mesh convergence 1

[sasank]

Hallo!
Can any body explain me how to check the mesh convergence.
i.e, How we can decide whether the FE mesh of 100 or 200 elements will yield correct results? Is there any criteria to decide the number of elements in a FE Mesh

 

[vineet1977]

Hai,

Mesh convergence-structural analysis

Increase the number of elements gradually. Then plot the stress or dispalcement(field variable) of some reference point in critical portions of your model against the number of elements. The point at which the there is no change in field varaiable with further increase in elements,then that is the minimum requiste number of elements to resolve the field variables.
Adaptive meshing is a better automatic technique to obtain mesh convergence. It decides and distributes the element length in an optimal way based on the field varaible varaiation.
The mesh convergence is said to be obtained beyond which increasing the number of elements willn't increase the accuracy of results considerably in consideration to economy.

Vineet vineet

 

[pja]

From Cook:
Convergence rate in general goes like(assuming no singularities in the model..ie cracks)
-O(h^(p+1)) for a field quantity
-O(h^(p+1-r) in representing the rth derivative of a field quantity
-O(h^(2*(p+1-m))) in representing strain energy(in structural mechanics)
where
-h is the characteristic length of an element(length in a linear element)
-p is the degree of the highest complete polynomial is the element field quantity ie for a basic 4 node plane element p=1 since only xy is present among all the quadratic terms(x^2,y^2 and xy)
-2m is the order of the highest derivative of the field quantity in the governing differential equation

so what does all this mean? Basically that generally displacement values converge faster then stress values with mesh refinement. Also if order of error analysis is wanted h can be replaced by (# elements)^(-1/n) where n is dimensionality of the problem(1 for 1-d,2 for 2-d etc)

 

[zuardy]

yes, i agree with vineet1977 : Increase the number of elements gradually. This is what i refer as manually checking of mesh convergence. Normally, You should increase (refine) the elements in the critical region (high stress gradient) till they have negligible change. Or try the well known H-methode or P-Methode to obtain the convergence automatically.
regards

 

[nikolas]

Hey, Zuardy can you explain what do you mean by h-method and p-method. Well i am familiar with the h-elements and p-elements. is it something related to that or something else? please clear my doubt.

 

To my know, the therm p-methode is related to p-element, i.e. the elements used in p-methode are p-elements and so do h-methode.

cheers

 

[nikolas]

No i don't think Nikole its so read carefully what zuardy has written

 

[elogesh]

hai nikole and nikolas,

There was earlier few threads discussing about h & p-methods.

Anyway briefly

Real objects has infinite degrees of freedom. But actual objects has finite degrees of freedom. If degrees of freedom is increased the accuracy of results improves(This depends upon how many orders of accuracy you need).
There are two ways to increase the degrees of freedom.
One is increasing the no.of elements and hence nodes,that is h-method.
second method is increasing the polynomial order of the interpolation function used to approximate the field variable-p method.
H-method and p-method is basically for mesh convergence.
Regards,
elogesh