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Keywords: thin pipes, Fourier series, variational methods, system of ordinary differential equations, boundary conditions, point load..

Summary

A displacement formulation for circular cylindrical thin pipes when subjected to radial loads is presented. The pipes considered are straight steel pipes used for water, oil or gas transport purpose. Parts of piping structures can also be considered in this type of analysis. The pipe is a cylindrical shell, usually considered thin, inextensible, with two parameters used for the deformation: the longitudinal direction and the circumferential direction. Trigonometric functions in the circumferential direction are combined with unknown analytic functions in the longitudinal direction to define the shell displacements. These analytic functions are the ovalization and warping. The objective of the work, presented in this paper, is to evaluate the radial displacement when a load is applied on the surface of the pipe. The method formulates the total energy as a functional of these two unknown functions and then, using a variational procedure, obtains the conditions for the minimum of the total energy functional. These consist of a system of differential equations, whose solution is achieved in terms of the functions ovalization and warping. When this system of differential equations is combined with a Fourier series (where only a few terms, usually between four and eight, are taken), the solution is analytic; for suitable boundary conditions, results are obtained. Two load cases are considered. The first one is the case of pinching forces in the middle of the pipe, for which the load is represented as a Fourier series. The boundary conditions use the symmetry of the problem. The second case studied is a point load on one edge. The pipe is clamped on the opposite edge. For this example the authors present a new approach which involves analytic functions to represent this kind of load and also the search for appropriate boundary conditions that includes the shear force. The geometric parameters for these problems are the shell thickness, the length and the radius of the pipe. Results for the two different load cases are presented and compared with the ones published using the finite element method with a multi-nodal ring element and also with commercial codes solutions. The results with the analytical solution used in this work show good agreement with the ones obtained by numerical solutions with finite elements. The analytical solution presented performed quite well even considering a low number of trigonometric terms in the Fourier expansions, particularly for the pinching cylinder.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 106 PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: Paper 59 Deformation Analysis of Thin Cylindrical Pipes subjected to Radial Loads L.R. Madureira¹, F.Q. Melo² and R.C. Barros³ ¹Department of Mechanical Engineering, Faculty of Engineering, University of Porto, Portugal ²Department of Mechanical Engineering, University of Aveiro, Portugal ³Department of Civil Engineering, Faculty of Engineering, University of Porto, Portugal doi:10.4203/ccp.106.59 purchase the full-text of this paper Full Bibliographic Reference for this paper L.R. Madureira, F.Q. Melo, R.C. Barros, "Deformation Analysis of Thin Cylindrical Pipes subjected to Radial Loads", in , (Editors), "Proceedings of the Twelfth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 59, 2014. doi:10.4203/ccp.106.59 Keywords: thin pipes, Fourier series, variational methods, system of ordinary differential equations, boundary conditions, point load.. Summary A displacement formulation for circular cylindrical thin pipes when subjected to radial loads is presented. The pipes considered are straight steel pipes used for water, oil or gas transport purpose. Parts of piping structures can also be considered in this type of analysis. The pipe is a cylindrical shell, usually considered thin, inextensible, with two parameters used for the deformation: the longitudinal direction and the circumferential direction. Trigonometric functions in the circumferential direction are combined with unknown analytic functions in the longitudinal direction to define the shell displacements. These analytic functions are the ovalization and warping. The objective of the work, presented in this paper, is to evaluate the radial displacement when a load is applied on the surface of the pipe. The method formulates the total energy as a functional of these two unknown functions and then, using a variational procedure, obtains the conditions for the minimum of the total energy functional. These consist of a system of differential equations, whose solution is achieved in terms of the functions ovalization and warping. When this system of differential equations is combined with a Fourier series (where only a few terms, usually between four and eight, are taken), the solution is analytic; for suitable boundary conditions, results are obtained. Two load cases are considered. The first one is the case of pinching forces in the middle of the pipe, for which the load is represented as a Fourier series. The boundary conditions use the symmetry of the problem. The second case studied is a point load on one edge. The pipe is clamped on the opposite edge. For this example the authors present a new approach which involves analytic functions to represent this kind of load and also the search for appropriate boundary conditions that includes the shear force. The geometric parameters for these problems are the shell thickness, the length and the radius of the pipe. Results for the two different load cases are presented and compared with the ones published using the finite element method with a multi-nodal ring element and also with commercial codes solutions. The results with the analytical solution used in this work show good agreement with the ones obtained by numerical solutions with finite elements. The analytical solution presented performed quite well even considering a low number of trigonometric terms in the Fourier expansions, particularly for the pinching cylinder. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £65 +P&P)
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