Minimal support - 2D Axisymmetric Model 3

[sdra2]

Hi

I have some experience in applying 3-2-1 supports for 3D FEA models to remove rigid body motion in analyses, and am trying to replicate the idea for a 2D axisymmetric model.

I have geometry in the +x, +y quadrant of the XY plane. Within the model I have constrained 2 points along a line that is parallel to the y-axis (the axis of revolution). The first point removes translations in x and y, whereas the 2nd point removes translation in x, to prevent rotation about the z-axis.

I was expecting there to be no reaction to these constraints when the part is loaded. This is true of the y direction, but not of the x direction, where I am getting significant reaction forces at both constrained points. My model has (balanced) loads in the y direction only. There are not significant moment reactions.

What am I missing? Is my method wrong for axisymmetric models, or maybe even wrong completely for a 2D model??

Any pointers would be greatly appreciated! Thanks.

 

[EdR]

You do not need constraints in the x direction....If the axis of rotation is the y-axis then you are generating a solid which is implicitly constrained in the x direction by the fact that it is a solid....Any added constraints in the x direction imply a lack of movement of the solid in the radial direction.....

Ed.R.

 

[rb1957]

are you modelling a 2D model in 3D space ?

you've modelled a portion of an axisymmetric part ... btw i don't think of a quadrant as axisymmetric, i would call by doubly symmetric (axisymmetric describes something like a rocket (a cyclinder). i don't think you've got the boundary conditions right ... you've modelled a quadrant of a disc, the edges of the quadrant cannot move away from the edge, but they can move along the edge and out-of-plane; similarly there can be no rotation about some axes ... picture the motion of the common line from both sides, some motions are disallowed bacuse the adjacent quadrants move in opposite directions, some are allowed cuase they move consistently.

 

[GBor]

sdra2,

Can you upload a picture of your file? What software are you using (a few that I know of require 2-D models to be in the Y-Z plane, others require that you specify your axis of symmetry).

 

[corus]

In axisymmetric geometry you only need one restraint to prevent rigid body motion, and that is in the axial direction, ie. the Z direction for R-Z geometry. Forget about X and Y but think of R and Z, Radial and Axial.

corus

 

[sdra2]

Thanks for all of the replies.

EdR / corus - I have realistic restraints now.

rb1957 - it's not a 3D model that has been "quartered" - my plane section to be rotated lives in the top right quadrant of the XY plane, with rotation about the y-axis defining the axisymmetry.

GBor - I am using Ansys Workbench which requires 2D models to be in the XY plane, and axisymmetric models are rotated about the y-axis by default.

Would the restraints that I used previously have been correct for a plane stress model in 2D? It is extremely rare that I have models that can be represented as 2D equivalents, and should I be fortunate enough to be able to do so again, it would be nice to search the forums and find my own post (my memory isn't great!).

 

[johnhors]

"Would the restraints that I used previously have been correct for a plane stress model in 2D?" Yes

The minimum number of supports = the number of degrees of freedom that an object is allowed by your modelling domain.

Hence in 3D , where an object has 3 translations plus 3 rotations = 6 degrees of freedom , your 3-2-1 support conditions give 3 + 2 + 1 = 6

In 2D for plane stress/strain , an object can translate in the X and Y directions and rotate about the Z axis = 3 degrees of freedom, you use a 2-1 support condition, one point is fixed in X and Y the second point if it is a X shift from point 1 is fixed in Y or fixed in X if it is a Y shift from the first point (as you did)


2D axisymmetric models are a special case as Corus pointed out.


Planes of symmetry will also reduce the number of minimum supports necessary:-

One plane of symmetry applied to a 3D model - an object can translate in two orthogonal directions within the plane and rotate about an axis normal to the plane. Thus a 2-1 minimal support is used (similar to the 2D plane stress/strain model)

Two planes of symmetry applied to a 3D model - now the object can only translate in one direction (parallel to the line formed by the intersection of the two planes) and only a single support in this one direction is necessary.

Three planes of symmetry applied to a 3D model - no supports are necessary, the object has no freedoms left.

One plane of symmetry applied to a 2D model - an object can only translate in one direction (parallel to the plane) and thus requires a single support in this direction.

Two planes of symmetry applied to a 2D model - as with three planes in a 3D model there are no remaining freedoms left.

 

[rb1957]

maybe i'm wrong on this (wouldn't be the 1st time, won't be the last either), i appreciate that a model that is axisymmetric can be represented by a piece of the model but i'd've thought that the constraints would be more than the minimum 6 dofs (ie redundant) ... in order for the model to react the whole body.

say you're modelling a 1/2 panel (1 axis of symmetry). i would constrain the model everywhere along the symmetry in the in-plane normal to the symmetry ... way more constraints than simple rigid body. i would constrain 1 node in the other in-plane direction for rigid body reasons. of course there are a bunch more constriants (out-of-plane, rotations), but i'm using the in-plane normal direction as an example of redundant constraints to account for symmetry.

 

[GBor]

rb,

Using symmetry to simplify your model, your boundary conditions are correct and reasonable. However, using axi-symmetry, those constraints are built in to the constuitive equations and are unnecessary. In fact, unless your axisymmetric model extends all the way to the axis of axisymmetry, you are overconstraining the model.

For instance, a doughnut with a y-axis of symmetry would be modeled as a circle in the x-y plane along the positive x-axis, but you wouldn't have any nodes on the axis of symmetry to constrain. If that same model were centered on the x-axis as well, you could model it as a semi-circle and constrain the line of nodes on the x-axis so that they didn't move in the y-direction.

In the first case (pure axi-symmetry), the doughnut would need constraints depending on the loading, but it would be allowed to expand (say this is a thermal model) away from the axis of anti-symmetry and the diameter would get bigger (if we're adding heat), but this expansion would still be symmetric about the centerline of the doughnut, so we can simplify the model further by removing the symmetric portion (the lower or upper half) and adding boundary conditions to represent that motion. You could not, however, remove the left or right side because the vertical centerline of the doughnut will move away from the axis of axi-symmetry.

I imagine this is 'clear as muddy water'...

 

[rb1957]

but then you have to tell the FE code that this is an axi-symmetric model ? and if you do that, won't it set up the constraints automatically ?

so then what's the post about ? trying to manually constrain an axisymmetric model ? so then you'd have to implement all the required constraints, no ?

alice clark ?

 

[GBor]

In my "doughnut" example, you still have to stop it from infinitely sliding up the y-axis or spinning about the z-axis. With enough load, you could also potentially expand infinitely in the x direction, so you may need some additional constraints there as well.

There is nothing analytically invalid about stretching infinitely away from the origin of your axi-symmetry, nothing about hurling infinitely into space alond the axis of axi-symmetry...would have to look closer to see about spinning infinitely around the out-of-plane axis, but my little mental exercise tells me it is OK...

I think these are the constraints that are being discussed, but you do make a point regarding having to "tell the FE code that this is an axi-symmetric model". It is difficult to determine if that was done correctly in this case.

 

[sdra2]

In the software I am using, you have a choice of 2D or 3D as 'analysis type', and then you can specify which behaviour the software should use for the model for a 2D environment (plane stress, axisymmetric, etc). It is also imperative to model on the +x axis of the XY plane, with the y-axis being the axis of axisymmetry/revolution by default.

Thanks again for all of your help guys.