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The aim of this test case is to validate the following functions:
The simulation results of SimScale were compared to the analytical results derived from [SCHAUM]. The mesh used was created using first order tetrahedralization meshing algorithm on the SimScale platform.
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The square box mass has a length, width and height of 1m with upper face partitioned in to half.
Tool Type : Code_Aster
Analysis Type : Linear static and dynamic
Mesh and Element types :
Case | Mesh type | Number of nodes | Number of 3D elements | Element type | Analysis type | Elastic support type – face EIGJ | Elastic support type – face IFJH | Elastic support type – combined (face EFGH) |
---|---|---|---|---|---|---|---|---|
(A-1) | linear tetrahedrals | 21 | 26 | 3D isoparametric | Static |
|
|
isotropic total |
(A-2) | linear tetrahedrals | 21 | 26 | 3D isoparametric | Dynamic |
|
|
isotropic total |
(B-1) | linear tetrahedrals | 33 | 61 | 3D isoparametric | Static | isotropic total | orthotropic total |
|
(B-2) | linear tetrahedrals | 33 | 61 | 3D isoparametric | Static | isotropic distributed | orthotropic distributed |
|
(B-3) | linear tetrahedrals | 33 | 61 | 3D isoparametric | Static | isotropic total and distributed | orthotropic total and distributed | isotropic total |
Material:
Constraints:
Case A-1/A-2:
Case B-1:
Case B-2:
Case B-3:
Case A-1/B-1/B-2/B-3:
(1)
$$x = \frac {mg}{k} = \frac {10.(9.81)}{9810} = 0.01 m$$
Case A-2:
(2)
$$x = \frac {v_o}{\omega} sin \omega t + x_o cos \omega t$$
where,
angular frequency, \(\omega\) = \(\sqrt \frac {k}{m}\) = \(\sqrt \frac {9810}{10}\) = 31.32 rad/s.
initial velocity, Vo = -0.01 m/s
position of initial release, Xo = -0.01 m
time, 2s <= t <= 4s
The equation (1), (2) used to solve the problem is derived in [SCHAUM].
Comparison of the displacement dz computed on face ABCD from SimScale case A-1/B-1/B-2/B-3 with [SCHAUM] equation (1).
Quantity | [SCHAUM] | Case A-1 | Error | Case B-1 | Error | Case B-2 | Error | Case B-3 | Error |
---|---|---|---|---|---|---|---|---|---|
x | 0.01 | 0.01 | 0 | 0.01 | 0 | 0.01 | 0 | 0.01 | 0 |
Comparison of the oscillations dz computed on face ABCD from SimScale case A-2 with [SCHAUM] equation (2).
[SCHAUM] | (1, 2, 3, 4, 5) (2011)”McGraw-Hill Schaum’s outlines, Engineering Mechanics: Dynamics”, pg 271-273, N. W. Nelson, C. L. Best, W. J. McLean, Merle C. Potter |
Last updated: January 29th, 2019
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