6. Convergence of the calculation: adjustment of the parameters#

The convergence of a calculation with the elements CABLE_GAINE is sometimes difficult to obtain given the different orders of magnitude involved. This is the reason why it is necessary to choose the penalty coefficient \(r\) carefully and to prefer a criterion of convergence by reference values (keyword RESI_REFE_RELA). The next two paragraphs give tips on how to use these points.

6.1. Penalization coefficient#

When writing the increased Lagrangian, the coefficient \(r\), the so-called penalty coefficient, was introduced. To choose the value of \(r\) (PENA_LAGR in the cohesive law CABLE_GAINE_FROT), on which we recall that the converged solution does not depend, or to explain the construction of the reference force used in the criterion RESI_REFE_RELA (see § next), it is necessary to conduct a quick dimensional analysis.

For the choice of \(r\), we can see in the previous equations that it makes sense for it to be of the order of magnitude of \(\frac{\lambda }{u}\).

\(u\) is the order of magnitude of the expected trips.

\(\lambda\) is the frictional force per unit length, i.e. the shear stress (friction) integrated around the perimeter of the cable. If we take a typical \({\sigma }^{\mathit{ref}}\) constraint expected in concrete in the vicinity of the cable, \(\lambda\) will be of the order \(2\pi {r}_{\mathit{cable}}{\sigma }^{\mathit{ref}}\).

To obtain the best possible convergence, you must choose \(r\) of the order of magnitude of \(2\pi {r}_{\mathit{cable}}\frac{{\sigma }^{\mathit{ref}}}{{u}^{\mathit{ref}}}\).

6.2. Convergence criterion by reference values#

The use of a convergence criterion by value is often necessary to complete the calculation.

To do this, you must activate the keyword RESI_REFE_RELA in the CONVERGENCE factor keyword of STAT_NON_LINE or CALC_PRECONT. In the case of the CABLE_GAINE element, this keyword must be accompanied by three others:

  • a reference force (keyword EFFORT_REFE): expected voltage in the cable,

  • a reference displacement (keyword DEPL_REFE): a typical displacement of the structure,

  • a reference constraint (keyword SIGM_REFE): the order of magnitude of the expected stresses in the vicinity of the cable (the typical stress of concrete except in special cases), this constraint makes it possible to build a reference for \(\lambda\) using the section \(A\) of the cable using the section of the cable in the form: \({\lambda }^{\mathit{ref}}\mathrm{=}{\sigma }^{\mathit{ref}}\mathrm{\ast }\sqrt{A}\)