3. Modeling A#

3.1. Characteristics of modeling#

Discrete elements of stiffness, damping and mass.

_images/Object_9.svg

Characteristics of the elements:

DISCRET:

nodal mass

M_T_D_N

linear stiffness

K_T_D_L (\({k}_{\mathrm{N1N2}}=k/10\), \({k}_{\mathrm{N2N3}}=\mathrm{10k}\))

linear amortization

A_T_D_L

Boundary conditions: at node \(\mathrm{N1}\) DDL_IMPO \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=0\).

Node names: \(A=\mathrm{N1}\), \(C=\mathrm{N2}\), \(B=\mathrm{N3}\).

Calculation methods:

  • Integration into physical space with Newmark (\(\alpha =\mathrm{0,25}\), \(\delta =\mathrm{0,5}\))

No time \(\Delta t={10}^{-3}s\)

  • Full modal integration with Euler

No time \(\Delta t={10}^{-3}s\) then modal recombination

  • Full modal integration with 2nd order adaptive \(\Delta t\)

No initial time \(\Delta t={10}^{-3}s\) then modal recombination

  • Full modal integration with \(\Delta t\) adaptive using the Runge-Kutta order method (32). Relative error tolerance is \({10}^{-5}\).

  • Full modal integration with \(\Delta t\) adaptive using the Runge-Kutta order method (54). Relative error tolerance is \({10}^{-6}\).

Observation time: 3 s.

3.2. Characteristics of the mesh#

Number of knots: 3

Number of meshes and type: 2 meshes SEG2

3.3. Tested sizes and results#

  • Move (\(m\)) from point \(B\)

Time

Reference

(\(s\))

0.27

3.0927 E-3

0.53

8.7953 E-4

0.80

2.4669 E-3

1.25

-1.0980 E-3

1,51

7,8754 E-4

1.78

-5.6508 E-4

2.05

4.0502 E-4

2.31

-2.9012 E-4

2.58

2.0831 E-4

2.85

-1.4943 E-4

  • Speed (\({\mathrm{m.s}}^{-1}\)) of point \(B\)

Time

Reference

(\(s\))

0.11

1.8347 E-2

0.39

-1.3140 E-2

0.66

9.3509 E-3

0.93

-6.7080 E-3

1.11

-1.5863 E-2

1.37

1.1157 E-2

1.64

-7.9838 E-3

1.90

5.7108 E-3

2.17

-4.0998 E-3

2.44

2.9405 E-3

2.71

-2.1073 E-3

2.97

1.5105 E-3

3.4. notes#

The results are tested at the level of the respective peaks of movement and speed where the values are the most significant.