Engineers and scientists use finite element analysis (FEA) software to build predictive computational models of real-world scenarios. The use of FEA software begins with a computer-aided design (CAD) model that represents the physical parts being simulated as well as knowledge of the material properties and the applied loads and constraints. This information enables the prediction of real-world behavior, often with very high levels of accuracy.
The accuracy that can be obtained from any FEA model is directly related to the finite element mesh that is used. The finite element mesh is used to subdivide the CAD model into smaller domains called elements, over which a set of equations are solved. These equations approximately represent the governing equation of interest via a set of polynomial functions defined over each element. As these elements are made smaller and smaller, as the mesh is refined, the computed solution will approach the true solution.
This process of mesh refinement is a key step in validating any finite element model and gaining confidence in the software, the model, and the results.
The Mesh Refinement Process
A good finite element analyst starts with both an understanding of the physics of the system that is to be analyzed and a complete description of the geometry of the system. This geometry is represented via a CAD model. A typical CAD model will accurately describe the shape and structure, but often also contain cosmetic features or manufacturing details that can prove to be extraneous for the purposes of finite element modeling. The analyst should put some engineering judgment into examining the CAD model and deciding if these features and details can be removed or simplified prior to meshing. Starting with a simple model and adding complexity is almost always easier than starting with a complex model and simplifying it.
The analyst should also know all of the physics that are relevant to the problem, the materials properties, the loads, the constraints, and any elements that can affect the results of interest. These inputs may have uncertainties in them. For instance, the material properties and loads may not always be precisely known. It is important to keep this in mind during the modeling process, as there is no benefit in trying to resolve a model to greater accuracy than the input data admits.
A finite element model of a wrench and the computed stresses. The mesh is not shown.
Once all of this information is assembled into an FEA model, the analyst can begin with a preliminary mesh. Early in the analysis process, it makes sense to start with a mesh that is as coarse as possible – a mesh with very large elements. A coarse mesh will require less computational resources to solve and, while it may give a very inaccurate solution, it can still be used as a rough verification and as a check on the applied loads and constraints.
The first few iterations of a mesh refinement study of a wrench, starting with a very coarse mesh.
After computing the solution on the coarse mesh, the process of mesh refinement begins. In its simplest form, mesh refinement is the process of resolving the model with successively finer and finer meshes, comparing the results between these different meshes. This comparison can be done by analyzing the fields at one or more points in the model or by evaluating the integral of a field over some domains or boundaries.
By comparing these scalar quantities, it is possible to judge the convergence of the solution with respect to mesh refinement. After comparing a minimum of three successive solutions, an asymptotic behavior of the solution starts to emerge, and the changes in the solution between meshes become smaller. Eventually, these changes will be small enough that the analyst can consider the model to be converged. This is always a judgment call on the part of the analyst, who knows the uncertainties in the model inputs and the acceptable uncertainty in the results.
