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Making an ellipsoid bend
Posted 2014年6月24日 GMT-4 08:03 9 Replies
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I am trying to model the stresses that occur when an amorphous clump (modeled as an ellipsoid) morphs into a sort of mushroom top. In the COMSOL model, I have defined the ellipsoid shape and a Gaussian to apply force mainly to its center, and apply this force as a boundary load with the edges of the ellipsoid fixed. I'm getting roughly the right shape with this method, but I have a distinct shape that I want it to form, and its the COMSOL model doesn't quite match it.
So my issues are, in order of importance:
1) is there a way to get an ellipsoid (or any other shape) to conform to a particular, predefined geometry? For instance, if I have an AutoCad model of what the final shape for the ellipsoid should be, can I force any shape into becoming that shape and see the stresses that it took to get into that shape?
2) if #1 is not possible, is there a way to create some sort of resistance to motion or spring-like internal properties so I don't have to fix edges (such as there are in SolidWorks)? Right now, the edges of the ellipsoid are fixed, and applying a load near them causes them to become sharp and have extremely high force applied there. It would be great to have the entire thing bend without having to keep edges fixed.
3) I'm having issues getting the cross-sections to work properly. Right now, the cross section doesn't show the proper deformation (shown in the 2D plot titled "Stress cross section plot (cut plane 1)") and I have no idea why - it works fine when I change the cut plane to a XY or ZY plane, but XZ doesn't seem to show the proper deformation (banana-like).
Thank you!
So my issues are, in order of importance:
1) is there a way to get an ellipsoid (or any other shape) to conform to a particular, predefined geometry? For instance, if I have an AutoCad model of what the final shape for the ellipsoid should be, can I force any shape into becoming that shape and see the stresses that it took to get into that shape?
2) if #1 is not possible, is there a way to create some sort of resistance to motion or spring-like internal properties so I don't have to fix edges (such as there are in SolidWorks)? Right now, the edges of the ellipsoid are fixed, and applying a load near them causes them to become sharp and have extremely high force applied there. It would be great to have the entire thing bend without having to keep edges fixed.
3) I'm having issues getting the cross-sections to work properly. Right now, the cross section doesn't show the proper deformation (shown in the 2D plot titled "Stress cross section plot (cut plane 1)") and I have no idea why - it works fine when I change the cut plane to a XY or ZY plane, but XZ doesn't seem to show the proper deformation (banana-like).
Thank you!
9 Replies Last Post 2014年6月27日 GMT-4 04:01
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Posted:
1 decade ago
Hi RM,
Instead of a boundary load condition you can apply a fixed displacement boundary condition. That is maybe a start but I guess you do not know beforehand where a point on the original boundary will end up at the final boundary? Only the original and final shape.
Instead of a boundary load condition you can apply a fixed displacement boundary condition. That is maybe a start but I guess you do not know beforehand where a point on the original boundary will end up at the final boundary? Only the original and final shape.
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Posted:
1 decade ago
Hi Pieter,
Thanks for the response, and yes, exactly right - we don't know the x, y, and z displacement, just the final desired shape. I was thinking of somehow extrapolating an equation for the overall shape and plugging that into fixed displacement, but it seems that doesn't work.
Mostly, I'm just wondering if such an option exists in COMSOL to take a shape and squish it into another, predefined shape, and get the stresses required to do that squishing.
Thanks for the response, and yes, exactly right - we don't know the x, y, and z displacement, just the final desired shape. I was thinking of somehow extrapolating an equation for the overall shape and plugging that into fixed displacement, but it seems that doesn't work.
Mostly, I'm just wondering if such an option exists in COMSOL to take a shape and squish it into another, predefined shape, and get the stresses required to do that squishing.
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Posted:
1 decade ago
By the way, does your shape have rotational symmetry before and after deformation? That would make everything a bit more simple.
Anyway, the surface of your final shape is defined, so you have a known relationship between the x-, y- and z-coordinate of any point on your surface. So maybe you can apply a fixed displacement only in for example z-direction that is a function of the x- and y-displacement of that point (and this function would be determined by the relationship mentioned above).
Anyway, the surface of your final shape is defined, so you have a known relationship between the x-, y- and z-coordinate of any point on your surface. So maybe you can apply a fixed displacement only in for example z-direction that is a function of the x- and y-displacement of that point (and this function would be determined by the relationship mentioned above).
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Posted:
1 decade ago
Yes, it actually does have rotational symmetry - it essentially looks like a bowl with really fat walls. The issue I had was that the equation describing the shape would (ideally) be for the entire entire surface the shape, and would thus include deformation at the edges and on the top and bottom of the bowl. Is it possible to apply an equation-varying fixed displacement to an entire body that way?
I've attached my flawed COMSOL model here, in case that helps with visualization.
I've attached my flawed COMSOL model here, in case that helps with visualization.
Attachments:
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Posted:
1 decade ago
That looks interesting. But it does not have the rotational symmetry that I had in mind, so I think you can forget about that part. You could however simulate only one quarter of your geometry and apply two symmetry boundary conditions. Saves you some computational power and it is also easier later on (see below).
So you basically have two surfaces: one that is initially flat and one that is initialy half of an ellipsioid. The shape of these two surfaces is prescribed completely for the end product? And does the edge between these two surfaces have to stay in the same place?
So if for the initially flat surface the final shape is described by w=f(x,y) and for the other surface you can write a function u=g(z,y). If you know these functions you can put a prescribed displacement in the z-direction equal to f(x+u,y+v) for the initially flat surface. For the other surface (if you have used symmetry, otherwise you will have to cut it in half and treat the two halves separately) you can put a prescribed displacement in the x-direction equal to g(z+w,y+v). I think. Let me know what you think/if it works.
So you basically have two surfaces: one that is initially flat and one that is initialy half of an ellipsioid. The shape of these two surfaces is prescribed completely for the end product? And does the edge between these two surfaces have to stay in the same place?
So if for the initially flat surface the final shape is described by w=f(x,y) and for the other surface you can write a function u=g(z,y). If you know these functions you can put a prescribed displacement in the z-direction equal to f(x+u,y+v) for the initially flat surface. For the other surface (if you have used symmetry, otherwise you will have to cut it in half and treat the two halves separately) you can put a prescribed displacement in the x-direction equal to g(z+w,y+v). I think. Let me know what you think/if it works.
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Posted:
1 decade ago
Ya, so I changed the model in two ways that made me much happier with it: (1) added a spring foundation across the entire body instead of having a fixed constraint along the edge that caused singularities, and (2) adding two prescribed displacements, one on the top surface and one on the bottom. The prescribed displacements are defined by analytic global equations. Right now I have them as Gaussians, but I think they could be extrapolated from any surface (if you divide the surface into a top and bottom) and used to get the right displacement. I found it was easier to control the shape of the whole object by using two surface prescribed displacements rather than one body prescribed displacement. I've attached the improved model here.
The only thing that's a major issue now is the cross section (along an XZ plane) that doesn't deform with the actual body in the results 2D surface. If anyone has any idea what's up with that, I'd much appreciate it!
Thanks Pieter for all your help, I really appreciate it!!
The only thing that's a major issue now is the cross section (along an XZ plane) that doesn't deform with the actual body in the results 2D surface. If anyone has any idea what's up with that, I'd much appreciate it!
Thanks Pieter for all your help, I really appreciate it!!
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Posted:
1 decade ago
oops, forgot to attach...
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Posted:
1 decade ago
Well, I just hope that when I am stuck with some model one day that someone will help me as well.
The y-component in your cut plane is the z-component in the 3d geometry, so I think that in the deformation node (in your 2d plot) you have to put w instead of v for the y-component. That improves it but it still does not look as in the 3d picture, I don't know why.
The y-component in your cut plane is the z-component in the 3d geometry, so I think that in the deformation node (in your 2d plot) you have to put w instead of v for the y-component. That improves it but it still does not look as in the 3d picture, I don't know why.
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Posted:
1 decade ago
Fun fact - geometric nonlinearity is necessary. If you include that (and make the prescribed displacement along the body rather than on surfaces) it works out beautifully. Results are a little different in cross-section, but much smoother and what we expect.