Antifunicular of a two-dimensional arch

Replies to This Discussion

Permalink Reply by John Harding on September 12, 2013 at 11:11am

I know its not Karamba, but if I understand this correctly, you can use zero (natural) length springs in Kangaroo because when you load the system the x spacing won't change (i.e. only the vertical positions will be updated). The scale in the y-axis of your funicular shape will depend on the gravitational field you apply.

As the 2D system is statically determinate, so long as the form in the springs balances the load, then you have your funicular form. Equal masses will give you a parabola like shape (as in the picture below). Applying varying loads which you are doing will give an alternative funicular shape. It's a little like graphic statics but with springs.

Equal horizontal spacing assumed. Change each spring stiffness to vary in x. 

Having said all that, there's possibly an easier way of doing this with Karamba, I'm just a bit obsessed with springs $:)

Permalink Reply by Leonardo on September 12, 2013 at 11:24am

Dear John, 

thanks for your reply.

I know the method with zero length springs in Kangaroo but I would like to use another method with Karamba: set to zero all moments just moving points!

In the future I would perform some more complex examples that probably are impossible with Kangaroo :-D

Thanks for your help!

Permalink Reply by Karamba3D on September 12, 2013 at 12:24pm

Dear Leonardo,

if I understand you correctly you want to simulate a rope under large deformation.

Try this: divide your structure into small beam segments with small bending stiffness as compared to their axial stiffness. Use for example a circular profile with very small diameter (try different values for the diameter). Then analyze the structure with the LargeDeform-component.

Best,

Clemens

Permalink Reply by Leonardo on September 12, 2013 at 12:31pm

Dear Clemens,

thanks for your reply.

I have explored the method you propose and it works well. However I would like to use another methodology to find the antifunicular: to set to zero all moments just moving points vertically. I would like to know if exist a component where the input is the moment for each point, while the output is the vertical displacement in order to have zero moment. For pratical purposes this method is great!

Should I create a new component using C++?

Permalink Reply by Karamba3D on September 12, 2013 at 1:17pm

Dear Leonardo,

the component you describe above does not yet exist.

You could try to use the output of the 'Resultant Section Forces'-component, sum up moment you get there and use Galapagos or Goat to minimize it with the vertical node positions as the parameters to optimize.

Once you achieve such a zero moment structure the question remains whether it makes sense from a structural point of view:

- zero moments result for one load-case only.

- the structure will be sensitive to geometric imperfections.

If you connect the resulting arches you will get a grid shell like structure. For shells the exact geometry is less important (for getting small bending moments) than for arches. As long as they are doubly curved and curvature is large they perform well. 

The weak parts of shells are usually their free edges where they behave like arches.

C.

Permalink Reply by Leonardo on September 13, 2013 at 2:10am

Dear Clemens,

thanks for your tips!

Leonardo

Permalink Reply by Leonardo on October 9, 2013 at 10:36am

Dear Clemens, 

Just a question about "LaDeform" component: please could you explain me the use of "max disp" input data? I do not understand the words of the manual.

ps: I am trying to perform a non-linear calculation using "LaDeform" component with point-loads having different values and directions among them. 

Many thanks.

Best, 

Leonardo