4. Examples#
4.1. Calculation of static modes in unitary imposed displacement#
Calculation of static modes in unitary imposed displacement.
mode :math:`\Psi`solution de :math:`\mathrm{\{}\begin{array}{c}\Psi \mathrm{=}\mathrm{-}{K}^{\mathrm{-}1}\mathrm{\cdot }{}^{t}B^{\mathrm{-}1}\mathrm{\cdot }{\lambda }_{i}\\ B\mathrm{\cdot }\Psi \mathrm{=}{V}_{i}\end{array}`
|
with |
\(K\) |
: |
matrice de rigidité
|
\({V}_{i}\) |
: |
vecteur valant :math:`1.`pour les composantes :math:`\mathrm{DX}`et :math:`\mathrm{DY}`du groupe de nœuds base.
|
||
\({\lambda }_{i}\) |
: |
réactions d’appui sur la liaison :math:`B`du groupe de nœuds base.
|
||
MODE_STAT =_F (GROUP_NO = “base”, (AVEC_CMP =( “DX”, “DY”),), );
4.2. Calculation of static modes in unit imposed force#
Calculation of static modes in unit imposed force.
Fashion \(\Psi\) = \({K}^{-1}{F}_{i}\) |
with |
\(K\) |
: |
matrice de rigidité
|
\({F}_{i}\) |
: |
vecteur valant :math:`1.`pour les composantes :math:`\mathrm{DX}`et :math:`\mathrm{DY}`du groupe de nœuds base.
|
||
FORCE_NODALE =_F (GROUP_NO = “base”, (AVEC_CMP =( “DX”, “DY”),), );
4.3. Calculation of static modes (or pseudo-modes) with uniform unitary acceleration in the 3 directions#
Calculation of static modes with uniform unit acceleration in the 3 directions.
MATR_MASS = mass, PSEUDO_MODE =_F (AXE =( “X”, “Y”, “Z”),), );
4.4. Calculation of static modes (or pseudo-modes) under unitary imposed acceleration#
Calculation of static modes under unitary imposed acceleration.
MATR_MASS = mass, PSEUDO_MODE =_F (GROUP_NO = “base”, (AVEC_CMP =( “DX”, “DY”),), );
4.5. Calculation of coupling modes#
Coupling modes :math:`\Psi =T\Phi` are the static escalation of the :math:`\Phi` modes of the reduced problem
(4.1)#\[ \begin{align}\begin{aligned} [{T} ^ {T} (K- {\ omega} ^ {2} M) T]\ Phi =0\\ \ textrm {,}\end{aligned}\end{align} \]
where :math:`T` are static modes in imposed displacement. We obviously don't explicitly calculate :math:`T` in this case. The modes are calculated by an approximate method detailed in reference [:external:ref:`R4.06.02 <R4.06.02>`].
minter = MODE_STATIQUE (MATR_RIGI = stiffness, MATR_MASS = mass, MODE_INTERF =_F (GROUP_NO = “base”, AVEC_CMP =( “DX”, “DY”), NB_MODE =10, SHIFT =1. , ), );