Automatic Three-dimensional Mesh Generation Research Articles

Automatic three-dimensional geometry and mesh generation of periodic representative volume elements for matrix-inclusion composites

This paper introduces an efficient method to automatically generate and mesh a periodic three-dimensional microstructure for matrix-inclusion composites. Such models are of major importance in the field of computational micromechanics for homogenization purposes utilizing unit cell models. The main focus of this contribution is on the creation of cubic representative volume elements (RVEs) featuring a periodic geometry and a periodic mesh topology suitable for the application of periodic boundary conditions in the framework of finite element simulations. Our method systematically combines various meshing tools in an extremely efficient and robust algorithm. The RVE generation itself follows a straightforward random sequential absorption approach resulting in a randomized periodic microstructure. Special emphasis is placed on the discretization procedure to maintain a high quality mesh with as few elements as possible, thus, manageable for computer simulations applicable to high volume concentrations, high number of inclusions and complex inclusion geometries. Examples elucidate the ability of the proposed approach to efficiently generate large RVEs with a high number of anisotropic inclusions incorporating extreme aspect ratios but still maintaining a high quality mesh and a low number of elements.

A moving mesh generation strategy for solving an injector internal flow problem

The ability to handle complex geometries is an important part of transient calculations; therefore, the need for fully automatic mesh generation capable of dealing with such geometries is quite demanded. In this paper a specific approach to fully automatic three-dimensional mesh generation is presented. An approach to moving the generated mesh is also outlined. In particular, the simulation of a diesel injector needle movement is sought. The movement of the needle was calculated on the basis of injection rate experimental data and injection rate predicted data with steady state boundaries and geometry. The simulation was performed using the commercial code STAR-CD version 4.06 .

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

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.

An automatic three-dimensional finite element mesh generation system for the Poisson-Boltzmann equation

We present an automatic three-dimensional mesh generation system for the solution of the Poisson–Boltzmann equation using a finite element discretization. The different algorithms presented allow the construction of a tetrahedral mesh using a predetermined spatial distribution of vertices adapted to the geometry of the dielectric continuum solvent model. A constrained mesh generation strategy, based on Bowyer's algorithm, is used to construct the tetrahedral elements incrementally and embed the Richards surface of the molecule into the mesh as a set of triangular faces. A direct mesh construction algorithm is then used to refine the existing mesh in the neighborhood of the dielectric interface. This will allow an accurate calculation of the induced polarization charge to be carried out while maintaining a sparse grid structure in the rest of the computational space. The inclusion of an ionic boundary at some finite distance from the dielectric interface can be automatically achieved as the grid point distribution outside the solute molecule is constructed using a set of surfaces topologically equivalent to this boundary. The meshes obtained by applying the algorithm to real molecular geometries are described. © 1997 John Wiley & Sons, Inc. J Comput Chem18: 1570–1590, 1997

Numerical solution of the Poisson-Boltzmann equation using tetrahedral finite-element meshes

The automatic three-dimensional mesh generation system for molecular geometries developed in our laboratory is used to solve the Poisson–Boltzmann equation numerically using a finite element method. For a number of different systems, the results are found to be in good agreement with those obtained in finite difference calculations using the DelPhi program as well as with those from boundary element calculations using our triangulated molecular surface. The overall scaling of the method is found to be approximately linear in the number of atoms in the system. The finite element mesh structure can be exploited to compute the gradient of the polarization energy in 10–20% of the time required to solve the equation itself. The resulting timings for the larger systems considered indicate that energies and gradients can be obtained in about half the time required for a finite difference solution to the equation. The development of a multilevel version of the algorithm as well as future applications to structure optimization using molecular mechanics force fields are also discussed. © 1997 John Wiley & Sons, Inc. J Comput Chem18: 1591–1608, 1997

Intégration géométrie-maillage appliquée aux méthodes numériques

ABSTRACT The work presented here takes place in the general evolution of CAD/CAM systems on the way to a better integration of all functions involved in the design and manufacturing process of mechanical parts (concurrent engineering). We are propounding here an approach of the automatic three-dimensional FE mesh generation problem featuring a pre-optimization based on the a priori evaluation of a dual geometric model (CSG-Exact BREP) in order to identify, directly and automatically, geometric singularities causing stress concentration. This appoach permits to integrate, in a better way, the analysis step in the whole CAD/CAM process in order to achieve the concurrent engineering concept.

MSHGEN — a FORTRAN program on automatic two-dimensional and three-dimensional triangular mesh generation

A computer program on automatic generation of three-node or six-node triangular finite element mesh based on isoparametric mapping functions is presented. The program is written in FORTRAN-77 and implemented on an IBM-AT compatible personal computer. Given the boundaries of the surface of the structure, this program discretises the internal space into regular grids of user defined density and produce nodal coordinates and nodal connectivity with optional bandwidth/ profile reduction for efficient finite element analysis. Listing of the main part of the FORTRAN codings are included.

Shape design modelling using fully automatic three-dimensional mesh generation

A modeling approach based upon solid design primitives is demonstrated. A preliminary set of primitives is developed which can be assembled into complete solid models that are defined in terms of a small set of design parameters. Design variables are accessible through a formal relational databasem, thus making it possible to modify the design interactively or through an automated design system. A new fully automatic 3-D mesh generation capability is introduced. This capability automatically discretizes 3-D surfaces and solids utilizing only a geometric description. The importance of accurately representing surface geometry is stressed. It is observed that the most accurate finite element solution results are required on the surface of a part, making it necessary to precisely represent curved faces, edges and vertices. Two realistic design examples are presented in which it is shown that the mesh generation process is very efficient, taking just 79 seconds to generate 3700 solid elements.

Trends in automatic three-dimensional mesh generation

Some recent efforts on the development of methods to ensure the robustness of automatic three-dimensional mesh generation techniques are discussed. The topic areas considered are mesh entity classification, finite octree cell triangulation, and coarse mesh generation by element removal.

Toward automated finite element modeling for the unification of engineering design and analysis

The paper presents an approach to the unification of geometric modeling and finite element modeling based on automated procedures. It is argued that an automated finite element modeling approach is the only viable approach to carry out this unification. Specif topic areas considered are automatic three-dimensional mesh generation, its integration to solid model the need to account for differences between the geometric domain of a solid model and a finite element model, and a specific adaptive approach to determine when circular holes could be safely ignored in the stress analysis of plates subjected to inplane loading.

Mesh generation for computational analysis. Part II: Geometric and topological considerations for three-dimensional mesh generation

Successful use of finite-element analysis depends on an ability to model accurately the problem shape using geometric meshes. This paper deals with automatic three-dimensional mesh generation, reviewing the four major classes of mesh generator in use — interactive graphics, mapping, filling and cutting techniques — and presenting a new method which aims to solve some of the problems that arise when attempts are made to mesh irregularly shaped objects.