How to calculate displacements at the integration points?

[alexsh]

Hi there,

I'm trying to calculate the displacements of the element at the integration points (sections) of a displacement based element. I can only record the curvatures at the sections, so I thought I could calculate the deflection at the sections by the following method:
1) Get rotations at the section by multiplying the section curvature by the Gaussian weight for that section (constant curvature over the section weight)
2) Add rotations cumulatively up the height of the element
3) Get displacements at section by multiplying the cumulative rotation at each section by that section weight

When I use this 'manual' process to calculate the nodal displacement, the resulting nodal displacement is about 10% larger than from the Node Recorder displacement. I am wondering why this could be. Is this 'manual' integration a theoretically correct approach or am I making an incorrect assumption somewhere?

Thanks!

[selimgunay]

Could you try linear curvature distribution between the integration points and repeat the calculations?

[fmk]

you might want to look at the source code for the element .. as Selim mentioned, the disp beam element assumes linear curvature and constant axial deformation along the length .. the equations are pretty standard for beams, they can be seen here:

http://opensees.berkeley.edu/wiki/image ... EvsDBE.pdf

[alexsh]

Thank you for your help!

To summarize:
The calculated rotations from step (1-3) are not the actual rotations of the element at those integration points. They are 'arbitrary' parts that sum up to the total element rotation.

To get the displacement distribution, Gaussian Quadrature is not needed at all: to get the rotation distribution along the element (and therefore at each integration point), just integrate the linear curvature by hand up the height of the element (as @selimgunay points out). To get the displacement distribution, integrate the resulting rotation expression again.

[imansalehi]

for getting the rotation at each point of the element (x) you must integrate from 0 to x over curvature,

[Haibo]

Dear imansalehi, can you explain more about how to get the rotation?