The Effect of Element Type on Simulation Results
Finite Element Analysis (FEA) is a tool for the simulation of natural occurring phenomenon via the application of a technique called the Finite Element Method (FEM). This analysis type allows for solutions to be generated for a wide range of problems . As the technology becomes more widely available, its potential for improper use also increases. The market saturation of Computer Aided Drafting (CAD) tools, such as Solidworks, that also include simulation components has given access to simulation tools to those who typically would not have a full time use for FEA tools like Ansys or Abaqus. This article is being presented to demonstrate the different results that can be obtained through the purposeful misapplication of simulation conditions.
One of the simplest and most easily verified simulations is that of a cantilevered beam. The beam that will be studied will be rigidly fixed on one side and have a point load applied to the other.
- Length: 100 Inches . Width: 16 Inches . Height: 8 Inches . Modulus of Elasticity: 2.9E7 Poisson's Ratio: 0.3 . Applied Load: 10,000 Lbs.
The maximum stress in a beam undergoing a point load located at the end is simply the bending moment divided by the section modulus. For our case detailed above, the result is:
σ = 5,859 psi
Now let's compare this result to that of various mesh sizes and element types:
The results shown above are from Solidworks. The first set of results match our calculated result exactly (5,859 psi) while the second set of results show a maximum stress of 5,909 psi; slightly higher than what was calculated. The first case uses beam elements while the second case uses tetrahedral elements. The same analysis can be performed in Abaqus, which leads to similar results:
Basic Element Types:
There are element types for 1D, 2D and 3D simulation. In addition, each one of these element types can be further broken down by the number of nodes involved in the creation of the element geometry. For example, a hex element can have 8, 20, or 27 nodes.
1D
Beam/Truss - These element types are best for long, slender objects. It should be used when the length is significantly greater than the width and depth and when the cross-sectional properties are constant. Truss elements only allow 3 degrees of freedom (DOF) while beam elements allow for 6 DOF.
2D
Shell - This element type is best for components that are very thin, where having internal elements would not be relevant to the analysis being performed. An example of this is in the performance of analysis' related to sheet metal forming. Shell meshes can be either tri, quad or quad-dominated meshes.
3D
Tetrahedral (Tet) - Tetrahedral elements are used to fit complex geometry but result in less accurate results when compared to hexahedral elements. This element type should only be used when the complexity of a geometry is such that a Hex mesh will not work. Examples for ares to use Tet elements are in curves and acute angles.
Hexahedral (Hex) - This is the preferred element type when performing FEA. This is because Hex elements are computationally and numerically more efficient. In addition, for simulations that contain flows (Computational Fluid Dynamics), Hex elements can create an orthogonal grid to the estimated flow direction which helps to once again improve results and efficiency.
The elements discussed above can also be combined to create meshes that contain portions of each mesh type. A part mesh can be hex-dominated and use Tet meshing in areas where a hex mesh would not function properly.
Conclusion:
Ensuring that the proper element type is used can have a profound impact on the quality of the output data produced by performing FEA. While the results are relatively close to one another for the examples given in this article, it is possible to generate wildly different results by simply modifying the element type and mesh size.
Meshes can introduce stress concentrations in the form of sharp corners that typically do not exist in the real world. Understanding what element type to use, and when to use it will help produce more accurate results when performing FEA.
