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Voluminal Paving Stone Subjected to Harmonic Pressure

This harmonic pressure validation case belongs to solid mechanics. It aims to validate the following parameters:

  • Harmonic analysis
  • Harmonic pressure

The simulation results from SimScale were compared to the numerical results in [SDLV124]\(^1\).


Find below the plate geometry used for this validation case:

voluminal paving stone geometry
Figure 1: Geometry used in the present validation case.

The geometry is a thick rectangular plate made up of steel.

The node coordinates are tabulated below:

Table 1: Geometry dimensions in meters.

The node E will be used to compare the results between SimScale and [SDLV124]\(^1\).

Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Harmonic analysis

Mesh and Element Types: The mesh used for case A was provided by Code Aster. Mesh B is a 1st order mesh created in SimScale with the standard algorithm.

CaseMesh TypeNumber of NodesElement Type
(A)1st order hexahedral1764Standard
(B)1st order standard16870Standard
Table 2: Mesh characteristics.

Find below the mesh used for case A.

hexahedral mesh harmonic analysis
Figure 2: 1st order hexahedral mesh used for case A.

Similarly, for case B, the following mesh is used:

standard mesh harmonic analysis validation
Figure 3: 1st order standard mesh used for case B.

Simulation Setup


  • Steel (linear elastic)
    • \(E\) = 180 \(GPa\), \(v\) = 0.3
    • \(\rho\) = 7800 \(kg/m^3\)
    • Rayleigh damping
      • Alpha coefficient = 3e-5 \(1/s\)
      • Beta damping = 0.001 \(s\)

Boundary Conditions:

  • Constraint:
    • Fixed support on faces AA’B’B, BB’C’C, CC’D’D, and DD’A’A
  • Load:
    • Pressure of 1e5 \(Pa\) applied on face ABCD, with a harmonic frequency of 1500 \(1/s\)

Result Comparison

The results obtained from SimScale for the displacement magnitude DX at point E were compared to the results presented in [SDLV124].

CaseParameter[SDLV124]SimScaleError (%)
(A)Displacement magnitude DX [\(m\)]9.0386e-79.0529e-70.16
(B)Displacement magnitude DX [\(m\)]9.0386e-78.2366e-7-8.87
Table 3: Comparison of the results for DX on point E.

Inspecting the module of X displacement for case A in the post-processor:

module of displacement harmonic analysis post processing
Figure 4: Case A, showing the contours for the module of X displacement, in meters.

Last updated: July 1st, 2020

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