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

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

The models tested are DIS_T on SEG2 meshes. The stiffness characteristics of the discretes are therefore of the type: K_T_D_L, K_T_D_N, M_T_D_N.

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

Number of knots: 3, number of stitches: 2, elements SEG2: 1, elements POI1: 1.

Boundary conditions and loads
-------------------------------------

Nodes N1, N2, N3 are stuck in the Y and Z directions.

Nodes N1 and N3 are subject to displacement :math:`U(t)`, speed :math:`V(t)`, and acceleration :math:`\gamma (t)` in the X direction.

The condition while traveling as a function of time:

:math:`U(t)={U}_{0}.\mathrm{sin}(2\pi .\mathit{f.t})/(2\pi .f)` with :math:`f=0.5\mathit{Hz}` and :math:`{U}_{0}=\mathrm{6.0mm}`

The speed condition as a function of time: :math:`V(t)=\dot{U}(t)`

The accelerating condition as a function of time: :math:`\gamma (t)=\ddot{U}(t)`

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

The quantities are tested in non-regression (with the tolerances by default) and against the values obtained with modeling A, with an accuracy of :math:`1.0E-02`.

The sizes tested are:

• the displacement of the N2 node,

• the effort at the N2,

• the power dissipated in the non-linear device,

• the anelastic displacement of the non-linear device,

• the cumulative anelastic displacement of the non-linear device.

The moments used to test the different quantities are those when the effort reaches an extreme.


.. image:: images/100000000000034A00000253C1A00ED1E200D11B.png
    :width: 3.9366in
    :height: 2.7717in


.. _RefImage_100000000000034A00000253C1A00ED1E200D11B.png:

**Figure** 4.4-a **: Comparison of force-displacement response at the node** **N2.**


.. image:: images/100000000000034A0000025365D8ACDBCE4A6DB2.png
    :width: 3.9366in
    :height: 2.7717in


.. _RefImage_100000000000034A0000025365D8ACDBCE4A6DB2.png:

**Figure** 4.4-b **: Force vs time comparison at the node** **N2.**


.. image:: images/100000000000034A00000253690D7977A626E668.png
    :width: 3.9366in
    :height: 2.7717in


.. _RefImage_100000000000034A00000253690D7977A626E668.png:

**Figure** 4.4-c **: Comparison of dissipation vs time.**


.. image:: images/100000000000034A000002530B004840EB4FA8AB.png
    :width: 3.9366in
    :height: 2.7717in


.. _RefImage_100000000000034A000002530B004840EB4FA8AB.png:

**Figure** 4.4-d **: Comparison of anelastic displacement vs time.**


.. image:: images/100000000000034A000002533B80EA5991241FB3.png
    :width: 3.9366in
    :height: 2.7756in


.. _RefImage_100000000000034A000002533B80EA5991241FB3.png:

**Figure** 4.4-e **: Comparison of cumulative anelastic displacement vs time.**