3 General questions on FEA: 3

[3doorsdwn]

I've finished reading a few texts I had on FEA theory and I had a couple of general questions for those more knowledgeable than me:

1. For most of the solution techniques presented (i.e. Galerkin's, potential energy, etc.) the expression for the stiffness matrix tends to wind up being the same (i.e. Integral T[D] dv). Are there any applications [i.e. the solution techniques used] where this expression would be affected? Or does this pretty much stay the same.

2. As far as solid elements go(like the 8-noded brick element) they tend to have only three degrees of freedom at each node (i.e. translational). Are there any higher order elements/shape functions that allow rotational degrees of freedom for solids?

3. The texts I have all form the stiffness matrix for the 8-noded brick element by using the isoparametric system (and they indicate this is for convenience of computations). Is it possible to formulate an 8-noded brick element using the same approach as (say) a [non-isoparametric] tetrahedral element? Would doing so produce significantly different results (in comparison to the isoparametric formulation; assuming we are talking about straight sides in both cases (i.e. identical elements))?


Thanks in advance.

 

[kellnerp]

The answer to 1 is: Pretty much stay the same for static analysis.

The answer to 2 is: What would rotation at the node of a solid element mean? Since the shape function is based on displacements of the nodes how would you set this up for nodal rotations? The reason you have rotational dof on shell and beam elements is that you are assuming some kind of strain variation through the thickness.

The answer to 3 is: You better not get different results (within some small percentage)for different formulations. If so there is something wrong with the element formulation.

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"Node news is good news."

 

[3doorsdwn]

That's kind of what I suspected for #2. Just thought I'd ask (you never know what people could have come up with doing research).

Thanks kellnerp.

 

[johnhors]

Just to throw you all off balance a little, here is a solid element WITH rotational degrees of freedom !!!

http://uic.edu/depts/accc/software/ansys/html/elem_55/chapter4/ES4-72.htm

I don't think any other solver has attempted to do this, so this is very much an oddity and generally solid elements only have translational degrees of freedom at their nodes.

 

[corus]

Beam elements also have rotational degrees of freedom. For instance in 2D the dof will be x,y and a rotation about the z axis. With this extra degree of freedom you can then fit a cubic through the two nodal end points to describe the translations along the length of the beam. Johnhors example is the 1st time I've seen it applied to true solid elements, and might solve the problem of using 'linear' tets in structural analysis. A good thesis there for some student me thinks.

corus

 

[kellnerp]

The rotational stiffness of an isolated node or line of nodes is quite small and is typically inappropriate as the sole rotational constraint of the model or an adjacent beam or shell element.

This isn't quite the same behaviour as a shell or beam element's rotational dof. This is just part of the warning.

Ansys has this element [link Solid95 ]

http://uic.edu/depts/accc/software/ansys/html/elem_55/chapter4/ES4-95.htm

[/url] which might work for through the thickness modeling of thin, shell like regions.

SOLID95 elements have compatible displacement shapes and are well suited to model curved boundaries.

TOP
CSWP
BSSE

http://www.engtran.com

http://www.niswug.org

"Node news is good news."

 

[johnhors]

Kellnerp - isn't that just a standard serendipity 20 node brick element?

 

[3doorsdwn]

You defiantly through me for a loop with that element johnhors. It would be interesting to see the shape functions for that element.

 

[kellnerp]

Should be. The theory manual has this: ANSYS Theory Reference look around page 384.

These elements don't like distortion. So the aspect ratio needs to be watched. Again this can drive up the number of dof.

Sorry about the tgml. Should have been: SOLID95

ANSYS also has a reinforced concrete solid, SOLID65.



TOP
CSWP
BSSE

http://www.engtran.com

http://www.niswug.org

"Node news is good news."

 

[3doorsdwn]

When you think about it, (in most cases, for solids) rotational degrees of freedom shouldn't impact results if the model is meshed enough.

I've been meaning to try a 20-noded brick element for reinforced concrete. I've heard that it will converge faster than the [alternative] 8-noded brick element.

For cracked reinforced concrete action I've always just adjusted the modulus of elasticity (for plate elements) to simulate the cracked behavior. never been sure how to do it for solids.

I use to work somewhere where there was a big disagreement about when to switch over to solid elements for reinforced [around the perimeter] concrete pedestals. [I worked with this one guy who modeled a 12' x 12' pedestal with plate elements. He had about 4 elements per direction (and he made one set of them massless so the total weight would be right for the dynamic analysis he was doing). he didn't seemed concerned that the out of plane stiffness for the elements in the other direction would cause the model to be overly stiff (he didn't designate the elements as plane stress only).]