stress at upper face and lower face for shell

[jsboy]

I am interested to know the flow in Nastran to calculate the stress at upper face and lower face for shell element. Here, I am only talking about bending state because stress at membrane state is same throughout thickess direction. In my understanding by reading FE book, it is, first get stress resultant which is actually moment Mx, and using equation, sigma=(Mx/I)*z, to obtain the stress at upper and lower. Please throw some light on that.

 

[feadude]

I believe it is 6M/(t^2)
t is thickness of plate

 

[sean01]

jsboy

It sounds to me as if you are quoting part of an equation that was taught to me as the 'engineers theory of bending'. The full formula I think is something like

M = sigma = E
I y R

M is normally a couple (moment)
I is the moment of inertia about the neutral axis
sigma is the stress
y is the distance of the furthest point from the neutral axis
E is youngs modulus
R is the radius of gyration

I'd suggest that from the formula you have written Mx would be the moment produced along the x axis and z would be the equivalent of y.

Hope this helps !


Sean

 

[jsboy]

Thanks.
Does anyone know any website where I can download c++ source code for shell element?

 

[Breezer]

Nastran calculates the stresses at the top and the botton of the shell at the fiber distances for stress calculations Z1 and Z2 which are t/2 if not differently specified by the user. The definition of top and bottom obviously depends on the element definition (element normal, face 1 and face2). Axial and bending stresses at the centroid of the shell element are given by: sAXIAL = P/A and sBEND = Mc/I. Therfore you get on the tensile surface: s = sAXIAL + sBEND, and on the compressive surface,s = sAXIAL - sBEND.

Hope this helps.

 

[feadude]

Annher
Why do not you just plot the Von Mises stress which includes tension and compression due to bending as well as axial and shear stresses. It is normally used for onset of yielding for ductile materials like steel.

 

[Breezer]

feaude
You are right. Von Mises stresses - always a positive number - convenient and commonly used, works well especially for ductile material. But depending on the material and problem you wouldn’t always rely on the von Mises stresses. Think of a concrete or other composite structure where it is essential to differ between compressive and tensile stress.