Firstly, a tangential observation: For the mean dilatation element
(Q1-P0-P0), the dilation and pressure variables can be condensed out on an
element level and a modified one-field formulation remains. For this
element the "mean dilatation" means that one must compute
\bar{\theta} = 1/V_{e} * \int_{element} \theta (X) dV
where V_{e} is the volume of the element
V_{e} = \int_{element} dV
Could it be that your "centroid" value \bar{F} is to coincide with the mean
value of F? If so, then could you not just compute the element average in
the same way as for the mean dilation \theta?
J-P
On Thursday, December 22, 2016 at 5:10:04 PM UTC+1, cmhame...@gmail.com
wrote:
>
> The thing is though that I don't actually need to integrate at these
> points. The method still employ a 4node quad element in 2d or an 8 node hex
> element in 3d but only uses the element centroid to calculate the
> deformation gradient, no quadrature is actually done at that point so I
> feel like I need to interpolate otherwise the way deal makes the FESystem
> objects I'll now have quad points at all centroids that should be
> integrated, or am I misunderstanding something here?
>
> On Thursday, December 22, 2016 at 9:21:01 AM UTC-5, Denis Davydov wrote:
>>
>> Hi
>>
>> On Thursday, December 22, 2016 at 5:47:24 AM UTC+1, cmha...@gmail.com
>> wrote:
>>>
>>> I have gone through some of the tutorials previously and thought it was
>>> about time I actually tried to implement something on my own in the
>>> library.
>>>
>>> I am attempting to implement a finite strain code using the F-Bar
>>> method. Essentially this is a single field formulation which requires the
>>> calculation the of the deformation gradient at the element center. The
>>> trick here is though that the element centroid isn't a vertex.
>>>
>>> My question is, is there a way to "interpolate" the displacement
>>> gradient at the element center without explicitly making it a quadrature
>>> point or will I have to implement my own quadrature formula for this method?
>>>
>>
>> Yes, employ a custom quadrature formula with a single point with
>> coordinates {0.5, 0.5, 0.5} to feed it to FEValues.
>> There is no reason to figure out how to interpolate things, just use
>> Quadrautre<dim> and FEValues<dim> together to evaluate your solution at
>> quadrature point(s).
>>
>> Regards,
>> Denis.
>>
>>
>>>
>>> Thank you for any assistance that can be provided.
>>>
>>
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