Jean-Christophe Cuillière

Generation of a finite element MESH from stereolithography (STL) files

Abstract The aim of the method proposed here is to show the possibility of generating adaptive surface meshes suitable for the finite element method, directly from an approximated boundary representation of an object created with CAD software. First, we describe the boundary representation, which is composed of a simple triangulation of the surface of the object. Then we will show how to obtain a conforming size-adapted mesh. The size adaptation is made considering geometrical approximation and with respect to an isotropic size map provided by an error estimator. The mesh can be used “as is” for a finite element computation (with shell elements), or can be used as a surface mesh to initiate a volume meshing algorithm (Delaunay or advancing front). The principle used to generate the mesh is based on the Delaunay method, which is associated with refinement algorithms, and smoothing. Finally, we will show that not using the parametric representation of the geometrical model allows us to override some of the limitations of conventional meshing software that is based on an exact representation of the geometry.

An adaptive method for the automatic triangulation of 3D parametric surfaces

We have developed automatic mesh generation procedures based on advancing front methods and featuring a priori nodal density calculations. A crucial step in the overall method consists of discretizing the edges and surfaces of an input B-Rep structure with the ability to respect as closely as possible this nodal density function across the part, which is highly interesting for analysis or representation purposes. The work presented here focuses on the discretization of three-dimensional parametric surfaces with strong variations of curvature with respect to a nodal density function with steep gradients. This algorithm is particularly suitable for FE mesh generation purposes and also in many engineering applications for which a 3D model has to be triangulated. We will tackle, in this context, the use of the technique in order to mesh parametric surfaces with a specified discretization tolerance. In this paper, we also present a new quality indicator for triangular and tetrahedral meshes in the context of a priori nodal density constraints.

3D automatic remeshing applied to model modification

The design process usually involves modifications of an initial design solution. At this point in time, design tools do not allow us to perform these modifications efficiently enough. Particularly, when using FE methods, a new FE model has to be rebuilt in order to take into account any modification of the geometric model. We propose an original approach that allows the automatic remeshing of 3D parts, which provides a better integration of FE methods into the entire CAD/CAM process.

A direct method for the automatic discretization of 3D parametric curves

We have developed an automatic mesh generation system featuring an automatic and a priori refinement process based on feature recognition techniques and advancing front methods. A crucial step in the overall method consists in discretizing the edges and surfaces of the input B-Rep structure with the ability to respect as closely as possible a nodal spacing function across the parts that are most interesting for analysis or representation purposes. The work presented here focuses on the discretization of three-dimensional parametric curves with strong variations of curvature with respect to a nodal spacing function having steep gradients. This algorithm is particularly suitable for FE mesh generation purposes but also for many engineering applications for which a 3D model has to be triangulated. We will tackle, in this context, the use of the technique in order to mesh parametric curves with a specified discretization tolerance.

Re-meshing algorithms applied to mould filling Simulations in resin transfer moulding

In injection moulding processes such as Resin Transfer Moulding (RTM) for example, numerical simulations are usually performed with a fixed mesh, on which the displacement of the flow front is predicted by the numerical algorithm. During the injection, special physical phenomena occur on the front, such as capillary effects inside the fibre tows or heat transfer when the fluid is injected at a different temperature than the mould. In order to approximate these phenomena accurately, it is always better to adapt the mesh to the shape of the flow front. This can be achieved by implementing re-meshing algorithms, which will provide not only more accurate solutions, but also faster calculations. In order to represent precisely the shape of the saturated domain in the cavity, the mesh needs to be non-isotropic in the vicinity of the flow front. The size of the elements along the front is connected to the overall accuracy needed for the simulation; the size in the perpendicular direction governs the accuracy on the position of the moving boundary in time. Since these two constraints on element size are not related, the need for non-isotropic mesh refinement is crucial. In the approach proposed here, the mesh is changed at each time step from a background isotropic mesh used as starting point in the refinement algorithm. The solution needs to be projected on the new mesh after each re-meshing. This amounts to adopting a new filling algorithm, which will be validated by comparison to a standard simulation (without re-meshing) and with experimental data.

Automatic mesh pre-optimization based on the geometric discretization error

Abstract The design process usually implies modifications of an initial design solution. At this point in time, design tools do not allow us to perform these modifications efficiently enough. Particularly, when using FE methods a new FE model has to be rebuilt in order to take into account any modification of the geometric model. We propose an original approach that allows the automatic remeshing of 3D parts, which provides a better integration of FE methods into the whole CAD/CAM process. Optimization of automatic remeshing is achieved through mesh pre-optimization based on the discretization error. This introduces, in the FE analysis process, a mesh that represents a better approximation of the exact geometric model. This paper deals with the concept of mesh pre-optimization.

Integration of CAD, FEA and Topology Optimization through a Unified Topological Model

We have been involved in research work in the field of finite element analysis (FEA) integration with computer aided design (CAD) for several years and have developed several concepts and tools that have aroused interest and shown efficiency. In the meantime, both the evolution of our research developments (on topics like geometry comparison, geometry reconstruction and simplification, mixed-dimensional analysis and topology optimization) and the evolution of CAD systems and CAD kernels made us reconsider our database organization. This led to the design of an original development environment and database organization referred to as the Unified Topological Model (UTM). The main interests of this new CAD/FEA database organization is its ability to tackle multi-platform CAD/FEA integration (handling geometries coming from different CAD kernels), mixed-dimensional modeling and analysis (3D solid geometry mixed and integrated with surface geometry and curvilinear geometry) and topology optimization (TO) proce...

A mesh-geometry-based solution to mixed-dimensional coupling

When conducting a finite element analysis, the total number of degrees of freedom can be dramatically decreased using finite elements such as beams and shells. Because of geometric complexities, entire models (or portions of models) must be meshed using volume elements in order to obtain accurate simulation results. If however some parts of these models fit the description of shells or beams, then a mixed dimensional model containing shell, beam and volume elements side by side can be used. This approach, referred to as a mixed-dimensional analysis (MDA) can significantly reduce the time needed to mesh and solve the system. Unfortunately, problems arise when trying to connect the different types of element in part due to incompatibilities between the degrees of freedom, and due to the discontinuities between meshes generated independently. This paper presents a solution to these problems based on the generation of a compatible mesh composed solely of standard finite elements and without requiring the use of constraint equations. This mesh can then be exported to a standard FE solver without using specific connection elements.

Automatic and a priori refinement of three-dimensional meshes based on feature recognition techniques

Abstract This work presents the general evolution of CAD/CAM systems for a better integration of all functions involved in the design and manufacturing process of mechanical parts (simultaneous engineering). We are proposing here an approach of the automatic three-dimensional mesh generation problem featuring a pre-optimization scheme based on the “a priori” evaluation of a dual geometric model (CSG–Exact B-Rep) in order to identify, directly and automatically, geometric features causing stress concentration. We provide more precise knowledge on how geometric features are identified and used in order to calculate a nodal density field across the parts that is more interesting for analysis or representation purposes.

Generalizing the advancing front method to composite surfaces in the context of meshing constraints topology

Being able to automatically mesh composite geometry is an important issue in the context of CAD-FEA integration. In some specific contexts of this integration, such as using virtual topology or meshing constraints topology (MCT), it is even a key requirement. In this paper, we present a new approach to automatic mesh generation over composite geometry. The proposed mesh generation approach is based on a generalization of the advancing front method (AFM) over curved surfaces. The adaptation of the AFM to composite faces (composed of multiple boundary representation (B-Rep) faces) involves the computation of complex paths along these B-Rep faces, on which progression of the advancing front is based. Each mesh segment or mesh triangle generated through this progression on composite geometry is likely to lie on multiple B-Rep faces and consequently, it is likely to be associated with a composite definition across multiple parametric spaces. Collision tests between new front segments and existing mesh elements also require specific and significant adaptations of the AFM, since a given front segment is also likely to lie on multiple B-Rep faces. This new mesh generation approach is presented in the context of MCT, which requires being able to handle composite geometry along with non-manifold boundary configurations, such as edges and vertices lying in the interior domain of B-Rep faces.