4. B modeling#

4.1. Characteristics of B modeling#

The system is modelled by:

  • 3 discrete elements K_T_D_L,

  • 2 discrete M_T_D_N elements.

4.2. Characteristics of the mesh#

The mesh consists of 3 SEG2 meshes.

4.3. Tested sizes and results#

4.3.1. Natural frequencies#

MODE

Reference

Tolerance \((\text{\%})\)

\(1\)

\(1.000E+00\)

\(0.1\)

\(2\)

\(2.236E+00\)

\(0.1\)

4.3.2. Static training modes#

Fashion \(1\): absolute movements \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(0.6E+00\)

\(0.1\)

\(\mathrm{NO3}\)

\(0.4E+00\)

\(0.1\)

Fashion \(2\): absolute movements \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(0.6E+00\)

\(0.1\)

\(\mathrm{NO3}\)

\(0.4E+00\)

\(0.1\)

4.3.3. Static modes for static correction#

Fashion \(1\): absolute movements \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(1.317E-02\)

\(0.1\)

\(\mathrm{NO3}\)

\(1.216E-02\)

\(0.1\)

Fashion \(2\): absolute movements \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(1.216E-02\)

\(0.1\)

\(\mathrm{NO3}\)

\(1.317E-02\)

\(0.1\)

4.3.4. Global response on a full modal basis#

4.3.4.1. Global response on a complete modal basis (single-support calculation)#

The \(1\) and \(2\) modes are taken into account.

  • calculation \(n°1\)

COMB_MODE =” SRSS “

For each active \(\mathrm{ddl}\) \(2\) and \(\mathrm{3 }\):

  • \(\mathrm{1 }\) mode response: \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\)

  • \(\mathrm{2 }\) mode response: \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\)

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative mode)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(1.01321E-02\)

\(0.1\)

\(\mathrm{NO3}\)

\(1.01321E-02\)

\(0.1\)

Global response on a complete modal basis (single-support calculation via a multi-support calculation correlated with the same \({\mathit{SRO}}_{\mathit{NO}1}\) spectrum at both supports) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The \(1\) and \(2\) modes are taken into account.

  • calculation \(n°2\)

COMB_MODE =” SRSS “

For each active \(\mathrm{ddl}\) \(2\) and \(\mathrm{3 }\):

  • \(\mathrm{1 }\) mode response: \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\)

  • \(\mathrm{2 }\) mode response: \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\)

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative mode)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(1.01321E-02\)

\(0.1\)

\(\mathrm{NO3}\)

\(1.01321E-02\)

\(0.1\)

4.3.4.2. Global response on a complete modal basis (correlated multi-support calculation)#

  • calculation \(n°3\)

COMB_MODE =” SRSS “

For each active degree of freedom \(2\) and \(\mathrm{3 }\):

  • answer of mode \(\mathrm{1 }\): \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\) (accumulation of supports)

  • answer of mode \(2\): \({R}_{2}={\mathit{Rm}}_{21}+{\mathit{Rm}}_{22}\) (accumulation of supports)

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative mode)

absolute displacements: \(\mathit{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathit{NO}2\)

\(7.22208e-3\)

\(0.1\)

\(\mathit{NO}3\)

\(7.22208e-3\)

\(0.1\)

  • calculation \(n°4\)

COMB_MODE =” SRSS “

For each active degree of freedom \(2\) and \(\mathrm{3 }\):

  • answer of mode \(\mathrm{1 }\): \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\) (accumulation of supports)

  • answer of mode \(\mathrm{2 }\): \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) (accumulation of supports)

  • global answer: :math: R=left| {R} | {R} _ {1}right|+left| {R} _ {2}right| (accumulation of modes)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(7.98287e-3\)

\(0.1\)

\(\mathrm{NO3}\)

\(7.98287e-3\)

\(0.1\)

  • calculation \(n°5\)

COMB_MODE =” DPC “

For each active degree of freedom \(2\) and \(\mathrm{3 }\):

  • answer of mode \(\mathrm{1 }\): \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\) (accumulation of supports)

  • answer of mode \(\mathrm{2 }\): \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) (accumulation of supports)

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative mode)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(7.22208e-3\)

\(0.1\)

\(\mathrm{NO3}\)

\(7.22208e-3\)

\(0.1\)

  • calculation \(n°6\)

COMB_MODE =” CQC “

For each active degree of freedom \(2\) and \(\mathrm{3 }\):

  • answer of mode \(\mathrm{1 }\): \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\) (accumulation of supports)

  • answer of mode \(\mathrm{2 }\): \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) (accumulation of supports)

  • global response: \(R=\sqrt{{\rho }_{12}{R}_{1}{R}_{2}}\) (cumulative mode)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(7.21139e-3\)

\(0.1\)

\(\mathrm{NO3}\)

\(7.21139e-3\)

\(0.1\)

  • calculation \(n°7\)

COMB_MODE =” DSC “

For each active degree of freedom \(2\) and \(\mathrm{3 }\):

  • answer of mode \(\mathrm{1 }\): \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\) (accumulation of supports)

  • answer of mode \(\mathrm{2 }\): \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) (accumulation of supports)

  • global response: \(R=\sqrt{{\rho }_{12}{R}_{1}{R}_{2}}\) (cumulative mode)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(7.20071e-3\)

\(0.1\)

\(\mathrm{NO3}\)

\(7.20071e-3\)

\(0.1\)