Rotation Loading

This test lets you check analysis results for a beam with an applied rotation at one of its extremity. You will use either the 2D or 3D model.

Reference:

Analytical solution
 

Specifications

Geometry Specifications

Length:
L = 0.5 m

Square section:
a = 0.02 m

Analysis Specifications

Young Modulus (material):
E = 200 GPa

Poisson's Ratio (material):
ν = 0

Density:
ρ = 7800 kg/m-3

Mesh Specifications:

  • 3D model: 2 x 2 x 50 linear hexahedron elements (HE8)

  • 2D model: 4 x 8 linear quadrangle elements (QD4)

Restraints:
Clamp on face A: Tx = Ty = Tz = Rx = Ry = Rz = 0

Loads (rotation force):

  • Angular Velocity: 3000 rad/s

  • Angular Acceleration: a=0 rad/s2

The direction of the rotation axis through the center of the clamped section A is (1,0,-1).
 

Results

  • Analytical solution

    In the beam axis:

    where:

    • Ux(0)=0

    The displacements of all the points of the beam in the global axis are given by:

    where:
     

    For r=500 mm, the result of the analytic solution is:
    Ux=Uy=Uz=8.44374 mm

  • The table below presents the analysis results:

Displacement

Analytical solution 
[mm]

Values

 

Linear Hexahedron
(HE8)

Linear Quadrangle
(QD4)

Computed Results
 [mm]

Normalized Results

Computed Results
 [mm]

Normalized Results 

Ux

8.44374

8.44374

1

8.44372

0.999998

Uy

8.44374

8.44377

1.000004

8.44377

1.000004

Uz

8.44374

8.44374

1

8.44376

1.000002

To Perform the Test:

The rotationloadingHE8.CATAnalysis document presents a complete analysis, computed with a mesh formed of linear hexahedron elements (HE8).

The rotationloadingQD4.CATAnalysis document presents a complete analysis, computed with a mesh formed of linear quadrangle elements (QD4).

To compute the case with linear quadrangle elements (QD4) and linear hexahedron elements (HE8), proceed as follow:

  1. Open one of the CATAnalysis documents.

  2. Compute the case and activate the Deformed mesh.1 and Translational displacement vector.1 images called Deformed mesh.