Examples ======== Calculation of static modes in unitary imposed displacement ---------------------------------------------------------- .. code-block:: text Calculation of static modes in unitary imposed displacement. +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----+----------------------+-+---------------------------------------------------------------------------------------------------------------------------------------+ | .. code:: |with|:math:`K` |:| .. code:: | + + + + + + | 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}` | | | | matrice de rigidité | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----+----------------------+-+---------------------------------------------------------------------------------------------------------------------------------------+ | | |:math:`{V}_{i}` |:| .. code:: | + + + + + + | | | | | vecteur valant :math:`1.`pour les composantes :math:`\mathrm{DX}`et :math:`\mathrm{DY}`du groupe de nœuds base. | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----+----------------------+-+---------------------------------------------------------------------------------------------------------------------------------------+ | | |:math:`{\lambda }_{i}`|:| .. code:: | + + + + + + | | | | | réactions d’appui sur la liaison :math:`B`du groupe de nœuds base. | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----+----------------------+-+---------------------------------------------------------------------------------------------------------------------------------------+ .. code-block:: text mstat = MODE_STATIQUE (MATR_RIGI = stiffness, MODE_STAT =_F (GROUP_NO = 'base', (AVEC_CMP =( 'DX', 'DY'),), ); Calculation of static modes in unit imposed force ---------------------------------------------------- .. code-block:: text Calculation of static modes in unit imposed force. +----------------------------------------------+----+---------------+-+---------------------------------------------------------------------------------------------------------------------------------------+ |Fashion :math:`\Psi` = :math:`{K}^{-1}{F}_{i}`|with|:math:`K` |:| .. code:: | + + + + + + | | | | | matrice de rigidité | +----------------------------------------------+----+---------------+-+---------------------------------------------------------------------------------------------------------------------------------------+ | | |:math:`{F}_{i}`|:| .. code:: | + + + + + + | | | | | vecteur valant :math:`1.`pour les composantes :math:`\mathrm{DX}`et :math:`\mathrm{DY}`du groupe de nœuds base. | +----------------------------------------------+----+---------------+-+---------------------------------------------------------------------------------------------------------------------------------------+ .. code-block:: text mstat = MODE_STATIQUE (MATR_RIGI = stiffness, FORCE_NODALE =_F (GROUP_NO = 'base', (AVEC_CMP =( 'DX', 'DY'),), ); Calculation of static modes (or pseudo-modes) with uniform unitary acceleration in the 3 directions ---------------------------------------------------------------------------------------- .. code-block:: text Calculation of static modes with uniform unit acceleration in the 3 directions. .. csv-table:: "mode :math:`\Psi` = :math:`{K}^{-1}(M{A}_{i})` ", "with", ":math:`K` ", ", ":", "stiffness matrix" "", "", ":math:`M` ", ", ":", "mass matrix" "", "", ":math:`{A}_{i}` ", ":", "unit vector in the :math:`i` direction." .. code-block:: text mstat = MODE_STATIQUE (MATR_RIGI = stiffness, MATR_MASS = mass, PSEUDO_MODE =_F (AXE =( 'X', 'Y', 'Z'),), ); Calculation of static modes (or pseudo-modes) under unitary imposed acceleration ----------------------------------------------------------------------------- .. code-block:: text Calculation of static modes under unitary imposed acceleration. .. csv-table:: "mode :math:`\Psi` = :math:`{K}^{-1}(M{A}_{i})` ", "with", ":math:`K` ", ", ":", "stiffness matrix" "", "", ":math:`M` ", ", ":", "mass matrix" "", "", ":math:`{A}_{i}` ", ":", "unit vector for components :math:`\mathit{DX}` and :math:`\mathit{DY}` of the group of nodes :math:`\mathit{base}`" .. code-block:: text mstat = MODE_STATIQUE (MATR_RIGI = stiffness, MATR_MASS = mass, PSEUDO_MODE =_F (GROUP_NO = 'base', (AVEC_CMP =( 'DX', 'DY'),), ); Calculation of coupling modes ---------------------------- .. code-block:: text Coupling modes :math:`\Psi =T\Phi` are the static escalation of the :math:`\Phi` modes of the reduced problem .. math:: :label: eq-1 [{T} ^ {T} (K- {\ omega} ^ {2} M) T]\ Phi =0 \ textrm {,} .. code-block:: text 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 `]. minter = MODE_STATIQUE (MATR_RIGI = stiffness, MATR_MASS = mass, MODE_INTERF =_F (GROUP_NO = 'base', AVEC_CMP =( 'DX', 'DY'), NB_MODE =10, SHIFT =1. , ), );