1. Introduction

There is an extensive bibliography on pipe modeling and numerous finite elements of straight and bent pipes are available in major finite element codes. Summaries have already been carried out [bib1], [bib5], [bib6], in the past which have been completed by incorporating the latest known developments in the field [bib11]. The important effects to be taken into account are swelling due to internal pressure and the ovalization of the transverse sections by combined plane and anti-plane flexions. The hypothesis of small rotations and deformations is assumed for the purposes of this document.

It is a linear element with 3 or 4 nodes, of the curved or straight beam type with local plasticity taking into account ovalization, warping and swelling. Beam kinematics is enriched with shell kinematics to describe the behavior of cross sections. This kinematics is discretized in \(M\) Fourier modes whose number \(M\) must be both sufficient to obtain good plasticity results and not too large to limit the calculation time. The literature encourages us to use \(M\mathrm{=}6\) [bib9], [bib13] in plasticity. In elasticity, for thick pipes, you can be content with \(M\mathrm{=}2\) or \(M\mathrm{=}3\).