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Buckling behaviour of a beam

'Beam with solid elements

To start with, this contribution mainly focuses on the use of Salome and Code Aster, not on the results and the mechanical justifications of the code that has been used. So no garantees that the results will be correct upto the fifth decimal place, which they are not. I do hope though that this information is useful. For me it has been, because I had to think about some commands and look through the documentation and learn from that. In case of mistakes, errors and the like, please notify me, or better, you are invited to correct them yourself. Enjoy.

'Critical load according to Euler

The construction is a prismatic beam with diameter 1 and length 50 mm. The material is steel. According to Euler the the critical load with fixed i.e clamped boundary conditions at both ends of the beam is

Fcr = pi*pi*E*Ixx/(k*L)^2
, k = 0.5 for clamped boundary conditions, or
Fcr = 2.02 N.

File:Kw beam1.jpg * File:Kw beam2.jpg

The construction is readily defined in the Geometry module of Salome by Cylinder, radius 0.5 and length 50 mm, at the origin of the coordinate system. The axial direction of the beam coincides with the global z axis. The two axial faces of the beam are denoted by 'bot' and 'top'. The boundary conditions are are dx=dy=dz=0 at the 'bot' and dx=dy=0, dz=-0.2 mm at 'top'.