## How to apply shear load and moment on thin-walled cylinder FEM

## How to apply shear load and moment on thin-walled cylinder FEM

(OP)

How do I apply a shear load, V, and bending moment, M on a thin-walled cylindrical shell FEM to capture the correct bending stresses and shear stresses according to beam theory? According to beam theory, the bending stress is a function of sine, fb = M*Sin(theta)/(Pi*r^2*t) and the shear stress is a function of cosine, fv = V*Cos(theta)/(Pi*r*t) where theta is the angle above the neutral axis.

Thanks!

Thanks!

## RE: How to apply shear load and moment on thin-walled cylinder FEM

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

## RE: How to apply shear load and moment on thin-walled cylinder FEM

(hint, as a function of theta)

depending on your FEA code, there may be a built-in function.

i'll give you another hint for free, i think your expressions will not give you the answer you desire. think in terms of shear flow (it'll be easier to apply shear force to your model (rather than shear stress) ... derive the shear flow around the open end of the tube (i think your expression for shear stress is the vertical component of the shear stress, but i could be wrong ... on the face of it, it doesn't look right) ... the FEA should solve the moment stress based on the applied shear forces

## RE: How to apply shear load and moment on thin-walled cylinder FEM

Model that.

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

## RE: How to apply shear load and moment on thin-walled cylinder FEM

seriously, i'd suggest reading primers on FEA or the manual for your code (it should have good examples to show the features of the code and how to apply them).

it may be a flash of the blindingly obvious, but you are modelling a tube (rather than a section of the tube) and you know that M = V*d (and this time (only, maybe) i'm not trying to be sarcastic).

## RE: How to apply shear load and moment on thin-walled cylinder FEM

Probably the best way is to apply rigid links to the free end of the nozzle as rb1957 says. and apply your loads to the central node that connects to the nodes onto the cylinder/nozzle. I guess you'd have to apply a counter moment to offset the moment you were applying from the shear load if that wasn't in the direction of the actual moment you require. The problem then is the distance you need to apply these rigid links and forces from the area of interest at the connection so they don't have a localised effect which wouldn't be seen in real life. The norm is to take six times the wavelength of the shell, or about 4.5 x sqrt(rt) for axisymmetric forces, so I'd double that for asymmetric loads applied to the cylinder.

corus

## RE: How to apply shear load and moment on thin-walled cylinder FEM

Therefore, I was looking for a good way to apply the shear load and moment to the cylinder such that I would get the correct bending stress due to the applied moment and shear stress due to the applied shear load.

## RE: How to apply shear load and moment on thin-walled cylinder FEM

Are you interested in the stresses near the point of application of the loads? If not then you can afford to be a bit crude. Otherwise you'll need to apply them element by element.

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

## RE: How to apply shear load and moment on thin-walled cylinder FEM

have you asked the help desk ... they usually are very helpful.

if you for another approach to apply the loads then calc the grid forces ... work from shear flow to distribute the shear forces and torque, work from areas (and 2nd MoI) to distribute axail force and moments (remember, plane sections remain plane).

your detailed structure must be very complicated, that you can't apply hand methods ...

## RE: How to apply shear load and moment on thin-walled cylinder FEM

Greg Locock

## RE: How to apply shear load and moment on thin-walled cylinder FEM

## RE: How to apply shear load and moment on thin-walled cylinder FEM

femarie

## RE: How to apply shear load and moment on thin-walled cylinder FEM

## RE: How to apply shear load and moment on thin-walled cylinder FEM

For example, you have a beam axial load, Fx, an applied shear load, Vy, and an applied beam moment Mz. The x-axis is down the length of the cylinder. The equivalent running load, Nx = Fx/(2Pi*R)- Mz*sin(theta)/(Pi*R^2), where R is the radius and t is the thickness. The shear running load, Nxtheta = Vycos(theta)/(Pi*R). The forces can be determined by Fx = Nx*dl = Nx*R*theta*dtheta and Fxtheta = Nxtheta*dl = Nxtheta*R*theta*dtheta. The Y and Z components can then be determined from Fxtheta by mulitplying by Rsin(theta) or Rcos(theta).

Therefore, instead of applying point loads and moments at a center nodes and using RBE2 elements to spider out the loads around the circumference of the cylinder, I have calculated the equivalent nodal forces around the circumference of the cylinder. It should be OK to apply an axial load, Fx, using the RBE3 method, but applying the shear load and moment using the RBE3 method will not give the correct stresses in cylinder as those predicted by beam theory.

Thanks all to those who replied to my question.

## RE: How to apply shear load and moment on thin-walled cylinder FEM

## RE: How to apply shear load and moment on thin-walled cylinder FEM

## RE: How to apply shear load and moment on thin-walled cylinder FEM

Although very tricky to set could bring to a better load distribution.

Onda

## RE: How to apply shear load and moment on thin-walled cylinder FEM

## RE: How to apply shear load and moment on thin-walled cylinder FEM

in any case, wouldn't the RBE3 web detect the different stiffness at the mid-side, and proportion the load correctly ?

## RE: How to apply shear load and moment on thin-walled cylinder FEM

An RBE3 element cannot detect stiffness at a node, as this is a function of the overall model stiffness, an unknown before the model is solved.

Consider a face of a twenty noded brick (with 90 degree corners and straight sides - no curvature) , then for a uniform pressure the equivalent nodal forces are as follows:-

At each mid-side node one third of the total load is applied (in the direction of the applied force).

At each corner node one twelfth of the total load is applied in the opposite direction.

This pattern of loading is determined entirely by the element formulation, of which a RBE3 element would know nothing.

## RE: How to apply shear load and moment on thin-walled cylinder FEM

In this case You could apply the shear load with a RBE3 with a weight function of the location.

## RE: How to apply shear load and moment on thin-walled cylinder FEM

of couse, you could mesh with CQUAD4s ... but where'e the fun in that ;)

## RE: How to apply shear load and moment on thin-walled cylinder FEM

## RE: How to apply shear load and moment on thin-walled cylinder FEM

This is somewhat equivalent to an impedance matching problem.

Greg Locock

## RE: How to apply shear load and moment on thin-walled cylinder FEM

The statically equivalent loading method was the best overall in comparsion with beam theory results. The results show that the RBE3 method for applying the loads is very good for applying axial forces and moments, but does poorly for applied shear forces. For shear forces, the results show that the RBE3 elements produce a rigid-body like(sliding) motion with a corresponding high Ny force at the top of the cylinder. The results also show that RBE2 method for applying loads is good for shear forces, but introduces high Ny forces at the load application point for applied axial forces and moments.