Mesh Generation

The methods used to generate a mesh on existing geometry are discussed in this chapter. The definitions used to describe the process are first presented, followed by descriptions of interval specification, mesh scheme selection, and available curve, surface, and volume meshing techniques. The chapter concludes with a description of the mesh editing capabilities, and the quality metrics available for viewing mesh quality.

Element Types

For each entity topology-type in the model geometry, Trelis can discretize the entity using one, or several, types of basic elements, for each order entity in the geometry (vertex, curve, etc.). Trelis uses a basic element designator to describe the corresponding entity, or entities, in the mesh, and a given geometric topology entity can be discretized with one, or several, of basic elements types in Trelis. For example, a geometric surface in Trelis is discretized into a number of faces, where faces is the basic element designator for surfaces. These faces can consist of two types of basic elements, quadrilaterals or triangles. The basic element designators corresponding to each type of geometric entity, along with the types of basic elements supported in Trelis, are summarized in the table below.

For each basic element, Trelis also supports several element type definitions, whose use depends on the level of accuracy desired in the finite element analysis. For example, Trelis can write both linear (4-noded) and quadratic (8- or 9-noded) quadrilaterals. The element type definition is specified after meshing occurs, as part of the boundary condition specification. See Finite Element Model Definition for a description of that process and the various element types available in Trelis.

Each mesh entity is associated with a geometric entity which "owns" it. This associativity allows the user to mesh, display, color, and attach attributes to the mesh through the geometry. For example, setting a mesh attribute on a surface affects all faces owned by that surface.

Mesh Generation Process

Starting with a geometric model, the mesh generation process in Trelis consists of four primary steps:

  1. Set interval size and count for individual entities or groups. The size or interval is always applied to a specific geometric entity.
  2. Set mesh schemes. Trelis supports numerous meshing schemes for meshing solid model entities.
  3. Generate the mesh for the model. Use the mesh command to generate the mesh on a specified geometric entity.
  4. Inspect mesh for quality and suitability for targeted analysis.Trelis provides various quality metrics for the user to verify the suitability of the mesh for analysis. The quality command can be used to check the elements generated on a specific geometric entity.

There are also mechanisms for improving mesh quality locally using smoothing and local mesh topology changes and refinement. For complex models, this process can be iterative, repeating all of the steps above.

The mesh for any given geometry is usually generated hierarchically. For example, if the mesh command is issued on a volume, first its vertices are meshed with nodes, then curves are meshed with edges, then surfaces are meshed with faces, and finally the volume is meshed with hexes. Vertex meshing is of course trivial and thus the user is given little control over this process. However, curve, surface, and volume meshing can be directly controlled by the user. Each of the steps listed are described in detail in the following sections.

 

Geometry Entity Type
Basic Element Designator
Basic Element(s) In Trelis
Vertex Node Node
Curve Edge Edge
Surface Face Quadrilateral, Triangle
Volume (or Body) Element Hexahedron, Tetrahedron, Pyramid, Wedge