Henrik Sönnerlind
COMSOL Employee
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Posted:
1 year ago
Aug 17, 2023, 6:57 a.m. EDT
Here is one possible approach:
In the General Form PDE interface, set the frame to Material.
Then, you add Moving Mesh with Prescribed Deformation to the domain, and enter (u,v,w) as the deformation vector.
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Henrik Sönnerlind
COMSOL
Here is one possible approach:
In the General Form PDE interface, set the frame to *Material*.
Then, you add *Moving Mesh* with *Prescribed Deformation* to the domain, and enter (u,v,w) as the deformation vector.
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Posted:
12 months ago
Aug 25, 2023, 12:12 a.m. EDT
Updated:
12 months ago
Aug 25, 2023, 11:00 a.m. EDT
Here is one possible approach:
In the General Form PDE interface, set the frame to Material.
Then, you add Moving Mesh with Prescribed Deformation to the domain, and enter (u,v,w) as the deformation vector.
I appreciate your insightful answer. I have an additional inquiry. I'm curious about the scenario where a Solid Mechanics Interface coupled with General Form PDE for a time-dependent analysis, i.e. both two studies are added into the same component and the dependent variables of these two physics are coupld in some ways. In each computational step, the Solid Mechanics interface calculates the deformed structure as well as the deformation gradient that links the material and spatial frames. My question is, as these calculations progress, does the spatial frame x, y, z for the General Form PDE also undergo iterative updates according to the spatial frame of Solid Mechanics? Furthermore, are these evolving spatial coordinates employed for calculating spatial derivatives within the General Form PDE? I hope COMSOL can automatically handle it.
Something I would like to add is for the coupling between Solid Mechanics and Electrostatics interface, in the Equation View of Charge Conservation, we can see a clear definition of electric fields as follows:
From material frame,
es.EX = -VX
es.EY = -VY
es.EZ = -VZ
Transform to spatial frame,
es.Ex = spatial.invF11 es.EX+spatial.invF12 es.EY+spatial.invF13 es.EZ
es.Ey = spatial.invF21 es.EX+spatial.invF22 es.EY+spatial.invF23 es.EZ
es.Ez = spatial.invF31 es.EX+spatial.invF32 es.EY+spatial.invF33 es.EZ
I'm curious if, in the Discretization method of the General Form PDE, the selection of the Spatial frame implies an implicit transformation from material to spatial frame?
>Here is one possible approach:
>
>In the General Form PDE interface, set the frame to *Material*.
>
>Then, you add *Moving Mesh* with *Prescribed Deformation* to the domain, and enter (u,v,w) as the deformation vector.
I appreciate your insightful answer. I have an additional inquiry. I'm curious about the scenario where a *Solid Mechanics* Interface coupled with *General Form PDE* for a time-dependent analysis, i.e. both two studies are added into the same component and the dependent variables of these two physics are coupld in some ways. In each computational step, the *Solid Mechanics* interface calculates the deformed structure as well as the deformation gradient that links the material and spatial frames. My question is, as these calculations progress, does the spatial frame x, y, z for the *General Form PDE* also undergo iterative updates according to the spatial frame of *Solid Mechanics*? Furthermore, are these evolving spatial coordinates employed for calculating spatial derivatives within the *General Form PDE*? I hope COMSOL can automatically handle it.
Something I would like to add is for the coupling between *Solid Mechanics* and *Electrostatics* interface, in the *Equation View* of *Charge Conservation*, we can see a clear definition of electric fields as follows:
From material frame,
es.EX = -VX
es.EY = -VY
es.EZ = -VZ
Transform to spatial frame,
es.Ex = spatial.invF11 es.EX+spatial.invF12 es.EY+spatial.invF13 es.EZ
es.Ey = spatial.invF21 es.EX+spatial.invF22 es.EY+spatial.invF23 es.EZ
es.Ez = spatial.invF31 es.EX+spatial.invF32 es.EY+spatial.invF33 es.EZ
I'm curious if, in the *Discretization* method of the *General Form PDE*, the selection of the *Spatial* frame implies an implicit transformation from material to spatial frame?
Henrik Sönnerlind
COMSOL Employee
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Posted:
12 months ago
Aug 28, 2023, 2:34 a.m. EDT
If you use Spatial Frame in the General Form PDE, then the equations are interpreted in the current spatial frame, as given by the deformations from Solid Mechanics.
What you see in the equations for electrostatics is a slightly different case: Equations formulated on material frame, with results variables converted to spatial frame. Note that there is a setting in Charge Conservation (Solid/Nonsolid) which determines whether the equations are formulated on material or spatial frame.
-------------------
Henrik Sönnerlind
COMSOL
If you use Spatial Frame in the General Form PDE, then the equations are interpreted in the current spatial frame, as given by the deformations from Solid Mechanics.
What you see in the equations for electrostatics is a slightly different case: Equations formulated on material frame, with results variables converted to spatial frame. Note that there is a setting in *Charge Conservation* (Solid/Nonsolid) which determines whether the equations are formulated on material or spatial frame.
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Posted:
12 months ago
Aug 28, 2023, 7:22 p.m. EDT
Updated:
12 months ago
Aug 28, 2023, 7:20 p.m. EDT
If you use Spatial Frame in the General Form PDE, then the equations are interpreted in the current spatial frame, as given by the deformations from Solid Mechanics.
What you see in the equations for electrostatics is a slightly different case: Equations formulated on material frame, with results variables converted to spatial frame. Note that there is a setting in Charge Conservation (Solid/Nonsolid) which determines whether the equations are formulated on material or spatial frame.
Thank you for the detailed explanation! Your insights about the different frame choices and their implications in these fields are really helpful. I appreciate your response.
>If you use Spatial Frame in the General Form PDE, then the equations are interpreted in the current spatial frame, as given by the deformations from Solid Mechanics.
>
>What you see in the equations for electrostatics is a slightly different case: Equations formulated on material frame, with results variables converted to spatial frame. Note that there is a setting in *Charge Conservation* (Solid/Nonsolid) which determines whether the equations are formulated on material or spatial frame.
Thank you for the detailed explanation! Your insights about the different frame choices and their implications in these fields are really helpful. I appreciate your response.