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]\(^1\).

Geometry

Find below the plate geometry used for this validation case:

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

The node coordinates are tabulated below:

	A	B	C	D	E	A’	B’	C’	D’
x	0	0.35	0.35	0	0.1575	0	0.35	0.35	0
y	0	0	0.25	0.25	0.125	0	0	0.25	0.25
z	0	0	0	0	0	0.01	0.01	0.01	0.01

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.

Case	Mesh Type	Number of Nodes	Element Type
(A)	1st order hexahedral	1764	Standard
(B)	1st order standard	16870	Standard

Find below the mesh used for case A.

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

Simulation Setup

Material:

• 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].

Case	Parameter	[SDLV124]	SimScale	Error (%)
(A)	Displacement magnitude DX [\(m\)]	9.0386e-7	9.0529e-7	0.16
(B)	Displacement magnitude DX [\(m\)]	9.0386e-7	8.2366e-7	-8.87

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

Last updated: July 1st, 2020