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# 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]$$^1$$

## Geometry

The geometry used for the case is as follows:

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:

## Simulation Setup

Material:

• 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 $$m$$

## 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:

Following are the deformed shape plots for each mode, as taken from case C: Figure 4: Mode shape 1, 1.767 $$Hz$$ , simple bending in the XY plane Figure 5: Mode shape 2, 1.771 $$Hz$$ , simple bending in the XZ plane Figure 6: Mode shape 3, 7.539 $$Hz$$ , bending in the XZ plane, plus torsion Figure 7: Mode shape 4, 10.186 $$Hz$$ , double bending in the XY plane Figure 8: Mode shape 5, 18.524 $$Hz$$ , double bending in the XZ plane and torsion Figure 9: Mode shape 6, 27.302 $$Hz$$, double bending in the XY plane, plus torsion

References

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

Last updated: December 6th, 2021