B modeling
==============


Characteristics of modeling
-----------------------------------

For this modeling, the "cable" and "concrete" nodes are combined.

The figure below gives a simplified representation of the mesh.


.. image:: images/Object_17.svg
    :width: 416
    :height: 184


.. _RefImage_Object_17.svg:

The concrete plate is represented by 10 DKT elements, supported by 10 QUAD4 meshes.

A thickness :math:`e\mathrm{=}\mathrm{0,6}m` is assigned to it, as well as a concrete material for which the behaviors ELAS (Young's modulus :math:`{E}_{b}\mathrm{=}{3.10}^{10}\mathit{Pa}`) and BPEL_BETON are defined: the characteristic parameters of this relationship are set to 0 because the tension losses along the prestress cable are neglected.

Nodes :math:`\mathit{N1}`, :math:`\mathit{N5}`, and :math:`\mathit{N3}` are embedded: :math:`\mathit{DX},\mathit{DY},\mathit{DZ},\mathit{DRX},\mathit{DRY}` and :math:`\mathit{DRZ}` are locked.

The cable is represented by 5 MECA_BARRE elements, supported by 5 SEG2 meshes.

An area of right cross section :math:`{S}_{a}\mathrm{=}\mathrm{1,5}{.10}^{\mathrm{-}4}{m}^{2}` is assigned to them, as well as a steel material for which the behaviors ELAS (Young's modulus :math:`{E}_{a}\mathrm{=}\mathrm{2,1}{.10}^{11}\mathit{Pa}`) and BPEL_ACIER are defined: the characteristic parameters of this relationship are set to 0 (tension losses neglected), with the exception of the elastic limit stress for which a zero value is unlawful (:math:`{f}_{\mathit{prg}}\mathrm{=}\mathrm{1,77}{.10}^{9}\mathit{Pa}`).

Tension :math:`{F}_{0}\mathrm{=}{2.10}^{5}N` is applied to nodes :math:`\mathit{N5}` and :math:`\mathit{N6}`. This tension value is consistent with the cross-section and elastic limit values, for a strand-type pretension cable.

The calculation of the equilibrium state of the plate and cable assembly is carried out in a single step, the behavior being elastic.


Calculation steps and functionalities tested
-------------------------------------------

The main calculation steps correspond to the functionalities that we want to validate:


* operator DEFI_MATERIAU: definition of the behavioral relationships BPEL_BETON and BPEL_ACIER, in the particular case where the tension losses along the prestress cable are neglected (values by default parameters);


* operator DEFI_CABLE_BP: determination of a constant tension profile along the prestress cable, the losses being neglected; calculation of the coefficients of the kinematic relationships between the degrees of freedom of the cable nodes and the degrees of freedom of the "neighboring" nodes of the concrete plate;


* operator AFFE_CHAR_MECA: definition of a RELA_CINE_BP load;


* operator STAT_NON_LINE, option COMPORTEMENT: calculation of the equilibrium state taking into account the load type RELA_CINE_BP.


* operator POST_RELEVE_T, NOM_CMP ='N' across the entire field SIEF_ELNO.