Cylinder Under Rotational Force

Overview

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

centrifugal force

The simulation results of SimScale were compared to the numerical results presented in [HPLA100]. The mesh used in (A) and (C) was created with the automatic-tetrahedralization-tool on the SimScale platform. The mesh used in (B) und (D) was created locally.

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Geometry

	A	B	C	D
x [m]	0.0195	0.0205	0.0205	0.0195
y [m]	0	0	0	0
z [m]	0.01	0.01	0	0

To obtain the solid body the face ABCD is rotated 45° around the z-axis. Because of the symmetry of the cylinder only one quarter was modelled.

Analysis type and Domain

Tool Type : Code_Aster

Analysis Type : Static

Mesh and Element types :

Case	Mesh type	Number of nodes	Element type
(A)	quadratic tetrahedral	2893	3D isoparametric
(B)	quadratic hexahedral	2583	3D isoparametric
(C)	quadratic tetrahedral	17460	3D isoparametric
(D)	quadratic hexahedral	9285	3D isoparametric

Simulation Setup

Material:

isotropic: E = 200 GPa, $ν$

Constraints:

Face AA’BB’ and face CC’DD’ zero z-displacement
Symmetry boundary condition on face ABCD and A’B’C’D’

Loads:

Centrifugal force with a rotational speed $ω$

Reference Solution

\begin{matrix} (1) & u (r) = \frac{- (1 + ν) (1 - 2 ν)}{(1 - ν) E} ρ ω^{2} \frac{r^{3}}{8} + A r + \frac{B}{r} \end{matrix}

Comparison of the displacement $u_{r}$
Case	Quantity	[HPLA100]	SimScale	Error
(A)	$u_{r} (r = 0.0195 m)$ $u_{r} (r = 0.0195 m)$ [m]	2.9424E-013	2.83491E-013	3.653%
(A)	$u_{r} (r = 0.0205 m)$ $u_{r} (r = 0.0205 m)$ [m]	2.8801E-013	2.8972E-013	-0.594%
(A)	$σ_{z z} (r = 0.0195 m)$ $σ_{z z} (r = 0.0195 m)$ [N/m^2]	0.99488	0.992259	0.263%
(A)	$σ_{z z} (r = 0.0205 m)$ $σ_{z z} (r = 0.0205 m)$ [N/m^2]	0.92631	0.929711	-0.367%
(B)	$u_{r} (r = 0.0195 m)$ $u_{r} (r = 0.0195 m)$ [m]	2.9424E-013	2.94195E-013	0.015%
(B)	$u_{r} (r = 0.0205 m)$ $u_{r} (r = 0.0205 m)$ [m]	2.8801E-013	2.87966E-013	0.015%
(B)	$σ_{z z} (r = 0.0195 m)$ $σ_{z z} (r = 0.0195 m)$ [N/m^2]	0.99488	1.00893	-1.412%
(B)	$σ_{z z} (r = 0.0205 m)$ $σ_{z z} (r = 0.0205 m)$ [N/m^2]	0.92631	0.914645	1.259%
(C)	$u_{r} (r = 0.0195 m)$ $u_{r} (r = 0.0195 m)$ [m]	2.9424E-013	2.94234E-013	0.002%
(C)	$u_{r} (r = 0.0205 m)$ $u_{r} (r = 0.0205 m)$ [m]	2.8801E-013	2.88003E-013	0.002%
(C)	$σ_{z z} (r = 0.0195 m)$ $σ_{z z} (r = 0.0195 m)$ [N/m^2]	0.99488	0.995217	-0.034%
(C)	$σ_{z z} (r = 0.0205 m)$ $σ_{z z} (r = 0.0205 m)$ [N/m^2]	0.92631	0.926616	-0.033%
(D)	$u_{r} (r = 0.0195 m)$ $u_{r} (r = 0.0195 m)$ [m]	2.9424E-013	2.94237E-013	0.001%
(D)	$u_{r} (r = 0.0205 m)$ $u_{r} (r = 0.0205 m)$ [m]	2.8801E-013	2.88007E-013	0.001%
(D)	$σ_{z z} (r = 0.0195 m)$ $σ_{z z} (r = 0.0195 m)$ [N/m^2]	0.99488	0.994995	-0.012%
(D)	$σ_{z z} (r = 0.0205 m)$ $σ_{z z} (r = 0.0205 m)$ [N/m^2]	0.92631	0.926415	-0.011%

Last updated: January 29th, 2019

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Cylinder Under Rotational Force

Overview

Geometry

Analysis type and Domain

Simulation Setup

Reference Solution

Results

References

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