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The next image shows the prediction of the buckling mode at the symmetry plane from a finite element model.
This and the next image are from:
Evangelos Giakoumatos (Dept. of Mechanical Engineering, University of Thessaly, Greece),
“Nonlinear finite element analysis of steel pipe elements under pressure and bending”, Diploma Thesis, July 2002
ABSTRACT: The work investigates the response of elbows under in-plane bending and pressure, through nonlinear finite element tools, supported by experimental results from real-scale tests. The finite element analysis is mainly based on a nonlinear three-node "tube element", capable of describing elbow deformation in a rigorous manner, considering geometric and material nonlinearities. Furthermore, a nonlinear shell element from a general-purpose finite element program is employed in some special cases. Numerical results are compared with experimental data from steel elbow specimens. The comparison allows the investigation of important issues regarding deformation and ultimate capacity of elbows, with emphasis on relatively thin-walled elbows. The results demonstrate the effects of pressure and the influence of straight pipe segments. Finally, using the numerical tools, failure of elbows under bending moments is examined (cross-sectional flattening or local buckling), and reference to experimental observations is made.
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