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 

SpecificationsGeometry Specifications

Young Modulus (material): 

Poisson's Ratio (material): 

Mesh Specifications:


Restraints: 

Loads: 
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 
Parabolic triangle shell 
Linear quadrangle shell 
Parabolic quadrangle shell 

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:
Define the mesh using the Surface Meshing workshop in the Advanced Meshing Tools workbench.
In Generative Structural Analysis workbench, define analysis specifications as shown above.
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.