3. Modeling A#

3.1. Characteristics of modeling#

Discrete elements of stiffness, damping and mass.

_images/Object_8.svg

Characteristics of the elements:

DISCRET:

nodal masses

M_ TR_D_N

linear stiffness

K_ TR_D_L

linear amortization

A_ TR_D_L

No boundary conditions, in all nodes: \(\mathrm{DX},\mathrm{DY},\mathrm{DZ},\mathrm{DRX},\mathrm{DRY},\mathrm{DRZ}\) free.

Node names: \({P}_{1}=\mathrm{N1}\), \({P}_{2}=\mathrm{N2}\), \({P}_{3}=\mathrm{N3}\).

Calculation method:

Full modal integration with Newmark (\(\alpha =\mathrm{0,25}\), \(\delta =\mathrm{0,5}\)),

No time: \(\Delta t={10}^{-\mathrm{4s}}\) then modal recombination.

Observation time: \(\mathrm{5s}\).

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 point \({P}_{3}\)

Time

Move

Move

Difference

(\(s\))

Reference (\(m\))

Aster (\(m\))

(%)

0.09

6.7395 E-6

6.73326 E-6

-0.093

0.32

1.1019 E-5

1.10002 E-6

-0.171

1.18

3.6683 E-5

3.66122-5

-0.193

4.92

1.6615 E-4

1.65849 E-4

-0.181

  • Point \({P}_{3}\) speed

Time

Speed

Speed

Speed

Difference

(\(s\))

Reference (\({\mathrm{m.s}}^{-1}\))

Aster (\({\mathrm{m.s}}^{-1}\))

(%)

0.05

1.3425 E-4

1.34131 E-4

-0.088

0.32

-6.4111 E-5

-6.41097 E-4

-0.002

1.18

1.6104 E-5

1.60598 E-5

-0.274

3.55

4.4262 E-5

4.41720 E-5

-0.203

  • Acceleration of point \({P}_{3}\)

Time

Acceleration

Acceleration

Difference

(\(s\))

Reference (\({\mathrm{m.s}}^{-2}\))

Aster (\({\mathrm{m.s}}^{-2}\))

(%)

0.09

-3.5694 E-3

-3.56634 E-3

-0.086

0.18

-4.3924 E-3

-4.38933 E-3

-0.070

0.55

4.3766 E-3

4.37283 E-3

-0.086

1.18

4.2459 E-3

4.24264 E-3

-0.077

4.92

-4,2233 E-3

-4,21962 E-3

-0.087

  • Relative displacement of point \({P}_{3}\) in relation to point \({P}_{1}\)

Time

\({u}_{3}-{u}_{1}\)

\({u}_{3}-{u}_{1}\)

Difference

(\(s\))

Reference (\(m\))

Aster (\(m\))

(%)

0.18

8.0987 E-6

8.04800 E-6

-0.626

0.55

-6,2246 E-6

-6,21194 E-6

-0.203

0.82

5.3064 E-6

5.34121 E-6

0.656

1.18

-4.5552 E-6

-4.52071 E-6

-0.757

1.92

-3.0416 E-6

-3.04417 E-6

0.085

3.55

1.8448 E-6

1.82742 E-6

-0.942

4.92

1.4832 E-6

1.47526 E-6

-0.535

3.4. notes#

In addition to the comparison for the values tested, it is checked that the kinematic variables other than those related to the following translation \(x\) remain zero.