case.sif

! A reference case where a cantilever is subject to a constant pressure load f.
!
! For parameters EI/(GA) = eps we expect the deflection and the rotation at the 
! free end to be w(L) = L^4 f (1 + 4 eps)/(8 EI) and theta(L) = L^3 f/(6 EI).
! Here the SaveScalars module is set to output the variable values at the end. 
!
! This modification for eigenmodes
! P.R. 28.8.2023 (initial test case by M.M.)

Check Keywords "Warn"

Header
  Mesh DB "." "beam1d"
  Results Directory "results"
End

Simulation
  Max Output Level = 5
  Coordinate System = Cartesian 3D
  Simulation Type = Steady
  Output Intervals = 1
  Steady State Max Iterations = 1

  Post File = "timoshenko.vtu"
  vtu: Eigen Analysis = Logical True
End
 
Body 1
  Equation = 1 
  Material = 1
End

Material 1
 Youngs Modulus = Real 2.0e-1
 Shear Modulus = Real 1.0
 ! Youngs Modulus = Real 70.0e+9
 ! Shear Modulus = Real 26.0e+9

 ! Specify basis where the cross section parameters are expressed: 
 Principal Direction 2(3) = Real 0.0 0.0 -1.0

 ! Specify I_k:
 Second Moment of Area 2 = Real 1.0
 Second Moment of Area 3 = Real 1.0
 ! Specify A:
 Cross Section Area = Real 1.0
 ! Specify J_T:
 Torsional Constant = Real 1.0
 ! The density is used only in transient cases:
 Density = 2700.0
End


Equation 1 :: Active Solvers(1) = 1

Solver 1
  Equation = "Timoshenko Beam Equations"
  Procedure = "BeamSolver3D" "TimoshenkoSolver"

  Nonlinear System Max Iterations = 1

  Linear System Scaling = False
  Linear System Solver = "Direct"
  Linear System Direct Method = "umfpack"

  Eigen Analysis = True
  Eigen System Values = 12
  Eigen System Convergence Tolerance = Real 1.0e-6
End

! -------------------------------------------------------------------------
! The following can be used to save the deflection and the rotation
! at the end:
! -------------------------------------------------------------------------
Solver 2
  Equation = "Save Scalars"

  Procedure = "SaveData" "SaveScalars"
  Filename = eigen.dat
  Save Eigenvalues = True

! Show the 1st eigenvalue as the reference norm
  Show Norm Index = 1
End

Boundary Condition 1
  Target Nodes(1) = 1
  U 1 = Real 0.0
  U 2 = Real 0.0
  U 3 = Real 0.0
  Theta 1 = Real 0.0
  Theta 2 = Real 0.0
  Theta 3 = Real 0.0
End

Solver 2 :: Reference Norm = 1.50048419E-04
Solver 2 :: Reference Norm Tolerance = 1.0e-5