Boundary Conditions assignment fails on few boundaries

Numerical methods and mathematical models of Elmer
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CrocoDuck
Posts: 64
Joined: 12 May 2016, 13:15
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Boundary Conditions assignment fails on few boundaries

Post by CrocoDuck »

Hi there, I have been playing a while with this but I cannot get it right.

I am trying to solve for the modes of this plate using the SmitcSolver.

Image

On all the boundaries I wish to have a simply supported boundary condition, that is, I want the displacement in the z axis direction to be 0 along all boundaries. To my understanding this should do it, given that Deflection 1 should be normal (to surface?) displacement:

Code: Select all

Boundary Condition 1
  Target Boundaries(4) = 1 2 3 4 
  Name = "SimplySupported"
  Deflection 1 = 0
End
However, when I look at the Eigenfunctions, the longer edges (the one in red and the other in front of it) are not fixed:

Image

As a consequence, the Eigenfunctions are wrong and Eigenfrequencies larger than 10 kHz are significantly shifted. I have the gut feeling that instead to constrain the displacement along z the displacement along another direction was constrained.

Why is this happening? Is there any way to fix it? (I have prepared the simple geometry with FreeCAD and I meshed it both with Salome and Gmsh having the same results).

Whole sif file:

Code: Select all

Header
  CHECK KEYWORDS Warn
  Mesh DB "." "."
  Include Path ""
  Results Directory ""
End

Simulation
  Max Output Level = 5
  Coordinate System = Cartesian
  Coordinate Mapping(3) = 1 2 3
  Simulation Type = Steady state
  Steady State Max Iterations = 1
  Output Intervals = 1
  Timestepping Method = BDF
  BDF Order = 1
  Solver Input File = case.sif
  Post File = case.vtu
Coordinate Scaling = 0.001
End

Constants
  Gravity(4) = 0 -1 0 9.82
  Stefan Boltzmann = 5.67e-08
  Permittivity of Vacuum = 8.8542e-12
  Boltzmann Constant = 1.3807e-23
  Unit Charge = 1.602e-19
End

Body 1
  Target Bodies(1) = 1
  Name = "Panel"
  Equation = 1
  Material = 2
End

Solver 1
  Equation = Elastic Plates
  Eigen System Values = 10
  Eigen System Select = Smallest magnitude
  Procedure = "Smitc" "SmitcSolver"
  Variable = -dofs 3 Deflection
  Eigen Analysis = True
  Exec Solver = Always
  Stabilize = True
  Bubbles = False
  Lumped Mass Matrix = False
  Optimize Bandwidth = True
  Steady State Convergence Tolerance = 1.0e-5
  Nonlinear System Convergence Tolerance = 1.0e-7
  Nonlinear System Max Iterations = 5000
  Nonlinear System Newton After Iterations = 3
  Nonlinear System Newton After Tolerance = 1.0e-3
  Nonlinear System Relaxation Factor = 1
  Linear System Solver = Direct
  Linear System Direct Method = Umfpack
End

Equation 1
  Name = "DML"
  Active Solvers(1) = 1
End

Material 1
  Name = "Fibre"
  Damping = 4e-2
  Tension = 0.0
  Poisson ratio = 0.3
  Youngs modulus = 1.4e9
  Thickness = 3.25e-3
  Youngs modulus = 1.4e9
  Poisson ratio = 0.3
  Porosity Model = Always saturated
  Density = 265
End

Material 2
  Name = "Aluminium (generic)"
  Electric Conductivity = 37.73e6
  Damping = 4e-4
  Tension = 0.0
  Relative Permeability = 1.000022
  Youngs modulus = 70.0e9
  Heat Conductivity = 237.0
  Electric Conductivity = 37.73e6
  Electric Conductivity = 37.73e6
  Poisson ratio = 0.35
  Youngs modulus = 70.0e9
  Thickness = 8.1e-4
  Heat Capacity = 897.0
  Youngs modulus = 70.0e9
  Relative Permeability = 1.000022
  Sound speed = 5000.0
  Poisson ratio = 0.35
  Heat expansion Coefficient = 23.1e-6
  Poisson ratio = 0.35
  Porosity Model = Always saturated
  Mesh Poisson ratio = 0.35
  Electric Conductivity = 37.73e6
  Density = 2700.0
  Relative Permeability = 1.000022
End

Boundary Condition 1
  Target Boundaries(4) = 1 2 3 4 
  Name = "SimplySupported"
  Deflection 1 = 0
End

CrocoDuck
Posts: 64
Joined: 12 May 2016, 13:15
Antispam: Yes

Re: Boundary Conditions assignment fails on few boundaries

Post by CrocoDuck »

Ok, I think I am misinterpreting what normal displacement means. I assumed it was displacement locally orthogonal to the surface, like pointing in the z direction. Actually, after few more experiments, it appears it is actually displacement orthogonal to the boundary, in the xy plane. I would actually like to constrain the displacement of the boundary along the z direction. Is there any way to do it with SmitcSolver? Maybe I will have to give to the ShellSolver another go...
CrocoDuck
Posts: 64
Joined: 12 May 2016, 13:15
Antispam: Yes

Re: Boundary Conditions assignment fails on few boundaries

Post by CrocoDuck »

Sorry guys, misinterpretation after misinterpretation. After another good read at this I finally understood that Deflection 1,2,3 are respectively the transverse (normal) displacement of the (mid) surface and its derivatives in the x and y directions. I hope I got it right now. As such, the correct vector component to warp the surface should be the first one (Deflection 1, X in ParaView) and the results appear to make more sense now:

Image

Now I am up to investigate the shift of the higher eigenfrequencies from the expected ones. I guess I will try a denser meshing first.
CrocoDuck
Posts: 64
Joined: 12 May 2016, 13:15
Antispam: Yes

Re: Boundary Conditions assignment fails on few boundaries

Post by CrocoDuck »

The shift in the eigenfrequencies was due to the way I was computing the theoretically expected eigenfrequencies. After fixing the problem the agreement between Elmer and theory become rather amazing:

Image

If I am not wrong linear increasing error is exactly what you expect from FEM. I am pleased to see that error in the eigenfrequencies is within 2% all the way up to the end of the audible range (20 kHz). Cool!
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