How to solve space frame for temperature loading ?

[Son_new]

Hi all,

On official site there is an example manual, which shows how to do the thermal problem analysis but it's mostly for planar problems not for space frame element.

Any entry-point on that will be appreciated.

Regards,

[FEAP_Admin]

If you describe the general type of problem you would like to solve, it may be easier to answer.

[Son_new]

Actually I was trying to formulate(on matrix level) the frame/beam(6 DoF per node) elements under uniform or gradient temperature loading. I know that uniform temperature will cause only axial elongation in frame element which will result in as normal force F(temperature)= E*A*alpha*DeltaT, in order to add those forces into local and global stiffness matrices of frame element, temperature loading matrix should be composed in 12x1 matrix manner
K_temp = TRNANSPOSE[-F(temp) 0 0 0 0 0 F(temp) 0 0 0 ] (12X1)
and should be added appropriately to the RHS of linear equation system(LES) and the LES is solved with any solver Gauss elimination, LU decomposition etc.

Although the process is so simple for uniform temperature loading I couldn't succeed to obtain the correct results for temp loading, little more info on how actually it goes for the gradient temperature loading (I think it creates the beding moment which needs to be added to the K_temp matrix.


Regards,

[FEAP_Admin]

Hint:  Start from the basics:  eps = sig/E + alpha * Delta T(y) and the fact that in a beam eps = -kappa * y.

[Son_new]

Hint:  Start from the basics:  eps = sig/E + alpha * Delta T(y) and the fact that in a beam eps = -kappa * y.

Thanks,

I believe that there is the confusion for me due to the naming convention in the variables.

Here is my interpretation,
The first term stands for strain which express the strain for external loading(which is zero in my case) , second term is strain/elongation due to uniform thermal loading, with 2nd therm you suggest that if displacement is known then unknown can be found from Epsilon=kappa*Y where k is stiffness matrix and Y is the global displacements.  Kappa and epsilon is known so the Y global displacements can be found, right?

[FEAP_Admin]

It is best that you get a good book on Finite Element Analysis.  Let me suggest the comprehensive books by Zienkiewicz and Taylor.