r3.08.10 Item CABLE_GAINE

Summary:

The purpose of element CABLE_GAINE presented in this document is to model prestress cables that can rub or slide in their sheaths and therefore do not fully follow the movements of the concrete in which they are immersed. It therefore complements modeling BARREalliée with the operator DEFI_CABLE_BP, which makes it possible to model prestress cables that are completely adherent to concrete (see [R7.01.02]).

This element is very heavily inspired by the interface element described in [R3.06.13]. It models the cable interface with its jacket and the cable itself.

• 1. Variational formulation
  • 1.1. Potential energy and minimization
  • 1.2. Augmented Lagrangian
  • 1.3. Characterization of the saddle point
• 2. Discretization of the finite element
• 3. Static condensation
• 4. Integration
  • 4.1. Perfect grip
  • 4.2. Frictionless sliding
• 5. Discretized writing
  • 5.1. Ratings
  • 5.2. Discretization of optimality conditions
  • 5.3. Internal forces
  • 5.4. Stiffness matrix
• 6. Convergence of the calculation: adjustment of the parameters
  • 6.1. Penalization coefficient
  • 6.2. Convergence criterion by reference values