User Tools

Site Tools

wiki:sns:intactgh:ex_6

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
wiki:sns:intactgh:ex_6 [2023/07/26 14:41] – eliwiki:sns:intactgh:ex_6 [2024/02/02 11:28] (current) – graham
Line 2: Line 2:
 ===This example problem will demonstrate the different use cases of linear and quadratic elements for simulation.==== ===This example problem will demonstrate the different use cases of linear and quadratic elements for simulation.====
  
-First it’s important to understand exactly what differentiates linear elements from quadratic elements. The difference between basis order 1 (linear elements) and basis order 2 (quadratic elements) is how closely the elements conform to the geometry. This idea can be seen in here:+First, it’s important to understand exactly what differentiates linear elements from quadratic elements. The difference between basis order 1 (linear elements) and basis order 2 (quadratic elements) is how closely the elements conform to the geometry. This idea can be seen in here:
  
-{{ :wiki:sns:intactgh:elem1.png?600 |}} +{{ :wiki:sns:intactgh:elem1.png |}} 
-{{ :wiki:sns:intactgh:elem2.png?600 |}}+{{ :wiki:sns:intactgh:elem2.png |}}
  
 This means fewer quadratic elements than linear elements are required to accurately represent the geometry in simulation. Quadratic elements are more computationally expensive, so start with a low resolution than if linear elements were used.  This means fewer quadratic elements than linear elements are required to accurately represent the geometry in simulation. Quadratic elements are more computationally expensive, so start with a low resolution than if linear elements were used. 
Line 18: Line 18:
  
 One end of the beam is fixed, while a unit load is applied to the other end in x,y, and z directions, respectively, as well as a unit twisting load around the x axis. One end of the beam is fixed, while a unit load is applied to the other end in x,y, and z directions, respectively, as well as a unit twisting load around the x axis.
-{{ :wiki:sns:intactgh:elem3.png?800 |}}+{{ :wiki:sns:intactgh:elem3.png? |}}
  
 ====Analysis==== ====Analysis====
Line 24: Line 24:
  
 The results can be seen here: The results can be seen here:
-{{ :wiki:sns:intactgh:elem4.png?800 |}}+{{ :wiki:sns:intactgh:elem4.png? |}}
  
 Notably, the resolution for the linear element test needed to be much higher to achieve an error of <1%. Even with fewer elements, the quadratic elements had a smaller error.  Notably, the resolution for the linear element test needed to be much higher to achieve an error of <1%. Even with fewer elements, the quadratic elements had a smaller error. 
-{{ :wiki:sns:intactgh:elem5.png?800 |}}+{{ :wiki:sns:intactgh:elem5.png? |}}
  
 For thin geometries, linear elements fail at high aspect ratios. This is because as the elements decrease in size to accurately capture the geometry, the total number of elements increases drastically. This relationship can be seen below.  For thin geometries, linear elements fail at high aspect ratios. This is because as the elements decrease in size to accurately capture the geometry, the total number of elements increases drastically. This relationship can be seen below. 
-{{ :wiki:sns:intactgh:elem6.png?800 |}}+{{ :wiki:sns:intactgh:elem6.png? |}}
 Quadratic elements can capture the geometry at a cell size larger than the thinnest portion of geometry. This makes them especially good for geometries that include a thin portion. Quadratic elements can capture the geometry at a cell size larger than the thinnest portion of geometry. This makes them especially good for geometries that include a thin portion.
  
wiki/sns/intactgh/ex_6.1690404062.txt.gz · Last modified: 2023/07/26 14:41 by eli