Home / Examples / Stress Analysis [Galileo] / Example 48: Buckling Analysis

Example 48: Buckling Analysis

General

The buckling analysis is performed on an H-shaped steel structure.
The structure's buckling load factor and the buckling modes are solved.
Unless specified in the list below, the default conditions will be applied.

Results will vary depending on Femtet version and the PC environment.

Analysis Space

Item	Settings
Analysis Space	3D
Model Unit	mm

Analysis Conditions

The analysis type is buckling analysis

Item	Settings
Solver	Stress Analysis [Galileo]
Analysis Type	Buckling Analysis

Model

An H-shaped sheet body is created on XY plane. It is extruded to form an H-shape pillar.
The bottom face is fixed. The top face is loaded downward and fixed in X and Y directions. Uniform displacement is set on it.*

* The uniform displacement prevents the rotational displacement.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	H_shape	104_Stainless_steel *

* Available from the material DB

Boundary Conditions

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
Fix/Face	Mechanical	Displacement	Select all X/Y/Z components. UX=0, UY=0, UZ=0
Force/Face	Mechanical	Load	Select [Set the total load]. X=0.0, Y=0.0, Z=-1000
Fix_xy/Face	Mechanical	Displacement	Select X and Y components. UX=0, UY=0 Select [Uniform Displacement] Select UX, UY and UZ.

* As the boundary conditions (Force and Fix_xy) need to be set on the same face, select Add in the second boundary condition setting.

Results

The following will be output on the Output Window or the log file.

<<Buckling Analysis>>

Buckling load factor

Mode[ 0] = 2.88264161e+002

Multiply the original load with the buckling load factor to acquire the buckling load.

Field values such as displacement, strain, stress, etc acquired by the buckling analysis are all relative.

In this model, the buckling load factor is 288.

The applied load on “Force" is 1000 [N]. Therefore, the buckling load is calculated to be 288 [KN].

The Z-direction displacement is shown below by contour. The contour diagram shows the magnitude of displacement. The displacement is relative.

Compare with Theoretical Values

The buckling load for a H-shaped pillar is given by the following formula.

In this case,

B/2 = 7e-3 [m]

b = 86e-3 [m]

H = 50e-3 [m]

h = 5e-3 [m]

E = 2e11 [Pa]

L = 2.0 [m]

μ＝4, which means that there is no horizontal or rotational displacement for either end.

These values yield I = 14.7e-8 [m4] and Pbkl = 290 [KN]

The result of Femtet matches this Pbkl quite well.