Finite element analysis of circular cross sections subjected to combined loading

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1 ISSN Finite element analysis of circular cross sections subjected to combined loading #1 Ajinkya Patil *, #2 DevrajSonavane *, #3 Suhasini Desai * #123 Department of Mechanical Engineering, SavitribaiPhule Pune University Maharashtra Institute of Technology, Kothrud, Pune * Aker Sulutions, Hinjewadi, Pune, ABSTRACT The pipes used in horizontal tie-in systems of a subsea production facility are used in the transportation of oil and gas. These pipes are subjected to combined loading of internal pressure, axial force, bending moment and torsion. For the design of pressure piping ASME b31.8 code is used. The code does not consider the effect of torsion in combined loading. In thehorizontal piping system the effect of torsion is significant and cannot be neglected. Hence the paper presents finite element analysis of a pipe subjected to combined loading of internal pressure, axial load, bending moment and torsion. The analysis is done for the elastic limit state only. The analysis is useful in deciding the thickness of the pipe. The results can be used for establishing the yield surface and yield curve for a given combination of loads. Keywords pipes, combined loading, limit state, horizontal connection systems, circular cross sections ARTICLE INFO Article History Received :18 th November 2015 Received in revised form : 19 th November 2015 Accepted : 21 st November, 2015 Published online : 22 nd November 2015 I. INTRODUCTION A subsea production system consists of a subsea completed well, seabed wellhead, subsea production tree, subsea tie-in to flowline system, and subsea equipment and control facilities to operate the well as shown in figure 1[5]. For flowlines, the subsea tie-in systems are used to connect tree to manifold, tree to tree, and pipeline end to tree or manifold. For subsea control systems, the subsea tie-in systems are used to connectumbilicals to tree or manifold. Subsea fields have been developed using a variety of tie-in systems in the past decades. Different types of horizontal and vertical tie-in systems and associated connection tools are used for the tiein of flowlines, umbilicals, and other applications. Figure 1.Subsea field layout Risers, pipelines and piping in the oil and gas industry have to be designed to have adequate mechanical strength against loading appropriate for its intended use. Determination of minimum required wall thickness to resist

2 these loads is of major importance in the design to achieve the required safety margin against the relevant structural failure modes. This is of special importance for deep-water risers and pipelines and high-pressure systems made of modem ductile and tough metals, in order to save weight without jeopardizing the structural safety. Several design codes used for design against burst and gross plastic deformation use plasticity based design equations. When comparing these equations, there is a wide variation in factor of safety from code to code. Such a large variation in safety factors indicates the need for better understanding of pipe behavior. Figure 2. Horizontal tie-in system A typical horizontal connection system is as shown in figure 2[6]. Pipes used in horizontal connection systems are subjected to a combination of loads-internal pressure, axial thrust, bending moment and torsion as shown on figure 3[7]. Hence it is necessary to determine what combination of loads will lead to the failure of these pipes. Limit state equations for subsea pipes subjected to axial force, bending moment and internal pressure for burst and gross plastic deformation have been proposed by researchers. To check the validity of the equations and to find out their deviation from the FEM results, finite element analysis is necessary. Thus FEA is performed by using ABAQUS software. Amran [1] has proposed such load interaction relation taking a combination of two loads at a time. Bai [2] has proposed equations to calculate the ultimate moment capacity of a pipe subjected to combined loading of axial thrust + bending + pressure. Finn [3] has also proposed load interaction relations taking combined loading of axial + bending + pressure.ajinkya Patil et all [4] proposed load interaction formulae for the elastic limit taking a combination of pressure, axial force, bending moment and torsion into account. These formulae are verified using FEA in this paper. II. METHODOLOGY A pipe having the following specifications is modelled in ABAQUS. Outer diameter =100mm Inner diameter = 96mm Length = 1000mm Young`s modulus = 210,000 MPa The pipe is considered as a cantilever beam with loading applied at its free end as shown in figure 4. A reference point is created at the centre of the section of the free end. This reference point is coupled to the cross-section at the free end by a continuum coupling. Axial, Bending and Torsion loads are applied at this point. Pressure is applied at the internal surface. A cylindrical co-ordinate system is considered with the datum at the centre of the cross section of the fixed end. At the fixed end the UX(displacement in radial direction) value is allowed, and the UY and UZ(displacement in and z directions) is given zero value. The cross section of the pipe is partitioned into two equal parts. The part is seeded and meshing is carried out. A meshed model of thick pipe is as shown in figure 5. The partitioning edge is also seeded such that there are 5 elements across the thickness as shown in figure 6.. This is to capture the complete effect of bending moment. Figure 4. FEA model of a pipe Figure 5.Meshed model of thick pipe Figure 3. Forces, moments and their directions

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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