Static condensation

[mbr]

Hello,

I want to implement a quadratic nonconforming element based on Fortin and Soulie in a user-element. This requires an additional 7th degree of freedom, in addition to a standard Lagrangian second order element. This additional DOF can be condensed out. The condensation part seems clear, I just have to perform some Gaussian elimination steps after the assembling of an elemental stiffness matrix. I'm currently struggling with the update of the internal DOF (which I planned to store using the history values).

My actual plan is to do this update just before the calculation of the tangents of an iteration. This would require the solution u[n+1][k-1]. I think I could access this values using a combination of ul(,,1) an ul(,,3). At this point I'm not sure about the definition of ul(,,3). What is it's value in the first iteration of a new time-step t_(n+1)? Is u[n+1][k] in this case the converged solution of the previous time step u[n][kend] and u[n+1][k-1] the solution u[n][kend-1]?

If this is the case I could probably get along or are there any other suggestions how to implement the update step for static condensation?

Kind regards,
Maximilian

[Prof. R.L. Taylor]

Look at ./elements/solid2d/sld2d3.f on how we treat the internal equations for the enhanced strain element. This does a static condensation and recovery.

[mbr]

Dear Prof. Taylor,

I apologize for the late reply. Tank you for the hint. I will take a look on the enhanced strain element.

Kind Regards,
Maximilian

[Prof. R.L. Taylor]

Another option is to make it an element variable and let it be solved along with the other equations.  In that case you declare "nlm" in "hdatat.h" and receive the result back in "ule(*,1)" in  "lmdata.h".

look at programmer manual for where to put the element equations in the element arrays "p" and "s"

[mbr]

Dear Prof. Taylor,

I have now implemented my element based on static condensation on the element level. But thank you for this second hint. I haven't thought about elemental variables. These could get very helpful in the future.

Kind regards,
Maximilian