r3.08.06 Finite elements of straight and curved pipes with ovalization, swelling and warping in elasto-plasticity

Summary:

This document presents the modeling of a finite pipe element that can be used in elasticity or plasticity pipe calculations. Pipes, curved or straight, can be relatively thick (ratio of thickness to radius of the cross section up to \(0.2\)) and are subject to various combined loads - internal pressure, plane and anti-plane flexures, torsion, extension - and can have a non-linear behavior.

This line element combines both shell and beam properties. The average fiber in the pipe behaves like a beam and the pipe surface behaves like a shell. The element produced is a pipe element that is straight or curved in small rotations and deformations, with elasto-plastic behavior under plane stresses.

Three models, corresponding to three different types of elements, are available:

• TUYAU_3M, which takes into account a maximum of 3 Fourier modes, and which can rely on 3-knot or 4-knot meshes.

• TUYAU_6M, which takes into account up to 6 Fourier modes, and is based on 3-knot meshes.

• 1. Introduction
• 2. The different shell and beam theories for the finite elements of straight or bent pipes
  • 2.1. The pipe in beam theory
  • 2.2. The pipe in linearized shell theory
  • 2.3. Analysis of straight and angled pipes
• 3. Combined shell-beam elements for straight and curved pipes
  • 3.1. Cinematics
  • 3.2. Law of behavior
  • 3.3. Deformation work
  • 3.4. Internal elastic energy of the elbow
  • 3.5. Work of forces and external couples
  • 3.6. Principle of virtual work
  • 3.7. Generalized efforts
• 4. Numerical discretization of variational formulations
  • 4.1. Discretization of displacement fields and deformation fields for the beam part
  • 4.2. Discretization of the displacement and deformation fields for the additional part
  • 4.3. Discretization of the total deformation field
  • 4.4. Stiffness matrix
  • 4.5. Mass matrix
  • 4.6. Shape functions
  • 4.7. Digital integration
  • 4.8. Discretization of external work
• 5. Geometric characteristics of the pipe element
• 6. Pipe-pipe connection
  • 6.1. Construction of a particular generator
  • 6.2. Connection from one element to another
  • 6.3. Digital implementation
• 7. Hull-to-hose and 3D-hose connections
  • 7.1. Process followed
  • 7.2. Pipe kinematics.
  • 7.3. Shell kinematics
  • 7.4. Calculation of the average displacement on the S section
  • 7.5. Calculation of the average rotation of the S section
  • 7.6. Calculation of the average swelling of section S
  • 7.7. Calculation of Fourier coefficients on section S
  • 7.8. Implementation of the method
• 8. Implementation of element TUYAU in Code_Aster
  • 8.1. Description
  • 8.2. Modeling data
  • 8.3. Linear elasticity calculation
  • 8.4. Nonlinear calculations
  • 8.5. Post-treatment
  • 8.6. Quiz: SSLL106A
• 9. Conclusion
• 10. Bibliography
• 11. Description of document versions