r3.08.04 Beam element with 7 degrees of freedom to take warpage into account

Summary:

This document presents element POU_D_TG, which is a finite right beam element taking into account the warping of sections. It allows the calculation of beams with thin cross sections and an open profile, with hampered or free twisting.

For flexure, normal and shear forces, this element is based on element POU_D_T, which is a straight beam element with transverse shear (Timoshenko model).

For element POU_D_TG, the cross section is assumed to be constant (of any shape) and the material is homogeneous and isotropic, with linear elastic behavior.

The POU_D_TGM element is to be used for non-linear behaviors.

This reference documentation is based on the general reference documentation for beams, in linear elasticity [R3.08.01]. It describes the specificities of the right beam element with POU_D_TG warpage.

• 1. Field of use
• 2. Notations
• 3. Kinematics specific to twisting with warping
• 4. Right beam element with warping: stiffness and mass matrices
  • 4.1. Traction - compression the degrees of freedom are \(u\) or \(\mathrm{DX}\)
  • 4.2. Flexion in the Gxz plane, degrees of freedom: w, qy or Dz, Dry
  • 4.3. Flexion in the Gxy plane, degrees of freedom: g, qz or Dy, Drz
  • 4.4. Torsion and warping, degrees of freedom: qx, qx, x or Drx, Grx
  • 4.5. Eccentricity of the torsional axis in relation to the neutral axis
• 5. Geometric stiffness - Prestressed structure
• 6. Loads
  • 6.1. Distributed loads, options: CHAR_MECA_FR1D1D and CHAR_MECA_FF1D1D
  • 6.2. Gravity loading, option: CHAR_MECA_PESA_R
  • 6.3. Thermal loading, option: CHAR_MECA_TEMP_R
  • 6.4. Loading by imposed deformation, option: CHAR_MECA_EPSI_R
• 7. Torsor of efforts - Nodal forces and reactions
  • 7.1. Available options
  • 7.2. The twister of efforts
  • 7.3. Calculation of nodal forces and reactions
• 8. Bibliography
• 9. Description of document versions