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Buckling, BEAM56G2

: Problem description: Trace out the complete load-displacement history of the column at the critical state determined in section VII.3 and compare these results with the linearized solution therein. The flexural stiffness EI_y<EI_z.

$\begin{figure} \centering\hspace{0pt} \epsfclipon\epsfxsize=6cm\epsffile{beam56g2.ps} \end{figure}$

Mesh: Four hexahedra--see appendix B.1.

Material properties: $E=2\times 10^5$ MPa, $\nu=0.3$ .

Support: Two point support. Statically determinate.


u=v=w=0 node:	 24 
u=w=0 node: 	 22       
v=w=0 node: 	 56       
w=0 node: 	 54

Loading: The load history is given as


F_x(t)=    -3280    -3290    -3490    -3500  unit: N
F_y=0, 		 F_z=1N

Solution: Note that F_x=-3290 is the theoretical load limit whereas F_x=-3490 is the critical force estimated by the eigenvalue computation on the mesh considered here. A small perturbation F_z=1 is added in the direction of the minimum bending stiffness in order to invoke the collapse mode in the total Lagrangian formulation. The load-deflection curve shown in the picture was computed with a refined substepping.

$\begin{figure} \centering\hspace{0pt}\rotate{ \epsfclipon\epsfxsize=6cm\epsffile{bea56g2.ps}} \end{figure}$

For the loading given we replace the end force with the equivalent surface tractions in the usual fashion, i.e.

$\begin{displaymath}q_x=\frac{F_x}{0.01\times 0.02}=-16.40,~-16.45,~-17.45,~-17.50~ \mbox{[MPa]} \end{displaymath}$

Execute from prompt:
>rmd3 beam56g2.I1
>rpd3 beam56g2.I2
>srh3 beam56g2.I3
>fefs beam56g2.I4
>hpp3 beam56g2.IP
>hpls beam56g2.IL
>str3 beam56g2.I5

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