Rod Shape Function

[sushi75]

Good evening all,

A very simple question, might seems obvious but I'm started to get confused...

When dealing with bar, the usual shape function is a linear one: N(x)=ax+b

However, I wonder why don't we choose a degree 2 shape function after all? The exact solution of the displacement is polynomial (degree 2)

Perhaps, it's because we assume that strain=du/dx=constant, in the small displacements assumption?
In that case that would justify the linear interpolation of the displacement.

So I'm still a bit in the dark, and I cannot find any answer to that question!

Thanks for your help :-D

Tom

 

[IDS]

Tom - yes, in a linear elastic analysis both axial and bending displacements are assumed to be negligible.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[sushi75]

Thqnks IDS, so in theory it would not be impossible to have a bar element with 3 nodes and 3 shapes functions, but it would not be relevant in line with linear elastic?

I have also noticed in Patran, there is only one option for rod element; so I believe the linear shape function is the best option.

What about the other software?

Thanks!

Tom

 

[rb1957]

there are FE codes with 3 node (ie parabolic shape function axial members (RODs and BEAMs) to be compatible with parabolic shell elements; but NASTRAN prefers you combined a parabolic CQUAD8 with 4 linear CRODs. Yes, you're correct that they are incompatible shape functions but that's what NASTRAN makes you do. Why ? you'd need to ask them that !

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