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Thick plate under pressure

Overview

The aim of this test case is to validate the following functions:

  • distributed pressure
  • nodal stresses

The simulation results of SimScale were compared to the numerical results presented in [NAFEMS]. In addition to the meshes described in [NAFEMS], the meshes used in (A) and (B) were set up using an automatically created tetrahedral mesh and a refined hexahedral mesh was used in (G).

Import validation project into workspace

Geometry

ThickPlateUnderPressure-geometry

Geometry of the plate

  A B C D A’ B’ C’ D’
x [m] 0 0 3.25 2 0 0 3.25 2
y [m] 1 2.75 0 0 1 2.75 0 0
z [m] 0.6 0.6 0.6 0.6 0 0 0 0

The point B’’ is located in the middle of edge BB’. The same applies to point C’’ and edge CC’.

\[\begin{equation}\label{edgeBC} (\frac{x}{3.25})^2 + (\frac{y}{2.75})^2 = 1 \end{equation}\]\[\begin{equation}\label{edgeAD} (\frac{x}{2})^2 + y^2 = 1 \end{equation}\]

The gradient of edge BC is defined via equation \(\eqref{edgeBC}\) and for the edge AD via equation \(\eqref{edgeAD}\).

Analysis type and Domain

Tool Type : Code_Aster

Analysis Type : Static (linear elastic)

Mesh and Element types :

Case Mesh type Number of nodes Element type
(A) quadratic tetrahedral 26761 3D isoparametric
(B) quadratic tetrahedral 174707 3D isoparametric
(C) linear hexahedral 36 3D isoparametric
(D) quadratic hexahedral 111 3D isoparametric
(E) linear hexahedral 105 3D isoparametric
(F) quadratic hexahedral 349 3D isoparametric
(G) quadratic hexahedral 52941 3D isoparametric
ThickPlateUnderPressure-mesh-b

Mesh used for the SimScale case (B)

ThickPlateUnderPressure-mesh-f

Mesh used for the SimScale case (F)

Simulation Setup

Material:

  • isotropic: E = 210 GPa, \(\nu\) = 0.3

Constraints:

  • Face DCD’C’ zero y-displacement
  • Face ABA’B’ zero x-displacement
  • Face BCB’C’ x and y displacements fixed
  • z-displacement fixed along the edge B’‘C’‘

Loads:

  • Pressure of 1 MPa on Face ABCD

Results

Comparison of the stress \(\sigma_{YY}\) at point D obtained with SimScale and the results presented in [NAFEMS].

Comparison of \(\sigma_{YY}\) in [MPa] at point D
Case [NAFEMS] SimScale Error (%)
(A) 5.38 5.44473 1.20%
(B) 5.38 5.39614 0.30%
(C) 5.38 3.98345 -25.96%
(D) 5.38 5.47091 1.69%
(E) 5.38 5.10811 -5.05%
(F) 5.38 5.71058 6.14%
(G) 5.38 5.38599 0.11%

References

[NAFEMS](1, 2, 3, 4) (1987)”The Standard NAFEMS Benchmarks”, The international association for the engineering analysis community