Modeling A
==============

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

Mass-spring systems are modelled by discrete elements with 3 degrees of freedom DIS_T.

**Problem modeling 1:**


.. image:: images/Object_3.svg
    :width: 467
    :height: 195


.. _RefImage_Object_3.svg:

**Figure** 3.1-a **:Modeling of a mass-spring system impacting a rigid wall**

Node :math:`\mathrm{no1}` is subject to an imposed acceleration :math:`{\gamma }_{1}(t)`. We calculate the relative displacement of node :math:`\mathrm{no2}`, its training displacement, and its absolute displacement.

An obstacle of type PLAN_Z (two parallel planes) is used to simulate the impact of the mass-spring system on a rigid wall. The normal to the shock plane is axis :math:`Z`, NORM_OBST: (0. 0. 1.). In order not to be hampered by the rebound of the oscillator symmetrically, this one pushes this one very far away (cf. figure).

From where:

• the origin of obstacle ORIG_OBST: (—1. 0. 0. );

• and the corresponding game game: 1.1005

**Problem modeling 2:**


.. image:: images/100000000000025800000112AD7819110BD920D0.jpg
    :width: 4.3165in
    :height: 1.9028in


.. _RefImage_100000000000025800000112AD7819110BD920D0.jpg:

**Figure** 3.1-b **: Modeling two mass-spring systems that collide**

Node :math:`\mathrm{NO1}` is subject to enforced acceleration :math:`{\gamma }_{1}(t)`, node :math:`\mathrm{NO4}` to :math:`{\gamma }_{2}(t)=–{\gamma }_{1}(t)`. We calculate the relative displacement of the nodes :math:`\mathrm{NO2}` and :math:`\mathrm{NO3}`, their training displacement and their absolute displacement.

The shock conditions between the two mass-spring systems are simulated by an obstacle of type BI_PLAN_Z (plane obstacle between two mobile structures). The normal to the shock plane is chosen along the :math:`Z` axis, i.e. NORM_OBST = (0. 0. 1.).

The thicknesses of material surrounding the shock nodes in the direction in question are specified by the operands DIST_1 and DIST_2. In the case treated, we choose DIST_1 = DIST_2 = 0.4495 so that at the initial moment, the two shock nodes are separated from the game :math:`J=2j={10}^{-3}\mathrm{mm}` (cf. figure).

The time integration is carried out with the Euler algorithm and a time step of :math:`\mathrm{2,5}\mathrm{.}{10}^{-\mathrm{4s}}`. The calculations are archived every 8 time steps.

We consider a reduced amortization :math:`\xi` of 7% for all the calculated modes.


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

The mesh associated with the problem composed of a mass-spring system abutting against a fixed wall and double shock is called the model that is associated with problem 2.

Mesh associated with the model model:

number of knots: 2;

number of meshes and types: 1 DIS_T.

Mesh associated with the bishock model:

number of knots: 4;

number of meshes and types: 2 DIS_T.