1. Reference problem#

_images/10000000000009C40000065E6827B592211D847D.jpg

1.1. Figure 1-1: numerical model meshNumerical model geometry#

  • Node coordinates \((m)\):

  • \(\mathit{N5}\mathrm{:}(0.42,\mathrm{-}0.93,0.176)\)

  • \(\mathit{N58}\mathrm{:}(0.412,0.0,0.0)\)

  • \(\mathit{N88}\mathrm{:}(1.4,0.0,0.45)\)

  • \(\mathit{N89}\mathrm{:}(1.5,0.0,0.45)\)

  • \(\mathit{N146}\mathrm{:}(0.42,0.93,0.176)\)

  • Thickness \((m)\):

  • \(\mathrm{e1}=0.05\) \(\mathrm{GROUP1}\)

  • \(\mathrm{e2}=0.01\) \(\mathrm{GROUP2},\mathrm{GROUP3},\mathrm{GROUP4},\mathrm{GROUP5},\mathrm{GROUP7}\)

  • \(\mathrm{e3}=0.011\) \(\mathrm{GROUP6}\)

  • \(\mathrm{e4}=0.016\) \(\mathrm{GROUP8}\)

  • formula

  • \(\mathit{GROUP10}\mathrm{:}(\mathit{N5},\mathit{N88},\mathit{N89},\mathit{N146})\)

1.2. Material properties#

      • \(\mathrm{GROUP1}\) to \(\mathrm{GROUP7}\)

  • \(E=7.2\times {10}^{10}\mathrm{Pa}\) Young’s module

  • \(\nu =0.34\) Poisson’s ratio

  • \(\rho =2700.0{\mathrm{kg.m}}^{-3}\) Density

      • \(\mathrm{GROUP8}\)

  • \(E=2.1\times {10}^{11}\mathrm{Pa}\) Young’s module

  • \(\nu =0.29\) Poisson’s ratio

  • \(\rho =7800.0{\mathrm{kg.m}}^{-3}\) Density

  • features for the \(\mathrm{GROUP9}\):

  • Stiffness matrix K_ TR_D_L: \(\left[\begin{array}{cc}K& -K\\ -K& K\end{array}\right]\)

with \([K]=\left[\begin{array}{cccccc}{10}^{12}& 0.& 0.& 0.& 0.& 0.\\ 0.& {10}^{12}& 0.& 0.& 0.& 0.\\ 0.& 0.& {10}^{12}& 0.& 0.& 0.\\ 0.& 0.& 0.& {10}^{8}& 0.& 0.\\ 0.& 0.& 0.& 0.& {10}^{8}& 0.\\ 0.& 0.& 0.& 0.& 0.& {10}^{8}\end{array}\right]\)

      • features for the \(\mathrm{GROUP10}\):

        • M_T_D_N mass matrix: \([M]=\left[\begin{array}{ccc}0.5& 0.& 0.\\ 0.& 0.5& 0.\\ 0.& 0.& 0.5\end{array}\right]\)

1.3. Boundary conditions and loads#

  • Imposed travel:

        • node \(\mathrm{N58}\): \(\mathrm{DRX}=\mathrm{DRY}=\mathrm{DRZ}=\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=0.0\)

1.4. Geometry of the experimental model#

_images/10000000000009C6000006607772B51676FDC276.jpg

Figure 1-2: experimental model mesh

Coordinates of the nodes formula \((m)\):

\(\mathit{N1011}\mathrm{:}(0.78;0.98;0.186)\)

\(\mathit{N1112}\mathrm{:}(0.42;\mathrm{-}0.98;0.186)\)

\(\mathit{N1205}\mathrm{:}(1.45;\mathrm{-}0.025;0.075)\)

Mesh group:

formula \(\mathit{NOEU}\): Set of the segment elements of the experimental model

1.5. Properties of the experimental model#

Characteristics for the formula \(\mathit{NOEU}\) mesh group:

        • K_T_D_N stiffness matrix: formula \(\left[\begin{array}{ccc}{10}^{12}& 0.& 0.\\ 0.& {10}^{12}& 0.\\ 0.& 0.& {10}^{12}\end{array}\right]\)

The mechanical characteristics of the experimental model are not intended to represent the physics of the structure, but to create the data structures necessary to read the experimental results (the operator LIRE_RESU in fact needs the matrices and nume_ddl associated with the structure to create the associated result data structure).