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Boundary problem deformation in structural mechanics
Posted 2009年12月4日 GMT-5 02:27 3 Replies
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Hello,
i have some problems to simulate the thermal expansion of a hollow sphere. i would like to simulate the thermal expansion (deformation) of a heated (500 K) hollow sphere in 3D. My problem is how can i simulate the increased inner radius of the sphere. I would like to simulate the "new" radius measured from the centre of the shpere. i have no idea to set a boundary like fixed on the centre of the sphere because there is no material. So it is difficult for me to set the boundary conditions correctly. i would like to simulate the fraction of the inner radius of the hollow sphere to the new inner radius at higher temperature. Thank you for any help of this problem.
best regards,
stephan
i have some problems to simulate the thermal expansion of a hollow sphere. i would like to simulate the thermal expansion (deformation) of a heated (500 K) hollow sphere in 3D. My problem is how can i simulate the increased inner radius of the sphere. I would like to simulate the "new" radius measured from the centre of the shpere. i have no idea to set a boundary like fixed on the centre of the sphere because there is no material. So it is difficult for me to set the boundary conditions correctly. i would like to simulate the fraction of the inner radius of the hollow sphere to the new inner radius at higher temperature. Thank you for any help of this problem.
best regards,
stephan
3 Replies Last Post 2009年12月21日 GMT-5 08:51
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Posted:
1 decade ago
Hi
I believe you have several ways to get there, and I would propose that you check at least two to be sure its correct.
1) why not by brute force make an 3D hollow sphere shell, set a 500°C temperature change in the subdomain properties and select the full inner surface of area "Area" calculated by hand or via an boundary integration and estimate the postprocessing boundary integration of int(sqrt(u^2+v^2+w^2)/Area, dx,dy,dz), this is the average radial expansion, and you average out any first order non-uniform meshing that might displace the centre of the sphere (as its not supported) note: r=sqrt(x^2+y^2+z^2) and delta_r=sqrt(u^2+v^2+w^2), or int(delta_r^2,dx,dy,dz)/Area over the inner surface is the rms deformation of your shell
2) you use 3 symmetry conditions to calculate only a 1/8 of a sphere shell, this would force the shell to expand symmetrically from"0,0,0" ad allow for finer mesh for the same RAM and time calculation.
3) or you say this is really a 1D problem in spherical coordinates and you "simply" reformulate your physics and solve it as a 1D problem (check the knowledge base for the spherical symmetry transformation)
up to you, have fun
Ivar
I believe you have several ways to get there, and I would propose that you check at least two to be sure its correct.
1) why not by brute force make an 3D hollow sphere shell, set a 500°C temperature change in the subdomain properties and select the full inner surface of area "Area" calculated by hand or via an boundary integration and estimate the postprocessing boundary integration of int(sqrt(u^2+v^2+w^2)/Area, dx,dy,dz), this is the average radial expansion, and you average out any first order non-uniform meshing that might displace the centre of the sphere (as its not supported) note: r=sqrt(x^2+y^2+z^2) and delta_r=sqrt(u^2+v^2+w^2), or int(delta_r^2,dx,dy,dz)/Area over the inner surface is the rms deformation of your shell
2) you use 3 symmetry conditions to calculate only a 1/8 of a sphere shell, this would force the shell to expand symmetrically from"0,0,0" ad allow for finer mesh for the same RAM and time calculation.
3) or you say this is really a 1D problem in spherical coordinates and you "simply" reformulate your physics and solve it as a 1D problem (check the knowledge base for the spherical symmetry transformation)
up to you, have fun
Ivar
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Posted:
1 decade ago
Hi Ivar,
thanks a lot for your help. I hope i can use your ways to get a solution. But my geometry is not such a hollow sphere but rather a half open hollow sphere. Do you think it is possible to use some of your ideas anyway? And i need the the solution/modelling implicitly in 3d. enclosed i have attached a picture of the geometry i think it helps you.
thanks a lot for your time and help
stephan
thanks a lot for your help. I hope i can use your ways to get a solution. But my geometry is not such a hollow sphere but rather a half open hollow sphere. Do you think it is possible to use some of your ideas anyway? And i need the the solution/modelling implicitly in 3d. enclosed i have attached a picture of the geometry i think it helps you.
thanks a lot for your time and help
stephan
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Posted:
1 decade ago
Hi Stephan
Your geometry is really nice and symmetrical, so why not use just one quandrant, or even a smaller part, you gain in nodes and elements hence calculation speed.This implies that the oterh BC (boudary conditions are symmetric).
One caveate with symmetry is modal structural analysis, as you will have to consider symmetric and anti-symmetric BC, and you must treat thease as separate cases and add the eigenfrequency lists by hand, requireing several simulations and some care to recombine the shapes
So you need to adapt slightly my previous formulas, and I would work in 3D cartesian space, but even you could use 2D axisymmetry (again depends on your loads or other external BC's).
Unfortunately COMSOL has no simple "projection" operator to cut a 3D volume and project directly the shape of its section into the 2D axisymmetric plane, a pity (but COMSOL does have a powerfull 2D axisymmetry "revolve" geometry function, but only this way, IF SOMONE OUT THERE HAS MADE A PROJECTION SCRIPT PLS POST IT to help us others too ;)
in any case the local deformation remains u,v,w so when you integrate this over the area (or its square u^2+v^2+w^2 you get the deformation or dr^2, when normalised over the area its the RMS deformation.
Pls check carefully the units as you must normalise over the area, the implicit integration of the "integration coupling variables", or the "postprocessing integrations" are sometime misleading if their meaning is not crystal clear in your mind
Always check your results against a simple hand calculation
Good luck
Ivar
Your geometry is really nice and symmetrical, so why not use just one quandrant, or even a smaller part, you gain in nodes and elements hence calculation speed.This implies that the oterh BC (boudary conditions are symmetric).
One caveate with symmetry is modal structural analysis, as you will have to consider symmetric and anti-symmetric BC, and you must treat thease as separate cases and add the eigenfrequency lists by hand, requireing several simulations and some care to recombine the shapes
So you need to adapt slightly my previous formulas, and I would work in 3D cartesian space, but even you could use 2D axisymmetry (again depends on your loads or other external BC's).
Unfortunately COMSOL has no simple "projection" operator to cut a 3D volume and project directly the shape of its section into the 2D axisymmetric plane, a pity (but COMSOL does have a powerfull 2D axisymmetry "revolve" geometry function, but only this way, IF SOMONE OUT THERE HAS MADE A PROJECTION SCRIPT PLS POST IT to help us others too ;)
in any case the local deformation remains u,v,w so when you integrate this over the area (or its square u^2+v^2+w^2 you get the deformation or dr^2, when normalised over the area its the RMS deformation.
Pls check carefully the units as you must normalise over the area, the implicit integration of the "integration coupling variables", or the "postprocessing integrations" are sometime misleading if their meaning is not crystal clear in your mind
Always check your results against a simple hand calculation
Good luck
Ivar