In the first edition of the “How to Improve an FEA Model” blog series, we discussed improving a finite element analysis (FEA) model using model simplification.
In the second edition, we’ll discuss improving an FEA model using proper mesh generation and the relevant decision factors associated with the process.
Proper Mesh Generation
In order to improve an FEA model, that are a number of decisions that need to be made for proper mesh generation. There are typically three areas Ansys-DfR considers when creating accurate meshes:
- Choosing shell vs. solid elements
- Choosing hex (brick) vs. tet (pyramids) elements
- Choosing the proper mesh size and mesh order
Shell Vs. Solid Element
More often than not, computer aided design (CAD) geometry will be composed entirely of three-dimensional bodies. However, in an FEA model, it may be advantageous to mesh some of those bodies with shell elements rather than solid 3D elements.
The advantages of shell elements:
Shell elements are 2D approximations of the 3D geometry that store the thickness of a body as a physical property and can be used for thin walled geometries with a length that is much greater than the thickness of the body, and when the shear deformation is insignificant (e.g., sheet metal chassis or the walls on a soda can). There are also special shell and beam reinforcement elements that can be used to model the thin copper layers inside a printed circuit board (PCB). New features inside Ansys Sherlock allow for the rapid generation of these reinforcement geometries. These reinforcements will enable the user to capture the effect the traces have on the board deformations efficiently and will be available in July 2020 R2.
Figure 1: Copper PCB features modeled as shell and beam reinforcements
Furthermore, properly incorporating shell elements into FEA models can greatly improve both simulation run time and the accuracy of results. When used appropriately, shell elements can typically generate a higher quality mesh on thin-walled structures (like sheet metal) with a much lower element count, resulting in more accurate results at a significantly reduced computational cost. CAD tools like the “Create Midsurface” feature in ANSYS Spaceclaim can aid in preparing geometries for shell meshing.
Figure 2: Solid body (left) replaced with surface body (right) using Spaceclaim Midsurface Tool
It may seem intuitive to assume that: 3D meshing = more detail = more accurate results.
But this is not always the case. Particularly in cases of large bending, solid elements often create artificially stiff structures when they are used to mesh thin-walled geometries, resulting in inaccurate simulations. In addition, it can be very difficult to refine the mesh and generate enough elements through the thickness of a thin-walled structure in order to achieve accurate displacement and stress results.
Furthermore, if the geometry is complex enough, thin-walled structures may require a poor-quality mesh when solid elements are used, creating sliver-like elements with poor aspect ratios that can negatively affect results.
Hex vs. Tet Elements
When determining whether to use hexahedral (hex) elements or tetrahedral (tet) elements in an FEA model configuration, it’s important to keep in mind the overall shape and complexity of the object itself. The general rule of thumb is to mesh with hexahedral elements if possible. Hex or “brick” elements generally result in more accurate results at lower element counts than tetrahedral elements. However, if the object contains acute angles or other complex geometries, it may be necessary to mesh with tetrahedral elements.
Figure 3: An identical body meshed with hex elements (left) and tet elements (right)
As discussed in the first blog in this series, how and when to simplify geometry is key when deciding what type of elements will be needed to mesh a model.
It is preferable to simplify the model enough to mesh it entirely with bricks, but this is sometimes not feasible. For complex geometries that require tet meshes, care must be taken to ensure that the mesh does not result in inaccurate results. This usually means higher element counts, high order elements, and longer run times.
For these reasons, any model simplifications like fillet removal or body splitting that allows for hex meshing without significantly changing the geometry are highly recommended.
Mesh Size and Order
Properly understanding mesh order and size are key to finding the balance between accurate results and reasonable run times in an FEA.
Mesh size simply refers to the characteristic edge length of an element. A smaller mesh size will result in more elements in the model, resulting in longer run times and more accurate results. Order describes the shape function used to calculate element displacements.
First-order elements have nodes only at the corners of the elements and calculate displacement linearly between nodes. Second-order elements include midside nodes between the corners and calculate displacement quadratically. The additional detail in second-order elements typically results in increased accuracy, but a significantly increased computational cost.
Figure 4: A quadratic element (left) and a linear element (right). Nodes are highlighted in green. Note the midside nodes in between the corners on the second-order element.
The key to generating effective FEA meshes is to strike an appropriate balance between order and size for the particular problem that is being analyzed. When possible, it is recommended to use second-order elements and iteratively refine the mesh until the results converge. However, for much larger problems that solve on the order of days even with high-performance computing, this may not be feasible. In these cases, an analyst will need to use experience to make appropriate decisions regarding mesh size and order
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