Finite Element Mesh

During discretization we divided the mathematical model using different types of elements depending on the type of analysis i.e. 1D, 2D & 3D. This discretization produces a finite element mesh. There are different methods to create the mesh and also how to maintain the mesh quality and compatibility.

Meshing Practices

  • Manual Meshing

To start with one had to input the coordinate for all nodes and then define elements by defining the coordinates of how nodes connect to each other. This was later improved with mapped geometry meshing where the user defines the number of nodes along a line or a surface between the area of interest which is to be analysed and later this area of interest is meshed automatically along the defined nodes provided on the line or surface. This provided for a surface or volume mesh as required for analysis.

This was still a time consuming process and many FEA programs no longer support manual meshing.

  • Semi-Automatic Meshing

This follows the basic principles of CAD software’s where a mesh is created by extruding a plane surface. This means the model is first meshed into a 2D element and later the extrusion / revolution is provided in a number of steps, which depends on the layers of element required.

The limitation is that this is applicable only for a limited number of shapes.

  • Automatic Meshing

Automatic meshing is the widely used and practical meshing technique for complex models. Also this is only the meshing technique available in FEA software and recommended for engineers.

The execution of auto meshing depends on the FEA software. This provide user the choice for the selection of Mesh Size (Coarse or Fine), Mesh Preference (areas of special interest for mesh refinement).

Meshing a 3D cad model creates solid finite elements and meshing a surface create Shell or Membrane elements in 3D model 2D elements in 2-D models.

A combination of auto meshing and manual meshing can also be employed for models, where the manual meshing is used for complex areas and auto meshing for remaining part of the model.

Mesh Compatibility

It is a better approach sometimes to combine different elements in one mesh, where thin walls can be meshes with shell elements and larger parts with solid elements. To continue with this one must make sure the mesh with different elements is compatible to be analysed.

  • Element Compatibility

Two elements which make up a model are compatible along a boundary if they are of the same order. This means they have the common shape function and produce a continuous displacement field along the boundary. Displacement field mean all the displacement constituents (depending on the degree of freedom) are continuous. Element compatibility is automatically achieved when a same element types with common shape function in used to create the mesh.

  • Incompatible elements mesh

Sometimes compatibility must me imposed on the mesh created using same elements types with different shape functions are used in a mesh. Incompatibility can also occur in a mesh with same elements but with a different mesh density ratios in different areas, this occurs if the point of connection in the mesh groups do not have connection at required point nodes where the mesh transition starts.

  • Forcing Compatibility

In an incompatible mesh the compatibility is brought about by linking the displacements constituent of one element to the displacement constituents of other element or of one group of elements to another group of elements. This linking makes one element the master and the other one the slave. The displacement of the slave element must follow the displacement of the master element.

It is not advisable to use linking fix where stress values required are accurate.

Problems during meshing

One can realise from the above discussions that meshing is meticulous procedure and one cannot rely only on automeshers to do this task if reliable and usable results are required. The user should have the control to define meshing and avoid meshing errors.

  • Element distortion

Finite elements distort from their ideal share when they are assembled in a mesh. E.g. Triangular element for plane stress, Tetrahedral element for a solid element. Every element is allowed a range of distortions under which it can work properly. Amount of allowed distortion is a parameter dependent on the element type, element design etc. Degenerated element tend to make the mesh not usable or may provide unsound results.

Mesh quality can be verified with mesh check tools provide in the FEA software. Distorted elements are stiffer and they miscalculate the values of displacement and therefore the values of strain and stress are also miscalculated.

Element distortion is introduced into the FE model when automeshers fill the required shape with elements. Sometimes they distort the element shape beyond the acceptable limits.

  • Element insufficiency

For representing bending FE model require to be meshed with higher order elements with a more than one layer of elements. Shell elements can also be utilised for thin FE models.

Using a single layer with first order elements will represent the stress distribution incorrect across the elements and this condition is element insufficiency.

  • Incorrect mapping on the geometry

Meshing always require a well refined mesh selection to correctly map the geometry details by the elements. Higher order elements tend to map the details better with less number of elements compared to lower order elements which need higher number of elements to map the same geometry details.

  • Incorrect conversion of Shell models

It is important to convert a FE models meshed with shell elements by converting it into mid-plane surfaces. This process may cause problems like gaps in the mesh and can be overlooked in a complex mesh.

Converting a solid model to surface model for meshing with shell elements is a tedious process. It is recommended to create FEA specific surface model from scratch.