Deep Simply-supported Solid Beam

This test lets you check modal analysis results for a beam with 3D meshes formed of linear or parabolic hexahedron elements.

Reference:

ABBASSIAN F., Dawswell D.J., Knowles N.C., NAFEMS-Glasgow, Free Vibrations Benchmarks, pp438-452, November 1987.
 

Specifications

Geometry Specifications

Length:
L = 10 m

Width and Height:  
h = 3000 mm


Analysis Specifications

Young Modulus (material):
E = 200000 MPa

Poisson's Ratio (material):
ν = 0.3

Density:
 ρ  = 8000 kg_m3

Mesh specifications:
On x, y and z axis:

  • For linear hexahedron elements (HE8): 1 x 3 x 10 elements
  • For parabolic hexahedron elements (HE20): 1 x 1 x 5 elements

Restraints (User-defined):
In the skew coordinate system (applied to the box group):

  • On face ABCD: Tx = 0

  • On edge CC': Ty = 0

  • On edge DD': Ty = Tz = 0

 

Results

The results of the test are presented in the table below:

Mode
 

Reference solution
[Hz]

Parabolic hexahedron (HE20)

Linear hexahedron (HE8)

Frequencies
results
[Hz]

Normalized
results

Frequencies
results
[Hz]

Normalized
results

1

38.2

38.27

1.002

38.28

1.002

2

85.21

87.67

1.029

83.95

0.985

3

152.23

157.5

1.035

157.57

1.035

4

245.53

259.01

1.055

264.92

1.079

5

297.05

306.06

1.030

298.33

1.004

To Perform the Test:

The Deep_simply_supported_solid_beam_HE8.CATAnalysis document presents a complete analysis of this case, computed with a mesh formed of linear hexahedron elements (HE8).

To compute the analysis with parabolic hexahedron elements (HE20), open the Deep_simply_supported_solid_beam.CATPart document, and proceed as follow:

  1. Define the mesh for the 2D surface presented in the CATPart document, using the Surface Meshing workshop in the Advanced Meshing Tools workbench.

  2. Extrude the mesh to obtain a 3D mesh.

  3. Define analysis specifications as indicated below.

  4. Compute the CATAnalysis and generate an image called Deformed mesh.

For a 3D hexahedron mesh, you need to create a mesh on a 2D part, then to extrude it with the Extrude Mesher in Translation icon, in the Advanced Meshing Tools workbench.