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CivilComp Proceedings
ISSN 17593433 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. Madureira^{1}, F.Q. Melo^{2} and R.C. Barros^{3}
^{1}Department of Mechanical Engineering, Faculty of Engineering, University of Porto, Portugal
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", CivilComp 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 multinodal 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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