1. Introduction

The finite elements TUYAU_3M and TUYAU_6M correspond to linear elements of straight or curved pipes. They rely on Timoshenko beam kinematics for the movements and rotations of the medium fiber and on shell kinematics for the deformations of the cross section (ovalization, warping, swelling). These transverse deformations are broken down into Fourier series. Modeling TUYAU_3M takes into account a maximum of 3 modes, while modeling TUYAU_6M takes into account 6 Fourier modes.

These models can be used for problems with relatively thick three-dimensional pipes, only in linear or non-linear mechanical analysis and in small displacements. Currently, no thermal or acoustic calculations are possible.

This document presents the possibilities of modeling TUYAU available in version 6 of the*Code_Aster*. We first present the possibilities of this type of modeling, then we briefly recall the formulation of finite elements and their differences with beam models. A list of the options available for each of the elements is also given. We end with the presentation of some academic test cases and finally we give some tips for use.

Straight or curved pipe elements are grouped under models TUYAU_3M and TUYAU_6M. The calculation options are defined in this document. The current possibilities of these pipe elements are as follows:

straight or curved pipe lines,

line element with 3 knots (SEG3) or 4 knots (SEG4),

relatively thick pipe: \(e/R<0.2\) where \(e\) represents the thickness and \(R\) represents the radius of the cross section,

internal pressure, plane and anti-plane flexions, twisting and extending,

short trips,

elasto-plastic behavior under plane stresses, or any nonlinear incremental stresses,

the cross section may be deformed by: * swelling due to internal pressure or the Poisson effect, * ovalization due to bending, * warping due to combined in-plane and out-of-plane flexures.

Compared to modeling TUYAU_3M, modeling TUYAU_6M allows a better approximation of the behavior of the cross section in the case where it deforms in a high mode, for example in the case of thin tubes where the ratio of thickness to radius of the cross section is \(<0.1\), and in the case of plasticity.

Modeling TUYAU_3M has 21 degrees of freedom per node (6 degrees of freedom of beam and 15 degrees of freedom of shell), while modeling TUYAU_6M has 39 degrees of freedom per node (6 degrees of freedom of beam and 33 degrees of freedom of shell).

For TUYAU_3M modeling, SEG3 and SEG4 meshes can be used.