this file analising the buckling of a simply supported beam in two cases. first case eigen value method for analisig a ideal beam under compressive load and in case two the beam has imperfection . the imperfection of beam is in the sacles of the mood that the eigen values method gives.

1. Buckling of a beam with two ended S.p:
The beam considerd in abaqus model :
2D, wire
Cross section : circule r=0.05mm and the length of beam =1m
Mechanical property :
Passion ratio:0.3
Elasticity moudel:200e9
At firs step the beam analysid with eigen valu method with out any geometric imperfection.the
beam objected the concentrated pressive force equal =1 at first and this force increase properly till
the firs mode of buckling appear. The following figures show the different moods of buckled beam.
Figure 1:first mood Figure 2:second mood
Figure 3 :third mood Figure 4: 4th
mood

2. In this project the beam analysed for 6 mood. The eigen values are equal with ciritical loads so
in ech mood we have special critical load, the following table show ciritical load for each mood.
The mood number eigen value
1 9.6894e10
2 3.8757e11
3 8.72e11
4 1.55033e12
5 2.4223e12
6 3.4884e12
Table 1: eigen value
Non linear analyz:
Because Nonlinear-static buckling analysis considers material nonlinearity while generating
buckling response, results are often more realistic than those of Linear buckling analysis. The
results of Nonlinear-static analysis are indicated by a plot of deformed configuration against load
application. This plot displays the softening behavior which indicates the onset of buckling.
In this analys the primary force was p=1 , then this pressive forc properly increase till reach the
ciritical force. The magnititude of ciritical force for each mood is same as the magnititude of
eigen value .
In next part we analys the beam with non linear geometri imperfection .
This analys done with Abaquse/CAE and the the scales of moods of eigen value analys
considered as non linear geometric imperfection.
Seris 1 :
This analys based on the node 11 in Abaquse/cae model.and the primary load is the amplititude
of critical load that gives eigen value analys.
Because of loosing load capacity carrying this analyzed is Displacement control
W0= .0.0*u1mood1+0.01U1mood2 W0= 0.05m
Series 2:
W0=0.001u1mood1+0.02u1mood2 W0=0.03m
Series 3:
W0=0.001u1mood1+0.01u1mood2 W0=0.02m

3. Fig 5: P/pcritical proper and deflection
Result and discussion:
The gradiant of p-w diagram shows that the ability of carrying load . with increasing the
geometric imperfection the gradiant of chart decreas.but at last the gradiant becom 0 and the
stiffness is proper with this gradiant. By increasing the geometric imperfection the beam will not
be in its ideal form no more. As the fig 5 shows the imperfection equall 0.03 has less deformed
from its ideal state.
0 0.005 0.01 0.015 0.02 0.025
p/pcritical
deflection magnititude
Series1
Series2
Series3