shell theory and shell elements ?

[caviac]

Hi all,
just a precision for me.

Is there a limit ratio between legth and thickness to be applied in theory of shell ?

Which ratio for part ?

Is there a ratio for elements too or is it applied for parts and after we can mesh the part with very small elements ?

Thx

caviac

 

[caviac]

Some people tell me that just the part has to follow the shell theory and you can mesh your part with small elements.

Others say that part and elements have to respect the shell theory criteria (length/thickness ratio)

Just to be clear...

 

[prex]

Your first sentence in the second post is the correct one.
If you mesh a shell with smaller and smaller elements, you'll approach the analytical solution of shell theory (more correctly: of the particular shell theory that's implemented by the elements you use) that can be obtained for some geometries.

prex

http://www.xcalcs.com

Online tools for structural design

 

[mtnengr]

I presume that you are interested in obtaining a complete solution where bending is prevalant. To obtain an estimate of the required mesh size, examine the solution of bending in a cylindrical shell of revolution.

The key parameter is the characteristic length and is defined as beta L = L(1- nu**2)**1/4 / (a h)**1/2, where L is the length of the shell, nu is Poisson's ratio, a is the radius and h is the thickness. If you examine the bending from an applied moment, the first zero cross over point ocurrs at x=PI/4. So to acquire the full benefit of bending in an element, beta x < PI/4. As bending diminishes, the element size can increase. Usually membrane forces do not require such a small element size.

Element distribution in the circumfrental direction is generally based upon the Fourier harmonics of the loads being applied. The higher the harmonic, the closer the element distribution will be required in the circumferental direction. Of course, the assumed isoparametric displacements being used in the FE will also have an effect on the accuracy of the solution.