How are geometry elements used for modifying a mesh?
Question:How are geometry elements used for modifying a mesh?
There are cases when you want to analyze with a higher precision certain zones of interest without affecting the time of the analysis. It is known that with the finite element method, as the node number increases (or the number of finite elements) so do the number of the rigidity matrix terms increase in number and automatically the equation numbers to compute increase resulting in a higher computation time for large models. Zones of interest can be concentrated loads, element intersections etc.
The options available in Advance Design shall be described. These options refer strictly to planar elements; for linear elements there are different options, described in a separate FAQ.
Next, some examples will be presented when a smaller mesh size in carefully selected zones could make the difference; the help elements are nodes and lines.Mesh modification using help elements:
First, define the structural model and from the menu select: Generate - Geometry - Point
Combining a mesh size of (1.00m) with refinement around the point of interest will result in a 58 nodes meshed system.
It can be observed that the mesh size of 1.00m does not mean that the displacements are wrong (see below an approximate calculus from theory of elasticity) but as the mesh size decreases we get closer to the exact solution.
Using two times the node numbers, but concentrated in the zone of interest, we obtain results closer to reality and also slightly larger.
In the case of stresses, the differences will be a little larger because of this particular case of a planar element with a point load in the center. From the theory of elasticity we could compute the tensions but with a large error. This is why the finite element method is used; it will provide better results as in best approximations.
We can observe a 60% increase of stresses around the point of application of the load in the smaller mesh size over the larger mesh size. To get to the same values would require meshing the slab to a general mesh size of 0.10m which means increasing the node number to a 2300 nodes, an extreme number of nodes for such a simple analysis.
Define the structural model and from the menu select: Generate - Geometry - Lines - Line
Draw the line according to your needs and select it. In the properties window activate the mesh option and define the step size; the options available are the same as for the linear elements, Number, Size, Spacing and Secondary size.
See FAQ: "How is the mesh size on linear elements modified"
For this example the general mesh size of the wall is kept to 1.00m and three lines have been generated having a mesh size modification of 0.20m in the zone of interest (wall - rung joint) together with mesh refinement of the rung itself at a 0.50m value.
The results that are analyzed are the moments from the wall and rungs; the displacements do not have notable differences.
The concentration of efforts in the wall at the level of each rung is more obvious in the case of a smaller mesh size. Also the results in the rungs are larger when the mesh size is smaller.
There is no specific solution for the application of each of the methods described in this document. The mesh must be done in the way that the model defined must simulate a behavior closer to reality without increasing the computation time. There should be a balance between satisfactory results and smallest computation time possible.
You should always perform a check in advance on a simplified model so as to see whether or not the results are satisfactory and can determine whether their application will not affect the calculated model results in an unwanted way.