Thick Plate Under Pressure

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

	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’.

(x3.25)2+(y2.75)2=1(1)

$$\begin{array}{}\text{(1)}& (\frac{x}{3.25}{)}^2+(\frac{y}{2.75}{)}^2=1\end{array}$$

 

(x2)2+y2=1(2)

$$\begin{array}{}\text{(2)}& (\frac{x}{2}{)}^2+y^2=1\end{array}$$

 

The gradient of edge BC is defined via equation (1)

$\text{(1)}$

 and for the edge AD via equation (2)

$\text{(2)}$

.

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

Simulation Setup

Material:

• isotropic: E = 210 GPa, ν
  $\nu$

   

  = 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 σYY

${\sigma }_{YY}$

 at point D obtained with SimScale and the results presented in [NAFEMS].

Comparison of σYY

${\sigma }_{YY}$

 

 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

Last updated: January 29th, 2019

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