3. Modeling A#

3.1. Characteristics of modeling#

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

Problem modeling 1:

_images/Object_3.svg

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

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

_images/100000000000025800000112AD7819110BD920D0.jpg

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

Node \(\mathrm{NO1}\) is subject to enforced acceleration \({\gamma }_{1}(t)\), node \(\mathrm{NO4}\) to \({\gamma }_{2}(t)=–{\gamma }_{1}(t)\). We calculate the relative displacement of the nodes \(\mathrm{NO2}\) and \(\mathrm{NO3}\), 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 \(Z\) 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 \(J=2j={10}^{-3}\mathrm{mm}\) (cf. figure).

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

We consider a reduced amortization \(\xi\) of 7% for all the calculated modes.

3.2. 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.