3. Modeling A#

3.1. Characteristics of modeling#

The figure below gives a simplified representation of the mesh.

_images/Object_16.svg

The concrete plate is represented by an element DKT, supported by a quadrangle mesh with 4 knots.

A thickness \(e\mathrm{=}\mathrm{0,6}m\) is assigned to it, as well as a concrete material for which the behaviors ELAS (Young’s modulus \({E}_{b}\mathrm{=}{3.10}^{10}\mathit{Pa}\)) 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.

Node \(\mathit{NB001001}\) is embedded: DX, DY, DZ, DZ, DRX, DRY, and DRZ are blocked. Node \(\mathit{NB002001}\) is pressed bi-laterally: DX and DZ are locked.

The cable is represented by 4 MECA_BARRE elements, supported by 4 mesh segments with 2 knots.

An area of right cross section \({S}_{a}\mathrm{=}\mathrm{1,5}{.10}^{\mathrm{-}4}{m}^{2}\) is assigned to them, as well as a steel material for which the behaviors ELAS (Young’s modulus \({E}_{a}\mathrm{=}\mathrm{2,1}{.10}^{11}\mathit{Pa}\)) 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 (\({f}_{\mathit{prg}}\mathrm{=}\mathrm{1,77}{.10}^{9}\mathit{Pa}\)).

Tension \({F}_{0}\mathrm{=}{2.10}^{5}N\) is applied to nodes \(\mathit{NC001001}\) and \(\mathit{NC001005}\). 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.

3.2. 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.