Buckling of a Straight Beam (In-Plane Buckling)

This test lets you compare analysis results for the buckling of a straight beam in CATIA with the Beam theory. In other words, you will study the quality of distorted membrane elements in a buckling analysis. You will use 2D meshes, with membrane elements.

Reference:

Beam Theory
 

Specifications

Geometry Specifications

Length:
L = 100 mm  

Width:
W = 12 mm  

Thickness:
th = 1 mm


Analysis Specifications

Young Modulus (material):
E = 1000 MPa

Poisson's Ratio (material):
ν = 0

Mesh Specifications:

  • Constrained points (using the points created in the CATPart)

  • Membrane elements

Restraints:
At point B: Tx = 0
At edge AB: Ty = Tz = Rx = 0

Loads:
The line forced density at edge CD is
Ty = -83.333 N_m
 

Results

The critical load is given by column buckling theory:

In this particular case, the result is Nc = 35.53 N.

The results of the solver computation and the normalized results (computed results divided by analytic solution) are given in the table below.
 

 

Linear triangle shell
(TR3)

Parabolic triangle shell
(TR6)

Linear quadrangle shell
(QD4)

Parabolic quadrangle shell
(QD8)

Mesh

 Regular 

 Irregular 

Regular

Irregular

Regular

Irregular

Regular

Irregular

Computed buckling factor [N]

317.435

287.831

35.483

35.537

36.135

47.478

35.221

35.272

Normalized Results

8.934

8.101

0.999

1.000

1.017

1.336

0.991

0.993

To Perform the Test:

The Buckling_StraightBeam_in_plane.CATAnalysis document presents the complete analysis of the buckling case, computed with an irregular mesh formed of parabolic triangle elements (TR6).

To compute the case with linear triangle (TR3), linear quadrangle (QD4) and parabolic quadrangle (QD8) elements, open the Straight_Beam.CATPart document and proceed as follow:

  1. Define the mesh using the Surface Meshing workshop in the Advanced Meshing Tools workbench.

  2. In Generative Structural Analysis workbench, define analysis specifications as shown above.

  3. Insert and compute buckling case solution in Generative Structural Analysis workbench.

To create an irregular mesh, use the Add/Remove Constraints icon in the Local Specifications toolbar, then select the points on the part.