C, E models
==================

Characteristics of the models
----------------------------------

The models are above all a test of DYNA_NON_LINE with keyword SCHEMA_TEMPS (FORMULATION =' ACCELERATION '), whose results are compared with DYNA_NON_LINE with keyword SCHEMA_TEMPS (FORMULATION =' DEPLACEMENT').

The mass-spring systems are modelled, as in modeling A, by a discrete element with 3 degrees of freedom DIS_T. Only modeling with one degree of freedom is tested.

**Problem modeling:**


.. image:: images/1000000000000126000000E45727437848CB9ED0.jpg
    :width: 2.1154in
    :height: 1.5835in


.. _RefImage_1000000000000126000000E45727437848CB9ED0.jpg:

**Figure** 7.1-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 element of type DIST_T on a POI1 mesh is used to simulate the impact of the beam on a rigid wall: any impacts between the beam and the obstacle are taken into account as being forces internal to this element. It is assigned a non-linear shock-type behavior (DIS_CHOC for modeling C and DIS_CONTACT for modeling E) via the definition of the characteristics DIS_CONTACT of the command DEFI_MATERIAU.

The thickness of material surrounding the shock node in the direction in question is specified by the operand DIST_1 of the DEFI_MATERIAU command. In the case treated, we choose DIST_1 :math:`=0.4495` and JEU :math:`=0.45` so that at the initial moment, the shock node and the obstacle are separated from the game :math:`j=5.{10}^{-4}\mathrm{mm}` (cf. figure).

The seismic load, due to the imposed movements of node :math:`\mathrm{NO1}`, is calculated by the operator CALC_CHAR_SEISME. A charge concept is then created from the VECT_ASSE operand of the AFFE_CHAR_MECA command.

We use the explicit NEWMARK integration diagram of the DIFFERENCES CENTREES type with a time step of :math:`{10}^{-3}s`. The calculation by DYNA_NON_LINE with keyword SCHEMA_TEMPS (FORMULATION =' ACCELERATION ') is performed in the modal space, the non-linearity being due to the shock and therefore remaining local.


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

The mesh associated with the model consists of 2 nodes, a SEG2 mesh of type DIS_T and a point mesh POI1 of type DIS_T.