# Finite element analysis of circular cross sections subjected to combined loading

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3 Figure 8. Stress distribution in thick pipe IV. RESULTS AND DISCUSSION The analytical results are compared with FEA results and graphs of utilization vs. serial number are plotted for both theoretical and FEA results (Abaqus). Figure 6.Meshed model showing 5 elements across the thickness III. FEA RESULTS For pressure, moment and torsion load there is variation in stresses along the wall thickness. In case of thin cylinders, analytical formulae for stresses due to pressure and tension load gives average stress through the thickness and there is very low variation in through thickness stress due to bending and torsion load. Hence linearized principal membrane stresses of FEA are directly compared with principal stresses calculated by analytical method. For thick cylinders, stress variation along the thickness is considerable for pressure, moment and torsional loads. The stresses at midpoint of thickness are very close to average through thickness stresses. Hence for thick cylinders linearized principal membrane stresses from FEA are compared with stresses at mean radius calculated by analytical method. The stress distribution in thin and thick pipe is as shown in figure 7 and 8 respectively. The load combination is chosen such that the analytical results give the value of utilization equal to 1. Tresca results for thin pipe Theoretical Figure 9. Graph of Tresca results for thin pipe Abaqus von Mises results for thin pipe Theoretical Abaqus Figure 10. Graph of von Mises results for thin pipe Figure 7. Stress distribution in thin pipe

4 Thick pipe outer surface (Tresca) Figure 11.Graph of Tresca results at the outer surface of thick pipe Thick pipe inner surface (von Mises) 1.40 Figure 14.Graph of von Mises results at the innre surface of thick pipe Thick pipe inner surface (Tresca) Figure 12. Graph of Tresca results at the inner surface of thick pipe Tresca results for thick pipe at mean radius Figure 15.Graph of Tresca results at the mid surface of thick pipe Thick pipe outer surface (von Mises) 1.40 Figure13.Graph of von Mises results at the outer surface of thick pipe von Mises results for thick pipe at mean radius Figure 16.Graph of von Mises results at the mid surface of thick pipe Fromfigure 9 and 10, it can be seen that for thin pipe the theoretical and FEA results coincide for most of the readings with a maximum error of 2%.

5 From Figure 11 and 12, we see that the theoretical and FEA results coincide for those readings for which the value of pressure is less than 70% of the pressure capacity. Similar deviation between theoretical and FEA can be seen in figure 13 and 14 for the von Mises criteria. Since the principal stresses at the mid surface are averaged, we see that there is very little deviation between theoretical and FEA results when the mid surface is considered V. CONCLUSION. For thin cylinders, cross section capacity based on FEA and analytical method are within 2% accuracy. For thick pipes, analytical formulation based on mean radius gives very close results to FEA which are within 4% accuracy for all load combinations considered. Thus for thick pipes stress linearization should be carried out to get accurate results. ACKNOWLEDGEMENT We would like to thank C.M. Venkateswaran, CEO, Aker Powergas and Subsea for giving us an opportunity to pursue our research. We would also like to thank Dr. L.K. Kshirsagar, Principal, Maharastra Institute of Technology, Pune for extending his support to our project. REFERENCES Amran Bin Ayob, The Effect of D/T on the Load Interaction Behavior of a Plain pipe, Journal of Pressure Vessel Technology, Volume 126, Issue 4, 2004 [2] Soren R. Hauch and Yong Bai, Bending Moment Capacity of Pipes, Journal of Offshore Mechanics and Arctic Engineering; 2000 [3] Finn Kirkemo, Burst and gross plastic deformation limit state equations for pipes: Part 1 Theory, International Society of Offshore Polar Engineers (ISOPE), 2001 [4] AjinkyaPatil, Limit state equations for circular cross sectionssubjected to combined loading, International journal of pressure vessel and piping technology; 2015 [5] [6] [7]

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