Efforts in statically indeterminate structures

[Junimech]

Hello everyone,

I'm optimizing the cross section dimensions of a space frame structure, using analytical stress equations to get my constraint function and finite element analysis to compute the beam efforts (axial and shear forces, bending and torsional moments) for a given initial design. Objective function would be the cross section area, since the material is given.
Is this a valid approach? Are the efforts independent of the cross section properties, even for statically indeterminate structures? All beams will have the same dimensions, and the length of them is also fixed.

Thanks in advance!

 

[bkal]

If the system is statically indeterminate, the beam efforts depend on their stiffness, i.e. their cross sections.

 

[rb1957]

not sure what a "constraint function" is, nor why you have to determine it with "analytical stress equations" outside of an FEA.

but yes your approach seems reasonable. a truss (or space frame) are simple applications for FEA.

another day in paradise, or is paradise one day closer ?

 

[Junimech]

Thank's for the insight bkal. I was looking at mechanics of material formulas and wondering if for instance by reducing the section, the stress wouldn't increase in the same proportion, thus the effort being the same.

 

[Junimech]

If I have the analytical expression for the von mises stress, having cross section dimensions as variables, I can formulate an optmization problem to minimize the mass (or cross section area), where as a constraint, the von mises stress (for a given loading case) has to be lower then what the material allows (times a design actor)

 

[rb1957]

if you change the area of an element, you'll change the relative stiffness of all the elements, and so load "effort?" will redistribute. different to a statically determinate structure, where the load is fixed (by equations of statics) so changing area simply changes stress.

another day in paradise, or is paradise one day closer ?

 

[Junimech]

Thank's rb1957. But let's say the cross section is the same for all beams. If they all change equally, doesn't the distribution of loads remain the same? That's what's bugging me

 

[bkal]

I would imagine that if all the structural elements respond in the same way (linear material, all in bending for example) than changing the cross section would only affect deformations. However, if some of them respond in bending, some predominantly in shear and some in axial force then this is not the case any more.

 

[rb1957]

sure if all the elements change the same then there's no relative change. i assumed you were talking about changeing one or two elements.

another day in paradise, or is paradise one day closer ?

 

[Naffoussi]

the strain energy method could be useful for your case...

Seif Eddine Naffoussi, Stress Engineer

http://www.Innovamech.com

33650 Martillac û France

 

[Junimech]

Can you be a bit more specific ? What's the advantage of using the strain energy, instead of the stress?

 

[rb1957]

strain energy is a standard solution for redundant structures (it's what FEA does, behind the curtain)

another day in paradise, or is paradise one day closer ?

 

[Junimech]

yes, that's what I thought.

 

[rb1957]

if all members have the same area then that simplifes the element stiffness (AE/L > k/L)

another day in paradise, or is paradise one day closer ?