Gauss Points and accuracy

[patolon]

Hello,

I think the title is a good summary of the question!

During FE process, the stiffness matrix requires integration, and it is approximated at the gauss points.

But I wonder how accurate this is. It's a bit strange not to try to calculate the exact value of the integral and instead just evalate at certain given points with a coefficient.

Is it the best and only way to calculate the integral?

Cheers!

 

[LRJ]

Isn't that what shape functions are used for?

 

[IDS]

The shape function defines the assumed strain distribution.

There are many ways of integrating the shape function, but calculating the weighted values at the Gauss Points is the quickest way, and gives the exact value of the integral, to machine accuracy.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[patolon]

AAh the calculated values at the Gauss points give the EXACT value of the integral?!! is it because shape functions are polynomial?

 

[ThomasH]

Hi

Gauss integration does not by itself introduce any errors. Read about it here:

https://en.wikipedia.org/wiki/Gaussian_quadrature

But there are other sources for error, like how well does the assumed shape functions describe the real displacement?

Thomas