Fixed Beam Under Gravitational Load¶
Overview¶
The aim of this test case is to validate the following functions:
gravitational load
The simulation results of SimScale were compared to the analytical results derived from [Roark]. The meshes used in (A) and (B) were created with the parametrizedtetrahedralizationtool on the SimScale platform and then downloaded. Both meshes were then rotated and uploaded again. These were used in case (C) and (D). With this method we achieve the exact same mash for the rotated and nonrotated case.
Analysis type and Domain¶
Tool Type : CalculiX/Code_Aster
Analysis Type : Static
Mesh and Element types :
Case 
Mesh type 
Number of nodes 
Element type 

(A) 
linear tetrahedral 
6598 
3D isoparametric 
(B) 
quadratic tetrahedral 
44494 
3D isoparametric 
(C) 
linear tetrahedral 
6598 
3D isoparametric 
(D) 
quadratic tetrahedral 
44494 
3D isoparametric 
Simulation Setup¶
Material:
isotropic: E = 205 GPa, \(\nu\) = 0.3, \(\rho\) = 7870 kg/m³
Constraints:
Face ABCD is fixed: \(d_x=d_y=d_z=0.0\)
Loads:
Case (A) and (B): gravitational load \(g\) = 9.81 m/s² pointing in the negative zdirection: \((0,0,1)\)
Case (C) and (D): gravitational load \(g\) = 9.81 m/s² now rotated +45° around the xaxis: \((0,1,1)\)
Reference Solution¶
The equation \(\eqref{ref4}\) used to solve the problem is derived in [Roark]. In equation \(\eqref{ref1}\) the gravitational load is converted in a line load \(w_a\).
Results¶
Comparison of the displacement at the free end in the direction of the gravitation vector.
Case 
Tool Type 
SimScale 
Error 


(A) 
CalculiX 
2.2597E4 
2.1340E4 
5.56% 
(B) 
CalculiX 
2.2597E4 
2.2559E4 
0.17% 
(C) 
CalculiX 
2.2597E4 
2.1340E4 
5.56% 
(D) 
CalculiX 
2.2597E4 
2.2560E4 
0.16% 
(A) 
Code_Aster 
2.2597E4 
2.1340E4 
5.56% 
(B) 
Code_Aster 
2.2597E4 
2.2559E4 
0.17% 
(C) 
Code_Aster 
2.2597E4 
2.1340E4 
5.56% 
(D) 
Code_Aster 
2.2597E4 
2.2560E4 
0.16% 