How to find the shape of a slab with minimum weight?

I have the finite element analysis results for a case of a steel/timber slab supported on flexible beams (two-way) loaded uniformly.

This is the model of the structure in STAAD Pro. The pink elements are slabs (plates) and blue members are the beams and columns.

Based on this data, I want to find the shape of slab with minimum weight that supports a given UDL.

Slabs are generally cuboids and are designed such that the

design actions <= allowable stresses.

This property is checked only at a few critical points like slab center and slab edge, and a rectangular shape ensures that design actions are strictly lesser than allowable stresses at all other points.

A minimum weight design will therefore try and achieve the equality of actions and stresses at all points.

How can this be achieved ?

Replies to This Discussion

Permalink Reply by Hannes Löschke on February 24, 2013 at 1:18pm

I'm probably getting you wrong here... There are several strategies do reduce weigth in slabs. If you create a parametric model for the strategy of your choice, you can analyze stress and displacement with KARAMBA. Galapagos can iteratively optimize the Stress/Displacement/Mass ratios.

Permalink Reply by djordje on February 24, 2013 at 5:43pm

I have never calculated slabs using Karamba, so Hannes's approach is probably the way to do it.

Based on your reply Chintan, I assume you are a structural engineer, so there is not much I could help you, as I am not.

But my modest approach would be to simplify the model by converting the one way span slabs into beams of 1meter in width and classical checking for the Sigma, Tau stress and Deflections: