Weights for internal Gauss point

GiD Postprocess
1

To use the full potential of contour plots for Gauss point results, we would like to use the internal Gauss points also for the simulation. Unfortunately, we could not identify the corresponding weights for all configurations of tets and triangles.

Could you specify the weights or give a reference for the definition of the internal Gauss points for GP_TRIANGLE_3, GP_TRIANGLE_6 and GP_TETRAHEDRA_10.

Thanks you for your assistance!

2

The description of the ‘GiD internal gauss points’ is available in the GiD customization manual - Postprocess data files

https://gidsimulation.atlassian.net/wiki/spaces/GCM/pages/2385543547/Gauss+Points

3

Thank you for your answer. I know the page in the customization manual. But we are looking for the weighting factors of the gauss points, not the positions.

4

It is not compulsory that you evaluate your integrals with these ‘gauss-points’ number or location, you can use the rules you want, but to express your results using our ‘defaults’ you must calculate the value of your field in our positions (e.g. extrapolating with element shape functions)

You can ask for quadrature rules for some element and amount of integration points to some AI, probably the location will be the same as our document.

e.g.

for a normalized reference triangle with area=1/2

1-gauss point: w=1/2

3-gauss points: w=1/6

6-gauss points

w=0.109951743655322/2 (points near corners)
w=0.223381589678011/2 (points close to mid-edges)

for a reference quadrilateral [−1,1]×[−1,1] (area=2x2=4)

1-gauss point: w=4

4-gauss point:s w=1

9-gauss points:

weights[]={0.5555555556,0.8888888889,0.5555555556}
wij=w[i]*w[j] (i,j from 0 to 2)

for a reference pyramid pyramid base 2x2 height=2 (volume=(4*2)/3)

5-gauss points
w=125/27 (near apex)
W rest=81/100 (near base)

etc.