curvature of forceBeamColumn & dispBeamColumn in pushover

[caosasa]

Dear all,
i find that in the pushover analysis of a pier,
if all elements of the pier is simulated with dispbeamcolumn and fiber section,
the curvature in all the integration points of an disp element is almost identical,
and the cuvature at node j of element 1 is different from the cuvature at node i
of element 2.
however, if all elements of the pier is simulated with nonlinearbeamcolumn and fiber
section, the curvature in all the integration points of an disp element is increasingly,
and the cuvature at node j of element 1 is the same as the cuvature at node i
of element 2.
My question is: is it normal for the dispbeamcolumn that curvature at node j of
element 1 is different from the cuvature at node i of element 2, and that the curvature
in all the integration points is almost identical?
thanks.

[caosasa]

one more question: in the dispelement, can the plastic rotation be computed as the
curvature at the i node multiplying the length of the element at the foot of piles or pier?

[vesna]

The displacement-based approach follows standard finite element
procedure where we interpolate section deformations from an
approximate displacement field and then use the PVD to form the element
equilibrium relationship. To approximate nonlinear element response, constant axial
deformation and linear curvature distribution are enforced along the
element length (exact only for prismatic linear elastic elements). This leads
to different curvature results at the same node.

[caosasa]

Dear vesna, thank you for your patience reply. Can i replicate
"To approximate nonlinear element response, constant axial
deformation and linear curvature distribution are enforced along the
element length (exact only for prismatic linear elastic elements)" as
the displacement-based approach is exact for prismatic linear elastic elements
and approximate for nonlinear element.
If so, can the approximation for nonlinear element be accepted?

[vesna]

If you model your element with several disp-based elements you can get close to the exact solution.

[wuhaoshrek]

vesna wrote:
> The displacement-based approach follows standard finite element
> procedure where we interpolate section deformations from an
> approximate displacement field and then use the PVD to form the element
> equilibrium relationship. To approximate nonlinear element response,
> constant axial
> deformation and linear curvature distribution are enforced along the
> element length (exact only for prismatic linear elastic elements). This
> leads
> to different curvature results at the same node.

Hi vesna,

I think the curvature is assumed to be linear between the neighbor integration points, and
it is muti-linear in one element, right?
by the way, what is PVD you mentioned, I can't find it in Google.

Thx.

[vesna]

within a displacement based element, curvature is assumed to be linear from node i to node j (not between integration points).

PVD stands for the principle of virtual displacements.

[caosasa]

Thank you vesna. i like you.

[caosasa]

wuhaoshrek wrote:
> vesna wrote:
> > The displacement-based approach follows standard finite element
> > procedure where we interpolate section deformations from an
> > approximate displacement field and then use the PVD to form the element
> > equilibrium relationship. To approximate nonlinear element response,
> > constant axial
> > deformation and linear curvature distribution are enforced along the
> > element length (exact only for prismatic linear elastic elements). This
> > leads
> > to different curvature results at the same node.
>
> Hi vesna,
>
> I think the curvature is assumed to be linear between the neighbor integration
> points, and
> it is muti-linear in one element, right?
> by the way, what is PVD you mentioned, I can't find it in Google.
>
> Thx.
wuhaoshrek：
你好，
我也是同济的，
能否留个qq，
或者你加我94二一16三4，
有问题的话请教你，
谢谢，
曹飒飒

[wuhaoshrek]

vesna wrote:
> within a displacement based element, curvature is assumed to be linear from
> node i to node j (not between integration points).
>
> PVD stands for the principle of virtual displacements.

Hi,vesna,

Can I have one more question? It is easy to understand linear curvature distribution within a
disp based element since the shape function is cubic Hermit function. BUT in force based element
it is only assumed that moment distribution in an element is linear, so how can we know that the
curvature distribution is linear between integration points?

thx

[vesna]

We do not know the distribution of curvature between integration points. We know the curvature values at integration points and to approximate curvature distribution along the element we draw linear distribution.

[wuhaoshrek]

vesna wrote:
> We do not know the distribution of curvature between integration points. We
> know the curvature values at integration points and to approximate
> curvature distribution along the element we draw linear distribution.

OK. I see, thank you vesna.

regarding the force based element, the internal force distribution is exact based on current element formulation only
when there is no external force applied along the element. however, in opensees we do could apply load to a element
using the command "eleLoad-". So if I enforce the eleload to an forcebeamcolumn elemnt(the moment is not linear
distributed anymore),does that mean the internal force distribution would not be exact any more?

best.

[vesna]

No, the force formulation is exact even if there is element load on that element.