2. Modeling A: C_ PLAN#

C_ PLAN modeling. Static analysis with linear elastic behavior.

2.1. Optimization settings#

The basic structure was built considering the following parameters:

  • No mesh for grid interpolation in the X direction PAS_X = 0.05m

  • No mesh for grid interpolation in Y direction PAS_Y = 0.05m

  • Maximum length of LONGUEUR_MAX element = 7m

  • Minimum distance between stress peaks TOLE_BASE = 0.026

The optimization of the basic geometry according to diagram 1 (optimization of sections [Code_Aster, CALC_BT]) is carried out with the following parameters:

  • Maximum number of iterations MAXITER = 200

  • Optimization convergence threshold RESI_RELA_SECTION = 0.000001

  • Maximum section evolution rate per iteration CRIT_SECTION = 50%

  • Minimum element section SECTION_MINI = 10-10 m2

The optimization according to diagram TOPO (optimization of more topological sections) is carried out with the following additional parameters:

  • Optimization convergence threshold RESI_RELA_TOPO = 0.00001

  • Maximum element elimination rate CRIT_ELIM = 0.5

  • Control of pseudo-random variables INIT_ALEA = 0

2.2. Basic structure built#

_images/10000000000005C2000003BC49EC94663907F01C.png

Image 2.2-1: Basic structure: C_ PLAN

The basic structure is thus built within the macro command CALC_BT based on the results of the 2D modeling and considering the parameters defined previously.

2.3. Optimization SCHEMA = “SECTION”#

_images/10000000000006CC000003C66FC244CDB66B50AE.png

Image 2.3-1: Optimized Structure:C_ PLAN, SCHEMA = SECTION

Figure 2.3-1 shows the forces distributed among the elements of the structure at the end of the optimization process according to diagram SECTION (optimization of sections only).

The following table shows the geometric characteristics of the elements of the basic structure at the end of the optimization procedure. In order to facilitate the comparison of results, the numbering of the items (first column) has been manually changed.

COORD XI

COORD YI

COORD XJ

COORD YJ

TYPE

N

N

A

L

ENEL_ELEM

B1

0.45

0.00

0.00

0.25

0.25

2.30

BIELLE

-1.01E+06

2.87E-02

2.31

2.31

3.87E+04

B2

0.45

0.00

0.00

7.00

0.00

0.00

BIELLE

-6.46E-01

1.00E-06

6.55

6.55

1.30E-03

B3

0.45

0.00

0.00

2.00

0.50

BIELLE

-9.16E+04

2.62E-03

1.63

1.63

2.49E+03

T1

0.25

2.30

2.30

2.03

2.03

1.97

TIRANT

1.27E+06

2.54E-03

1.81

1.81

5.46E+04

B4

0.25

2.30

2.30

2.65

4.65

BIELLE

-4.92E+05

1.41E-02

3.36

3.36

2.75E+04

B5

0.25

2.30

2.30

4.75

4.75

4.68

BIELLE

-9.14E+05

2.61E-02

5.09

5.09

7.75E+04

T3

2.03

1.97

1.97

2.65

2.65

4.65

TIRANT

3.49E-05

6.99E-04

2.75

2.75

2.29E+04

T5

2.03

1.97

1.97

4.75

4.75

4.68

TIRANT

3.74E-01

1.00E-06

3.84

3.84

2.56E-05

T2

2.03

1.97

1.97

7.00

7.00

0.00

TIRANT

1.26E+06

2.52E-03

5.35

5.35

1.60E+05

T6

2.03

1.97

1.97

7.45

7.45

1.40

TIRANT

4.34E-01

1.00E-06

5.45

5.45

4.90E-05

T4

2.03

1.97

1.97

2.00

2.00

0.50

TIRANT

1.08E+05

2.15E-04

1.47

1.47

3.77E+03

B6

2.65

4.65

4.65

4.75

4.75

4.68

BIELLE

-2.73E+05

7.80E-03

2.10

2.10

9.55E+03

T7

2.65

4.65

4.65

7.00

7.00

0.00

TIRANT

1.22E-01

1.00E-06

6.37

6.37

4.53E-06

T8

2.65

4.65

4.65

7.45

1.40

TIRANT

2.30E-01

1.00E-06

5.80

5.80

1.46E-05

T9

2.65

4.65

4.65

2.00

2.00

0.50

TIRANT

1.00E+00

1.00E-06

4.20

4.20

2.01E-04

B7

4.75

4.68

4.68

7.00

7.00

0.00

BIELLE

-2.70E+06

7.71E-02

5.19

5.19

2.34E+05

T10

4.75

4.68

4.68

7.45

7.45

1.40

TIRANT

1.09E-01

1.00E-06

4.25

4.25

2.39E-06

B8

4.75

4.68

4.68

2.00

2.00

0.50

BIELLE

-1.63E+05

4.65E-03

5.00

5.00

1.36E+04

T11

7.00

0.00

0.00

7.45

1.45

1.40

TIRANT

4.13E-01

1.00E-06

1.47

1.47

1.19E-05

B9

7.00

0.00

0.00

2.00

2.00

0.50

BIELLE

-1.36E+00

1.00E-06

5.02

5.02

4.45E-03

B10

7.45

1.40

1.40

2.00

0.50

BIELLE

-8.29E-01

1.00E-06

5.52

5.52

1.81E-03

Table 2.3-1 : ****Optimized structure:C_ PLAN, SCHEMA = SECTION **

2.4. Optimization SCHEMA = “TOPO”#

Figure 2.3.5-a and Table 2.3.5-a show the distribution of forces in the elements of the structure at the last iteration. As for that in the results of section 2.3.4, the numbering of the elements (first column of Table 2.3.5-a) was manually changed for the elements denoted T1 and T2.

_images/10000000000006C6000003C85BE299ACE8153B1A.png

Image 2.4-1: Optimized Structure:C_ PLAN, SCHEMA = TOPO

#

COORD XI

COORD YI

COORD XJ

COORD YJ

TYPE

N

N

A

L

ENEL_ELEM

B1

4.75

4.68

4.68

7.00

7.00

0.00

BIELLE

-2.73E+06

7.79E-02

5.19

5.19

2.36E+05

B2

0.45

0.00

0.00

0.25

0.25

2.30

BIELLE

-1.01E+06

2.87E-02

2.31

2.31

3.87E+04

B3

0.25

2.30

2.30

4.75

4.75

4.68

BIELLE

-1.08E+06

3.09E-02

5.09

5.09

9.18E+04

B4

0.25

2.30

2.30

2.65

4.65

BIELLE

-3.64E+05

1.04E-02

3.36

3.36

2.04E+04

B5

2.65

4.65

4.65

4.75

4.75

4.68

BIELLE

-2.02E+05

5.77E-03

2.10

2.10

7.07E+03

B6

4.75

4.68

4.68

2.00

2.00

0.50

BIELLE

-4.14E+04

2.32E-03

5.00

5.00

1.76E+03

B7

0.45

0.00

0.00

2.00

0.50

BIELLE

-9.16E+04

2.62E-03

1.63

1.63

2.49E+03

T2

0.25

2.30

2.30

2.03

2.03

1.97

TIRANT

1.33E+06

2.65E-03

1.81

1.81

5.72E+04

T1

2.03

1.97

1.97

7.00

7.00

0.00

TIRANT

1.34E+06

2.68E-03

5.35

5.35

1.71E+05

T3

2.03

1.97

1.97

2.65

2.65

4.65

TIRANT

2.59E-05

5.17E-04

2.75

2.75

1.69E+04

B8

7.00

0.00

0.00

2.00

2.00

0.50

BIELLE

-6.48E+04

1.50E-06

5.02

5.02

6.69E+06

Table 2.4-1 . Optimized structure: C_ PLAN, SCHEMA = TOPO