE model. To preserve the quality of the subject-specific mesh, a diffeomorphic non-rigid registration based on B-spline Free-Form Deformations (FFDs) is used, which guarantees a non-folding and one-to-one transformation. However, since the non-folding property is fulfilled locally at every point, non-diffeomorphic transformations are penalized by additional regularity constraints during registration. To evaluate the performance of the proposed approach, first, a publicly available CT-database is used to inspect the accuracy of capturing the complexity of the underlying geometry. Then, FE tongue meshes are generated for two patients and two healthy volunteers using MR images. The results confirm that the proposed method generates an appropriate representation of the underlying geome- try while preserving the quality of FE meshes for subsequent FE analysis, and enables its applicability across different kinds of 3D images without algorithmic modification. To demonstrate the benefit of the proposed implementation, one of the subject-specific FE tongue meshes is used to simulate the biomechanical response to the activation of an important tongue muscle, before and after cancer surgery.
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Tokamesh : A software for mesh generation in Tokamaks

Tokamesh : A software for mesh generation in Tokamaks

does not yield improved approximation results for polynomials of degree higher than 1”. Nevertheless we have developed a free boundary Grad-Shafranov solver using Clough- Tocher reduced cubic finite element (see section 1.1). The interest of this finite element fam- ily is that it can use the same mesh that the one where the initial data has been computed. Moreover, since the Grad-Shafranov equation is a non-linear one that must be solved with an iterative procedure, the initial data provides a convenient initial guess for this procedure. Non- homogeneous Dirichlet boundary conditions coming from the equilibrium data computed on the initial mesh are used and the non-linear system is solved by Picard iterations. Note that to take into account non-homogeneous Dirichlet boundary conditions, it has been necessary to develop a penalization method of Nischte type. Figure 15 compare the solution obtained for the computation an equilibrium in the JET tokamak with three different numerical methods : The original equilibrium computed with EFIT, a solution computed with a P1 finite element solver and the one computed with the C 1 Clough-Tocher finite element method. This Grad-Shafranov
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Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing

Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing

INSA Rouen, Groupe de Physique des Matériaux, CNRS UMR 6634, 76801 Saint Étienne du Rouvray, France A methodology is presented for the generation and meshing of large-scale three-dimensional random polycrystals. Voronoi tessellations are used and are shown to include morphological properties that make them particularly challenging to mesh with high element quality. Original approaches are presented to solve these problems: (i) ‘‘geometry regularization’’, which consists in removing the geometrical details of the polycrystal morphology, (ii) ‘‘multimeshing’’ which consists in using simultaneously several mesh- ing algorithms to optimize mesh quality, and (iii) remeshing, by which a new mesh is constructed over a deformed mesh and the state variables are transported, for large strain applications. Detailed statistical analyses are conducted on the polycrystal morphology and mesh quality. The results are mainly illus- trated by the high-quality meshing of polycrystals with large number of grains (up to 10 5 ), and the finite
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Direct multiphase mesh generation from 3D images using anisotropic mesh adaptation and a redistancing equation

Direct multiphase mesh generation from 3D images using anisotropic mesh adaptation and a redistancing equation

This thesis is divided into six chapters. Chapter 1 is the general introduction of this work. Chapter 2 introduces a new methodology to create anisotropic meshes based on image data. Anisotropic mesh adaptation is constructed using metric ten- sors, which are computed from the interpolation error estimate of the image data on the mesh. The interpolation of the data on the mesh and its adaptation have also been parallelized. Chapter 3 gives a new methodology to build a continuous phase function per object of a segmented image, by a redistancing procedure, coupled to mesh adaptation. Image processing techniques were implemented to improve and accelerate this redistancing-adaptation procedure. Chapter 4 describes the numer- ical approach used for multiphase flow problems, the Variational Multiscale Navier Stokes solver, based on a stabilized finite element method. Then, numerical simula- tions on real images are illustrated, including fluid-structure interactions or object’s interfaces dynamics. Finally, conclusions and perspectives are presented.
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Parametric finite element modeling of the thoracic spine. Geometry and mesh evaluations.

Parametric finite element modeling of the thoracic spine. Geometry and mesh evaluations.

Figure 1: Example of reconstructed vertebra compared with its model Conclusion Automated generation of parametric finite element models provides new possibilities for efficiently studying the influence of geometric parameters. Preliminary evaluations have been performed to validate the coherence of the model. In order to enhance the validation of the models, kinematic simulation will be performed, followed by a stress study. The parametric subject-specific modeling method has been applied to the thoracic spine, and paved the way for large-scale clinical studies or dynamic safety applications.
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Probing for Surface Mesh Generation through Delaunay Refinement

Probing for Surface Mesh Generation through Delaunay Refinement

Although the user-specified domain is often a reasonable thing to ask, there is often no prior knowledge about the number and location of the connected components in the practical applications. One way to tackle this issue is to resort to the same oracle through random initial queries, but this may have several drawbacks: the input shape can have arbitrarily small connected components which cannot be all detected in finite time. This is why we also ask for a strict lower bound of the minimum local feature size of the surface (the reach), which can also be seen as a precision parameter (we can ask for all the connected components greater than a given parameter to be meshed). Even with such reach parameter guaranteeing to seed all connected components would require systematic probing, which would generate overly complex meshes.
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CGALmesh: a Generic Framework for Delaunay Mesh Generation

CGALmesh: a Generic Framework for Delaunay Mesh Generation

convex hull of the lifted vertices (Figure 8). Note that after Delaunay refinement the final mesh may have a non-uniform density of ver- tices, reflecting a non-uniform sizing field that is the pointwise minimum between a (possibly non-uniform) user-defined sizing field and the local feature size of the meshed domain. To pre- serve this non-uniform density throughout the optimization process, the Lloyd and ODT energy integrals are computed using a weighted version of the error, where the weights are locally es- timated from the average length of edges incident to each vertex of the mesh after refinement. For both optimizers, at each optimization step, closed form formulas provide the new location of the mesh vertices as a function of the current mesh vertices and connectivity [30, 1]. Each optimization step computes the new position of all mesh vertices, relocates them and updates the Delaunay triangulation as well as both restricted Delaunay triangulations.
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Feature Preserving Mesh Generation from 3D Point Clouds

Feature Preserving Mesh Generation from 3D Point Clouds

A relevant alternative to the marching cubes and advanc- ing front strategies is the Delaunay refinement paradigm [ BO05 ]. In this method the surface mesh is intersection free by construction as filtered out of a 3D Delaunay triangula- tion. A number of additional guarantees are also provided after termination of the refinement process, such as a good shape of elements, a faithful approximation of geometry and normals, and a low complexity of the mesh. More interest- ingly in our context, Delaunay refinement is able to couple reconstruction and mesh generation. At the intuitive level, the refinement procedure is combined with a sensing al- gorithm probing an implicit surface defined from the data points. The probing is performed along Voronoi edges of sampling points which are not only longer than the short edges of the marching cubes but also data-dependent as they become more and more orthogonal to the sensed surface as the refinement process goes along.
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Sequential decision-making approach for quadrangular mesh generation

Sequential decision-making approach for quadrangular mesh generation

3 Formulation as a sequential decision-making problem Recombinations can be seen as actions that are applied step by step to the mesh. This implies that the overall problem can be seen as a discrete-time system for which one seeks a sequence of actions a t (the recombinations) that maximizes the sum of the rewards rðatÞ defined as the shape quality of the created quadrangles Qt, i.e. rðatÞ ¼ gðQtÞ 2 ½0; 1. The generic dynamics of this discrete system is given by equation Mtþ1 ¼ f ðMt; atÞ, where the mesh Mt 2 X is a state of the system and where at 2 AðMtÞ. X is called the state space and AðMtÞ is called the action space. We define Xf  X as the set of final states (meshes for which no allowed recombination remains).
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CGALmesh: a Generic Framework for Delaunay Mesh Generation

CGALmesh: a Generic Framework for Delaunay Mesh Generation

JEAN-DANIEL BOISSONNAT , Inria CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (CGAL). It generates isotropic simplicial meshes – surface triangular meshes or volume tetrahedral meshes – from input surfaces, 3D domains as well as 3D multi-domains, with or without sharp features. The under- lying meshing algorithm relies on restricted Delaunay triangulations to approximate domains and surfaces, and on Delaunay refinement to ensure both approximation accuracy and mesh quality. CGALmesh provides guarantees on approximation quality as well as on the size and shape of the mesh elements. It provides four optional mesh optimization algorithms to further improve the mesh quality. A distinctive property of CGALmesh is its high flexibility with respect to the input domain representation. Such a flexibility is achieved through a careful software design, gathering into a single abstract concept, denoted by the ora- cle, all required interface features between the meshing engine and the input domain. We already provide oracles for domains defined by polyhedral and implicit surfaces.
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Tokamesh : A software for mesh generation in Tokamaks

Tokamesh : A software for mesh generation in Tokamaks

cubic spline approximation of these isolines node sampling on each isolines (no need to have the same number of nodes on each isoline) → cloud a nodes. triangulation of the resulting set[r]

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Sparselizard - the user friendly finite element c++ library

Sparselizard - the user friendly finite element c++ library

The last step has created the ’u.pos’ output file, which gives the exaggerated displacement of the top surface in the thin cylinder geometry when the sides are clamped and a volume force is applied downwards. Open it with ’./gmsh u.pos’. You don’t see anything or it looks weird? Don’t worry, this is just because the simulation was performed using very few hexahedra in the mesh but with an order 3 interpolation! To visualise high order interpolations in GMSH do this:

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Finite element damage prediction of composite structures

Finite element damage prediction of composite structures

A meso-damage mechanics modeling of laminates, whose aim is to predict the behavior of any composite structure with respect to delamination through knowing only a few characteristics of the interface, has been detailed. Predictions was conducted on M55J/M18 material specimens. Finite element examples show that this approach is promising in the prediction of delamination under various circumstances. Numerical tools, which allow the computation up to failure of the behaviour of any stacking sequence, was presented. This work represents the first step towards a global prediction of composite structures up to the complete fracture.
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Finite Element Modeling of Electroseismics and Seismoelectrics

Finite Element Modeling of Electroseismics and Seismoelectrics

(a) (b) Figure 3. Biot’s equations case. (a) The computational domain is only the subsurface Ω = Ω s , with exter- nal boundaries Γ j and internal boundaries Γ jk . The outer normals νj and ν jk are also indicated. (b) Scheme for the twelve degrees of freedom associated with each element, eight to the solid displacements and four to the fluid displacements.

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Finite Element Analysis of Motorized Adjustable Platform

Finite Element Analysis of Motorized Adjustable Platform

This report explains the steps followed in performing finite element analysis. First a wire frame was developed of Wang’s design. Then the elements were given properties. Followed by applying the loads and defining the boundary conditions. Finally the program calculated the stresses and natural frequencies needed.

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Finite element analysis of fretting crack propagation

Finite element analysis of fretting crack propagation

Once cracks have been introduced within the mesh, finite element computation can be carried out to deter- mine the stress distributions in the neighbourhood of the crack tip during the fretting cycle. Due to the cyclic reci- procating motion of the counter body, both crack will al- ternatively open and close. As an example, Fig. 3 shows the mode I stress intensity factor for the left crack during one fretting cycle. As expected the left crack opens when the counterbody is moved to the right. By computing a complete fretting cycle, the stress intensity factor ranges ∆K I and ∆K II can be determined.
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