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  • Documentation

    Validation Case: 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 in this project is a 1st order mesh created in SimScale with the standard algorithm.

    CaseElement TypeNumber of NodesElement Technology
    (A)1st Order Tetrahedral16870Standard
    Table 2: Mesh characteristics

    Find below the mesh used for case A.

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

    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-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: November 29th, 2023