Results Postprocessing > Numerical Methods > 13.4 Averaging
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13.4 Averaging
For Fringe and other plots and reports that must display or report values at nodes from elemental data regardless of where the element results are computed, must be converted to results at element nodes. The interpolation functions are then used (e.g., by the graphics module for fringe plot and other operations) to compute the results at any point within the element. The interpolation functions may or may not be the shape functions that were used by the analysis program to compute the element results.
As a rule, each element sharing a common node has its own result values. To compute results for continuous fringe plots, these values need to be averaged and distributed to the sharing elements. The options for the averaging process are described below:
No Averaging
Each element retains its value at the element nodes. Or in other words, each element is its own averaging domain. This selection from the Averaging Domain pull down is called None. The fringe plot will have jumps (not continuous regions) at element boundaries.
Averaging Based on All Entities
All elements will contribute to the sum and will receive the averaged result regardless of whether only certain entities have been selected for the display of the fringe plot. All surrounding elements will contribute to the averaging process.
Averaging Based on Target Entities
Only the elements defined as the target entities will contribute to the sum and will receive the averaged result. Surrounding elements that are not part of the target entities will not contribute to the averaging process.
Averaging Based on Materials
Elements with the same material IDs will contribute to the sum and will receive the averaged result. The fringe plot will have jumps at material boundaries.
Averaging Based on Properties
Elements with the same property IDs will contribute to the sum and will receive the averaged result. The fringe plot will have jumps at property boundaries.
Averaging Based on Element Types
Elements of the same type will contribute to the sum and will receive the averaged result. The fringe plot will have jumps at element type boundaries.
Difference
The minimum and maximum results from the elements sharing a common node are computed. The difference is determined as the delta between the maximum and minimum contributor to each node. The fringe plot of this max difference indicates the quality of the mesh and the location where this mesh needs to be refined by comparing its values with the actual values of the results. Nodal results will have zero max-difference.
Sum
The sum of all contributing nodes will be displayed. This step skips the averaging.
Below are some examples of the averaging techniques. The model in Figure 13‑1 is used for illustration purposes. It consists of 8 QUAD4 elements and 4 TRI3 elements with a total of 17 nodes.
Figure 13‑1 Square Plate Model to Illustrate Averaging Techniques.
The above model is also broken up into various material and property sets as such:
Prop1
Mat1
Elem 1:3
Prop2
Mat2
Elem 6 8:9
Prop3
Mat3
Elem 4 7
Prop4
Mat1
Elem 10:13
Target1
Elem 1:3 6 10:11
Target2
Elem 4 7:9 12:13
Element Centroidal Results
The first illustration is the simple case of results at element centroids. Table 13‑1 below lists some scalar values of strain energy at each element centroid. The table is listed by node number with each element and corresponding strain energy value for all contributing elements associated with the particular nodes. The averaging domain columns on the right then list the averaged values for each node based on the averaging domain. Columns with more than one value per node indicate a boundary of the averaging domain and will therefore cause a plot discontinuity across boundaries. See Figure 13‑2 for visual effects of averaging domains.
Table 13‑1
Node
Element
Strain Energy
Averaging Domain
All
Property
Material
None
Type
Target
1
1
3.01
3.01
3.01
3.01
3.01
3.01
3.01
2
1
3.01
3.89
3.89
3.89
3.01
3.89
3.89
2
4.78
4.78
3
2
4.78
3.97
3.97
3.97
4.78
3.97
3.97
3
3.16
3.16
4
3
3.16
3.16
3.16
3.16
3.16
3.16
3.16
5
1
3.01
8.04
3.01
 
3.01
8.04
3.01
4
13.06
13.06
13.06
13.06
6
1
3.01
4.24
3.89
2.04
3.01
6.95
2.63
2
4.78
4.78
4
13.06
13.06
13.06
13.06
6.67
10
0.10
0.19
2.04
0.10
0.19
2.63
13
0.27
0.27
6.67
7
2
4.78
2.09
3.97
2.04
4.78
3.42
2.09
3
3.16
3.16
6
2.31
2.31
2.04
2.31
10
0.10
0.11
2.04
0.10
0.11
11
0.11
0.11
8
3
3.16
2.74
3.16
3.16
3.16
2.74
2.74
6
2.31
2.31
2.31
2.31
9
4
13.06
12.10
12.10
12.10
13.06
12.10
12.10
7
11.13
11.13
10
4
13.06
5.95
12.01
12.01
13.06
9.74
5.95
7
11.13
11.13
8
5.02
5.02
5.02
5.02
12
0.27
0.27
0.27
0.27
0.27
13
0.27
0.27
11
6
2.31
2.11
3.38
3.38
2.31
3.38
1.21
8
5.02
5.02
2.70
9
2.82
2.82
11
0.11
0.19
0.19
0.11
0.19
1.21
12
0.27
0.27
12
6
2.31
2.57
2.57
2.57
2.31
2.57
2.31
9
2.82
2.82
2.82
13
7
11.13
11.13
11.13
11.13
11.13
11.13
11.13
14
7
11.13
8.08
11.13
11.13
11.13
8.08
8.08
8
5.02
5.02
5.02
5.02
15
8
5.02
3.92
3.92
3.92
5.02
3.92
3.92
9
2.82
2.82
16
9
2.82
2.82
2.82
2.82
2.82
2.82
2.82
17
10
0.10
0.19
0.19
0.19
0.10
0.19
0.10
11
0.11
0.11
12
0.27
0.27
0.27
13
0.27
0.27
Element Nodal Results
The second illustration is the more complex case of results at element nodes. Table 13‑2 below is listed by element number with each node and corresponding von Mises stress for all nodes associated with the particular element. This case is identical to the element centroid case with the exception that each node can have a different value for each contributing element. In this example von Mises stress is derived first and then averaged. See Figure 13‑2 for visual effects of averaging domains.
Table 13‑2
Element
Node
von Mises Stress
Averaging Domain
All
Property
Material
None
Type
Target
1
1
266353
266353
266353
266353
266353
266353
266353
2
205495
236621
236621
236621
205495
236621
236621
6
194627
238950
263404
240096
194627
265783
209085
5
251128
330989
251128
251128
251128
330989
251128
2
2
267747
236621
236621
236621
267747
236621
236621
3
269673
247874
247874
247874
269673
247874
247874
7
288631
213334
254218
199024
288631
259671
213334
6
287859
238950
263404
240096
287859
265783
209085
3
3
226076
247874
247874
247874
226076
247874
247874
4
223550
223550
223550
223550
223550
223550
223550
8
216967
224325
216967
216967
216967
224325
224325
7
219806
213334
254218
199024
219806
259671
213334
4
5
410849
330989
410849
410849
410849
330989
410849
6
314864
238950
314864
314864
314864
265783
283747
10
316307
310705
326528
326528
316307
350090
310705
9
409360
381243
381243
381243
409360
381243
381243
6
7
270577
213334
270577
270577
270577
259671
213334
8
231683
224325
231683
231683
231683
224325
224325
12
231124
264210
264210
264210
231124
264210
231124
11
269415
265760
311763
311763
269415
311763
206152
7
9
353127
381243
381243
381243
353127
381243
381243
10
336749
310705
326528
326528
336749
350090
310705
14
331970
361658
331970
331970
331970
361658
361658
13
351258
351258
351258
351258
351258
351258
351258
8
10
397215
310705
397215
397215
397215
350090
310705
11
389998
265760
311763
311763
389998
311763
305499
15
384259
346068
346068
346068
384259
346068
346068
14
391346
361658
391346
391346
391346
361658
361658
9
11
275878
265760
311763
311763
275878
311763
305499
12
297297
264210
264210
264210
297297
264210
297297
16
331799
331799
331799
331799
331799
331799
331799
15
307878
346068
346068
346068
307878
307878
346068
10
6
144769
238950
198700
240096
144769
198700
209085
7
144769
213334
143829
199024
144769
143829
213334
17
144769
197728
197728
197728
144769
197728
143829
11
7
142890
213334
143829
199024
142890
143829
213334
11
142890
265760
196756
196756
142890
196756
206152
17
142890
197728
197728
197728
142890
197728
143829
12
11
250623
265760
196756
196756
250623
196756
305499
10
250623
310705
251626
251626
250623
251626
310705
17
250623
197728
197728
197728
250623
197728
251627
13
10
252631
310705
251626
251626
252631
251626
310705
6
252631
238950
198700
240096
252631
198700
283747
17
252631
197728
197728
197728
252631
197728
251627
Figure 13‑2 Differences in Plots Due to Averaging Domains - Note Discontinuities.