B modeling
==============


Characteristics of modeling
-----------------------------------

The discrete element modeling is the same as in § :ref:`3.1 <RefHeading___Toc823_2013950394>`. The only difference lies in the way in which the second mode is specified for all analyses on a truncated modal basis: the second mode is specified explicitly by imposing on the nodes :math:`\mathit{NO2}`, :math:`\mathit{NO}3` and :math:`\mathit{NO}4` a displacement :math:`\mathit{DX}` corresponding to the reference modal deformation of § :ref:`2 <RefHeading___Toc 21916_2013950394>`. This is representative of situations where certain modes are the result of experimental reconstruction and specified by imposed displacements.


Characteristics of the mesh
----------------------------

Same as § :ref:`3.2 <RefHeading___Toc 21931_2013950394>`.


Tested sizes and results
------------------------------

The tested quantities, reference values and tolerances are the same as in § :ref:`3.3 <RefHeading___Toc 21934_2013950394>`. This makes it possible to ensure that the various static correction methods work in the same way with (i) a fully calculated modal base or (ii) a modal base in which certain modes have been given by imposed displacements.

The results obtained are summarized in the table below:

Values for the relative displacement of node :math:`\mathrm{NO4}` at time :math:`t=\mathrm{19,4}s` (m):


.. csv-table::

    "modal basis", "Reference", "Tolerance"
    "truncated base", "-0.011301"," 0.1%"
    "full base", "-0.011301", "1.e -04%"
    "static correction*a posteriori*", "-0.011301"," 0.1%"
    "static correction*a priori*, pseudo-mode, with re-orthogonalization", "-0.011301", "1.e -04%"
    "static correction*a priori*, static force-imposed modes, with re-orthogonalization", "-0.011301", "1.e -04%"
    "static correction*a priori*, pseudo-mode, static force-imposed modes, with re-orthogonalization", "-0.011301", "1.e -04%"


Values for the relative displacement of node :math:`\mathrm{NO2}` at time :math:`t=\mathrm{19,4}s` (m):


.. csv-table::

    "modal basis", "Reference", "Tolerance"
    "truncated base", "7.33162E-04"," 123.0%"
    "full base", "7.33162E-04", "1.0E -04%"
    "static correction*a posteriori*", "7.33162E-04"," 19.5%"
    "static correction*a priori*, pseudo-mode, with re-orthogonalization", "7.33162E-04", "1.0E -04%"
    "static correction*a priori*, static force-imposed modes, with re-orthogonalization", "7.33162E-04", "1.0E -04%"
    "static correction*a priori*, pseudo-mode, static force-imposed modes, with re-orthogonalization", "7.33162E-04", "1.e -04%"