## Boundary Conditions assignment fails on few boundaries

Numerical methods and mathematical models of Elmer
CrocoDuck
Posts: 64
Joined: 12 May 2016, 13:15
Antispam: Yes

### Boundary Conditions assignment fails on few boundaries

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. 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: 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
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

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

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: 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

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: 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!