Gauss-Legendre

[Jhno]

Hi, I am new to the forum so if I post the question in the wrong section excuse me!
I am a new user to the finite element method and I am learning by myself so please don't get offended if my question seem a little stupid... there is much to learn on the FE subject.
Right now, am using the Opensees finite element program. The program uses Gauss point to display the stress in element.
I am not very familiar with Gauss point and so I do not understand where they are located in my element nor what their output represent.
The output looks a like this for a element stress output.
Gauss point 1 : (xx, yy, xy) $Value1, Value2, Value3
Gauss point 2 : (xx, yy, xy) $Value4, Value5, Value6
Gauss point 3 : (xx, yy, xy) $Value7, Value8, Value9
Gauss point 4 : (xx, yy, xy) $Value10, Value11, Value12
Question1 : I am not sure if I can take that the XX value at gauss point 1 is directly the principal stress in the X direction for that point?
Question 2 : If yes, how do I know where are the Gauss point located at?
Question 3 :Also, I did look at some wiki on the subject and found that the Gauss point have "weight" (this is the reason I ask Question 1).
Thanks for your help!
Here is a image of my element :

 

[IDS]

I have extracted Gauss Point data from:

https://pomax.github.io/bezierinfo/legendre-gauss.html

and copied into the attached spreadsheet, together with a plot of the positions for an eight-noded plate element, which will have 4 Gauss Points.

The Gauss Points are just a quick way of doing a numerical integration over an area. The procedure is:
[ol 1]
[li]Calculate the stress (or whatever you are integrating) at each Gauss Point.[/li]
[li]Take the weighted average (and in the case of a 2x2 integration the weights will all be 1)[/li]
[li]Multiply by the area[/li]
[/ol]

So in answer to your questions:
1. Yes the stresses at the Gauss Points are the estimated stress at that point, that is the interpolated stresses using the parabolic stress field defined by the deflections of the plate nodes, which may or may not be a good approximation to the actual stress in the element being modelled.

2. Locations are given for curves of order 2 to 64 in the attached file (not that you will ever need anything like 64x64 points in any real engineering application). The tables are for integration under a line. To extend them to a surface just use each possible combination of points. For a quadratic curve you need 2 points, so for a quadratic surface you get the 4 points as plotted. You will have to check the Opensees documentation to get the numbering of the points.

3. The weights are only used in the calculation of the integral, they do not affect the calculation of the stress at the point.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Jhno]

Thank alot for you help! I will be looking into that