optimal topology for axially loaded solid structure

[jsboy]

I ran a topology optimization for rectangular parallelepiped
with axial load on it in which objective function is to minimize compliance while constraining its volume. This gave me the structure where there is a big hole inside thoughout its axial direction and material is placed onto its outer face. Would someone please explain from engineering vewpoint why this is optimal structure in this case.

 

[corus]

Generally if you have a beam under bending then most of its strength comes from the distance to its outer fibers and you can remove the central area without too much affect on the maximum stresses. This is why you see some beams with holes along the central web. The same is true when you have a beam whose ends are restrained, the shear stress is at a maximum at the outer edges.

 

[jsboy]

Thanks corus for your help.
Does maximum shear stress occur at the outer fiber even for pure compression loading case? In my model that I described initially, loads are applied in longitudianl direction so that it behaves like compression case. I thought in this case stress =P/A, so as long as A is the same, it dose not matter where you have a material, either at the middle of rectangular cross section or at outer. But in my topology run, material at center of cross section is totally removed.

 

[sukit]

This is in the case of Topology optimization will generate the structural shape in which is the mean of minimization of objective function and corresponding with constrain.
I supposed that u used the minimum strain energy as the compliance for axially load on Pipe.So the elements will not be efficient in the center of pipe will be removed.Because the stress distribution from the point of load applied to uniformly distribute along the edge and surrounding of the global structure.
Thus,This is why the most optimum model look like!!
ANd further development is the combination of buckling analysis and strain energy as a multidisciplinary method.