3. Modeling#

3.1. Characteristics of modeling#

The skate is modelled by a single-node mesh (type POI1), located at rest in \(O\mathrm{=}(\mathrm{0,}\mathrm{0,}0)\). The obstacle is of the “PLAN_Z” type. To avoid having a shock with the symmetric plane, we shift the center of the two planes sufficiently: ORIG_OBST =( -0.5,0.,0.,.,). As the real game between the skate and the plane on the right must be \(1\mathit{mm}\), we use an artificial game JEU =( 0.5+game_shock).

_images/100000000000031A000001540392815A8755E460.tif

Figure 3.1-a : Modeled geometry

The temporal integration is carried out over a period of time \(T=4s\) either with the Euler diagram, or with the diagram of centered differences (“ADAPT_ORDRE2” which is forced at a constant time step thanks to the parameters COEF_MULT_PAS =1.0, COEF_DIVI_PAS =1.0). The problem is steep (the ratio of the stiffness between the free flight and contact phases is of the order of 5000), it is therefore necessary to use a very low time step equal to \(\Delta t\mathrm{=}4\mathrm{\cdot }{10}^{\mathrm{-}6}s\).

A calculation with “ADAPT_ORDRE2” is also carried out with an effectively variable step, the aim of which is not precision, but simply the verification of the adequacy between contact forces and kinematics.

3.2. Characteristics of the mesh#

The mesh consists of a single node and a single POI1 type mesh.

3.3. Tested sizes and results#

3.3.1. Energy and kinematic balance#

In the following tables, the values of the energy error and of a few moments of contact entry/exit are given.

  • Euler diagram:

Values

Reference

Aster

Tolerance

\({\mathrm{erreur}}_{\mathrm{globale}}^{\mathrm{énergie}}\)

0J

0.092 J

0.01J

1st contact entry (s)

2.4867876 E-02 s

2.4868 E-02 s

1.2E-5 s

1st contact output (s)

2.5260518 E-02 s

2.5264 E-02 s

1.2E-5 s

last contact entry (s)

3.886525493 E+00 s

3.886528 E+00 s

1.2E-5 s

last contact output

3.886916559 E+00 s

3.886916 E+00 s

1.2E-5 s

Table 4.1-1 : Results for the Euler schem

  • Diagram of centered differences:

Values

Reference

Aster

Tolerance

\({\mathrm{erreur}}_{\mathrm{globale}}^{\mathrm{énergie}}\)

0J

0.063M

0.1J

1st contact entry (s)

2.4867876 E-02 s

2.4868 E-02 s

1.2E-5 s

1st contact output (s)

2.5260518 E-02 s

2.5264 E-02 s

1.2E-5 s

last contact entry (s)

3.886525493 E+00 s

3.886528 E+00 s

1.2E-5 s

last contact output

3.886916559 E+00 s

3.886916 E+00 s

1.2E-5 s

Table 4.1-2 : Results for the centered differences scheme

3.3.2. Adequacy between contact force and kinematics#

Value

Reference

Aster

Tolerance

\({\mathrm{erreur}}_{\mathrm{globale}}^{\mathrm{force}}\)

0N

2.22E-10N

1.E-8N

Table 4.2-1 : Results for the adequacy between contact force and kinematic