Shell ForceFlow resultant computation (vs PrincStress)

In the following image, A, B and C are the Sources and ForceDirs in the ShellLineResults component.

Quoting Karamba manual, "If there are two ForceFlow (FF) lines, the resultant force between those in a predefined direction stays constant". This is what makes FF different from the PrincStress Lines.

It is then clear that:

resultant force between A–B = resultant force between B–C

1) If I had only one Source point, therefore only one FF line, how would the resultant force be computed for that line? What would be the boundary for computing the resultant force? Would Karamba take all the length of the beam, measured orthogonally from the SourceDir input?

2) Consequently, what is the correct way to compute the resultant force associated with each FF line in Karamba?

Replies to This Discussion

Permalink Reply by Karamba3D on November 28, 2016 at 12:28am

Dear Alessio,

the condition of constant resultant force holds for two flow force lines each. Therefore it is not the case that 'resultant force between A–B = resultant force between B–C'.

In order to calculate the force flow lines it is not necessary to determine the resultant force. If you want to determine for example the flow line in a liquid you can simply follow the path of one of its particles.

You could calculate the resultant force by integrating the stresses in the section perpendicular to the direction supplied for calculating the force flow lines.

Best,

Clemens

Permalink Reply by Lorenzo Greco on December 5, 2016 at 1:59am

Hi Clemens,

So how do you calculate flows with stresses? I guess you don't just connect the tip of (normalized?) vectors as this would be the stress path, right?

Are you just taking the component parallel to the vector provided?

Permalink Reply by Karamba3D on December 5, 2016 at 1:14pm

Hi Lorenzo,

the direction of the force flow is given by

alpha = artan(tau_xy/sigma_xx)

where x is an arbitrary direction, y the direction perpendicular to x, tau_xy the shear stress, sigma_xx the normal stress and alpha the direction angle. For details see the paper 'Die Visualisierung des Kraftflusses in Stahlbaukonstruktionen' by H. Moldenhauer (http://onlinelibrary.wiley.com/doi/10.1002/stab.201201473/abstract) - it is however written in German.

Best,

Clemens

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