Fill out the form to download

Required field
Required field
Not a valid email address
Required field
Required field
  • Set up your own cloud-native simulation in minutes.

  • Documentation

    Validation Case: Cantilever Beam With Off-Center Masses – NAFEMS Test FV4

    This validation case belongs to solid mechanics, with the case of a circular cantilever beam with two off-center point masses connected at the free end. The test case aims to validate the following parameters:

    • Point Mass boundary condition

    The simulation results of SimScale were compared to the reference results presented in [NAFEMS]\(^1\)


    The geometry used for the case is as follows:

    cantilever beam geometry
    Figure 1: Geometry model of the cantilever beam

    It consists of a straight beam of length 10 \(m\) and a circular, constant cross-section of radius 0.5 \(m\).

    Analysis Type and Mesh

    Tool Type: Code_aster

    Analysis Type: Frequency Analysis

    Mesh and Element Types:

    The tetrahedral meshes were computed using SimScale’s standard mesh algorithm and manual sizing. The following table shows an overview of the mesh characteristics:

    CaseMesh TypeNumber of NodesElement Type
    AStandard32 6631st order tetrahedral
    BStandard118 6961st order tetrahedral
    CStandard240 7572nd order tetrahedral
    Table 1: Number of mesh nodes and types of elements for each case.
    cantilever beam mesh
    Figure 2: Tetrahedral mesh for the beam, in this case corresponding to case C

    Simulation Setup


    • Linar Elastic Isotropic
      • \(E\) = 200 \(GPa\)
      • \(\nu\) = 0.3
      • \(\rho\) = 8000 \(kg/m^3\)

    Boundary Conditions:

    • Point Mass:
      • 1000 \(kg\) connected to face B at a distance of 2 \(m\)
      • 10000 \(kg\) connected to face B at a disance of 2 \(m\)
    simscale validation two off-center point masses boundary conditions
    Figure 3: Boundary conditions and remote point mass locations

    Reference Solution

    The reference solution presented in [NAFEMS]\(^1\) is of the numerical type. It is presented as the first six natural oscillation frequencies of the cantilever beam with the connected remote point mass. The values are presented in Table 2 alongside the comparison with SimScale results.

    Results Comparison

    Comparison of the first six natural frequencies for the run cases with the reference solution:

    ModeNAFEMSCase A
    Case B
    Case C
    Table 2. Natural frequencies ( \(Hz\) ) results comparison

    Following are the deformed shape plots for each mode, as taken from case C:

    simscale validation remote mass mode shape 1
    Figure 4: Mode shape 1, 1.767 \(Hz\) , simple bending in the XY plane
    simscale validation off-center point mass mode shape 2
    Figure 5: Mode shape 2, 1.771 \(Hz\) , simple bending in the XZ plane
    simscale validation remote mass mode shape 3
    Figure 6: Mode shape 3, 7.539 \(Hz\) , bending in the XZ plane, plus torsion
    simscale validation off-center point mass mode shape 4
    Figure 7: Mode shape 4, 10.186 \(Hz\) , double bending in the XY plane
    simscale validation off-center point mass mode shape 5
    Figure 8: Mode shape 5, 18.524 \(Hz\) , double bending in the XZ plane and torsion
    simscale validation remote mass mode shape 6
    Figure 9: Mode shape 6, 27.302 \(Hz\), double bending in the XY plane, plus torsion


    • NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks”, October 1990.

    Last updated: December 6th, 2021