| Author | Message | |||
     Patricio A. Greco (pagreco) Member Username: pagreco Post Number: 13 Registered: 08-2003 |
IŽm studing the example 3d_bimetal. For great deformations of the problem domain we must to redefine the mesh to get an exact solution . I would like to know how how to tell to the program that modify the mesh (with a defined law) in each iteration. I think that it is impossible there are a great problem beacuse the solution is only valid for small deformations. The program can represent the deformed domain, but I would like to define the domain using the extrusion method and then apply an arbitrary deformation before solve the problem. | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 89 Registered: 06-2003 |
FlexPDE is not at present able to move the mesh automatically. We have done preliminary work on a moving mesh version, and will turn our attention to completing that work as soon as version 4 is stable. In the meantime there are a few things you might try. It should be possible to define a coordinate transformation using a precomputed displacement to get modifications to the PDE's for larger displacements. You could then either pass these values from one run to the next through a TRANSFER file, or iterate directly for a stable displacement using SAVE() on the current displacement values. Alternatively, you could use TRANSFERMESH(x+u,y+v) to export the current mesh data and the deformed data. Then using a text editor or a special program, strip the mesh data and leave the deformed data as mesh coordinates. Use TRANSFERMESH again to pull this mesh into a second FlexPDE run. (Using version 3, this will only work in 2D, since TRANSFERMESH is not implemented in 3D. Version 4 could do it in 3D.) | |||
| Patricio A. Greco (pagreco) Member Username: pagreco Post Number: 14 Registered: 08-2003 |
Robert: The coordenate transformation es a good idea, IŽll try to implement it , and then IŽll comment. A last question regarding TRANSFERMESH function is if can I import an arbitrary mesh to the program version 4. Thank You | |||
| Gilson Gitirana Jr (ggitirana) Junior Member Username: ggitirana Post Number: 3 Registered: 11-2003 |
Have you considered using an eulerian approach (also know as large deformation formulation) for deriving the pde's governing your problem? The pde's would become nonlinear (not on the properties), but I guess FlexPDE should be able to handle them. | |||
| Wahbi JOMAA (jomaa) New member Username: jomaa Post Number: 1 Registered: 02-2004 |
I tried the idea posted by Robert G. Nelson about using "TRANSFERMESH(x+u,y+v)", but the problem is when i will use TRANSFERMESH again to pull this mesh into a second FlexPDE run i have to define boundaies and i can not define exactly the new bounadaries. Do you have an idea to define bounadary conditions on the deformed boundaries obtained from the first run. Thank you in advance | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 103 Registered: 06-2003 |
Oops. My mistake. Of course, FlexPDE requires that the boundary specifications match the TRANSFERMESH, so my second suggestion won't work. This leaves the transformation approach (Gitirana's large deformation formulation) as the only alternative. Sorry. | |||
| Jerry Brown (jerrybrown11743) New member Username: jerrybrown11743 Post Number: 2 Registered: 03-2004 |
Further to Gitirana's advice: For deformations that are too large for classical elasticity theory, I recommend that you look for Novoshilov's "Foundations of the Nonlinear Theory of Elasticity". He provides a nice development of the principles of finite deformation theory without using tensors. I have done a little bit of work with FlexPDE using Novoshilov's equations and got solutions that looked reasonable. The book is out of print. But, you can sometimes find used copies available at Alibris ( www.alibris.com/ ) and Amazon. | |||
| Robert White (bobzzwhite) New member Username: bobzzwhite Post Number: 2 Registered: 04-2004 |
I am also solving an elasticity problem involving large displacements. I need to transfer the displacements and the mesh from one solution to a new problem. Is there any way to solve the problem mentioned by Wahbi JOMAA. Perhaps one could transfermesh(x,y) and transfer(u,v). And then use the old boundary definitions with the new mesh. Does anyone have an example for using transfermesh? | |||
| Robert White (bobzzwhite) Junior Member Username: bobzzwhite Post Number: 3 Registered: 04-2004 |
As too the book mentioned by Jerry, I believe the authors name is spelled Novozhilov. Bob | |||
| Peter Cendula (cendo) New member Username: cendo Post Number: 1 Registered: 06-2007 |
Hi, how can this large displacement elasticity problem be now solved with moving meshes implemented? I guess that somehow deformation has to be divided into small pieces and the boundary moved exactly by the computed displacements in each time step. Time is only "virtual" here and this screwes me up. Thanks, Peter | |||
| Peter Cendula (cendo) New member Username: cendo Post Number: 2 Registered: 06-2007 |
Ok, here I attach the code for 2D bimetal bending (based on 3d_bimetal from samples). When the thermal strain is large (3%) the timestep soon decreases fatally. When it is smaller(e.g 0.5%) there are no problems with timestep. I think no BC/IC discontinuities are present but maybe the moving mesh is distorted? thanks in advance ;) peter
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 885 Registered: 06-2003 |
I did some work on this kind of problem some time ago and concluded that there is a fundamental ambiguity in moving the mesh based on distortions from an original shape which is no longer stored or referenceable. But I will have to review the problem again to recall exactly what the issue is. I will let you know when I have reconstructed the argument. |
2D Bimetal bending with thermal expansion