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buckling analysis of pipeline under external pressure

The buckling pressure of a uniform pipe under external pressure, can be evaluted by the linear analtical equation:

 

linear buckling pressure equation 

 I use abaqus to simulate this problem. I tried for different pipe length and boundray conditions, the buckling pressure varies a lot, and even larger than the linear analytical results. Does anyone know how long do I need to build for the model and how to set up the boundray conditions. Many thanks. 

 

pipe length and boundray condition 

 

 

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