In part 2 of our Meshing in FEA blog series we will discuss what important considerations you should make when meshing your FEA model.
What kind of analysis are you performing?
The type of analysis tends to dictate what meshing is required. There are some complex types of analysis and phenomena that require finer meshes to accurately capture the behavior, such as contact, fatigue, or creep analysis. Large deformation analysis, where the deformation of the model affects the stresses in the model, may also require a finer mesh. In non-linear materials, resolving higher harmonic content (shock waves) requires a much higher mesh density.
What are the areas of interest in your model?
It is inefficient to refine your whole mesh when the physical area of interest is particularly small. If you have specific areas for which you need a converged solution, then you should invest elements in those locations. For example, in mechanical analysis, areas where stress gradients are not required can use a coarser mesh. If you are unsure what the areas of interest are in the model, start with a coarse mesh to identify areas of the solution that change drastically and then use a finer mesh size for these areas in the following analyses.
How do detailed areas affect your results?
Complex geometries that have fine details like small holes and cut-outs can be difficult to consider as they require very small elements to model the intricacies. As such it is important to ask the question, how will these small details affect my result? Is this one of my areas of interest? Asking these questions can save a lot of time and bother, but it is important to strike a balance between accuracy and time.
How to connect different element types?
In part 1 of the series we discussed the different element types and their uses. We have included the table below for reference. It is important to take care when using multiple element types in one model as it is not always feasible to mesh all these together. Many intersections will need connections. For example, if you have a hybrid mesh with quadrilateral elements for one part and triangular elements for another part, the surface intersection of these parts will need to be bonded together as the surface nodes do not match perfectly.
|Continuum or solid element||The fundamental element type used for constructing meshes. Can be 2D (quads and tris) or 3D (hexahedral and tetrahedral)|
||For structures that have a dimension (e.g. thickness) that is significantly smaller than the other dimensions|
|Beam Element||For slender structures that resist twisting and bending at the node connections|
||For constraining parts of the structure|
|Membrane Element||For thin fabric-like surfaces|
||For modeling line-like structures that support loading along the axis of the element|
|Connector Element||For applying a behavior between two nodes, e.g. spring|
|Infinte Element||For thin fabric-like surfaces|
What is your element quality?
Once a mesh has been generated it is important to assess the quality of the elements in the mesh. Element quality refers to the structure of the individual elements; elements that are distorted from their basic shape can be less accurate. Poor quality elements can even result in numerical errors and instability in the model.
A popular metric for measuring element quality is aspect ratio. Aspect ratio is the ratio of the maximum edge length to the minimum edge length of an element. The ideal value for aspect ratio is 1, which means all sides of the element have the same length. For elements like hexahedra, however, this is more difficult to maintain so a general rule of thumb is to keep elements at an aspect ratio of 4 or less.
What accuracy do you require?
The big question that should be considered when meshing a model is how accurate do I need my results to be? If you are just quickly comparing two possible designs then you may be able to use a coarser mesh, but for accurate stress results you will need a finer mesh. The best way to find out the right mesh for your problem is to do a convergence study.
A convergence study is an investigation of how your outputs vary with element size. As the mesh transitions from coarse to fine, the results will converge to a steady value. It is up to the engineer to decide what level of error is suitable for the application. Generally the more elements used in a model, the more accurate the results will be at the cost of extended solve times. Performing convergence studies can help engineers to understand the optimal balance between accuracy and solve time.