The computational savings at the element level for this method is much more
efficient than the dilatation element because for each element I just need
to calculate one quantity instead of solving a linear system to remove the
static condensation from the displacement system.
On Thursday, December 22, 2016 at 11:22:40 AM UTC-5, Jean-Paul Pelteret
wrote:
>
> 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, cmha...@gmail.com
> <javascript:> 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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