# Parameter study of a single cross-section#

## Problem description#

This example carries out a simple parameter study of a single cross-section by varying two design variables. The base design of this cross-section has an airfoil profile with a main box-type spar, which is typically seen in helicopter rotor blades. Here, a template of this type of design is used (airfoil_gbox_uni.xml.tmp), which is provided along with the iVABS package. Two parameters, $$a^{wl}_2$$ and $$a^{wt}_2$$, control the locations of the front and back spar webs, as shown in Fig. 2.

The leading web location $$a^{wl}_2$$ is varied from 0.8 to 0.9. The trailing web location $$a^{wt}_2$$ is varied from 0.5 to 0.6.

Three beam properties are inspected in this example: torsional stiffness $$GJ$$, flap-wise bending stiffness $$EI_f$$, and chord-wise bending stiffness $$EI_c$$.

This example uses a full factorial study method multidim_parameter_study method of Dakota. Each dimension (design variable) is divided into two equal length intervals, resulting three levels (factors). Then all possible combinations of the two design variables are evaluated, i.e., nine evaluations in total.

## Input#

Base design template: airfoil_gbox_uni.xml.tmp

### Fixed parameters#

Table 1 Fixed parameters#

Keyword

Type

Value

Description

mdb_name

String

“material_database_us_ft”

Material database file name

airfoil

String

“SC1095.dat”

Airfoil data file name

airfoil_point_direction

Integer number

-1

Direction of point arrangement (clock-wise)

lam_spar_1

String

“T300 15k/976_0.0053”

Lamina choice for the spar layup

lam_front

String

“T300 15k/976_0.0053”

Lamina choice for the front (leading) layup

lam_back

String

“T300 15k/976_0.0053”

Lamina choice for the back (trailing) layup

lam_skin

String

“T300 15k/976_0.0053”

Lamina choice for the skin layer

lam_cap

String

“Aluminum 8009_0.01”

Lamina choice for the cap layer

mat_nsm

String

Material choice for the non-structural mass

mat_fill_front

String

“Rohacell 70”

Material choice for the front filling component

mat_fill_back

String

“Plascore PN2-3/16OX3.0”

Material choice for the back filling component

mat_fill_te

String

“Plascore PN2-3/16OX3.0”

Material choice for the trailing edge filling component

gms

Real number

0.004

Global mesh size (with respect to the scale of the actual cross-section)

rnsm

Real number

0.001

Radius of the non-structural mass (non-dimensional)

### Design variables#

Table 2 Design variables#

Design variable

Type

Lower bound

Upper bound

Description

a2p1

Real number

0.8

0.9

Horizontal location of the front (leading) spar web ($$a^{wl}_2$$ non-dimensional)

a2p3

Real number

0.5

0.6

Horizontal location of the back (trailing) spar web ($$a^{wt}_2$$ non-dimensional)

## Result#

A list of the study input and output of all evaluations can be found in the output file cs_param_study_tabular.dat.

Table 3 Input and output of all evaluations#

Eval. ID

$$a^{wl}_2$$

$$a^{wt}_2$$

$$GJ$$

$$EI_f$$

$$EI_c$$

[$$\mathrm{lb \cdot ft}$$]

[$$\mathrm{lb \cdot ft}$$]

[$$\mathrm{lb \cdot ft}$$]

1

0.8

0.5

1840.32471

11197.46512

415399.2403

2

0.85

0.5

1964.208757

11869.13028

443812.0122

3

0.9

0.5

2075.750735

12416.16107

477884.239

4

0.8

0.55

1725.977801

10608.58915

409504.7557

5

0.85

0.55

1849.543115

11280.24525

436552.1801

6

0.9

0.55

1960.98994

11827.27314

469132.32

7

0.8

0.6

1603.070759

9954.565352

407423.6863

8

0.85

0.6

1725.791505

10626.19938

433432.1767

9

0.9

0.6

1836.948701

11173.19896

464843.1338

Correlation matrices between inputs and outputs can be foundin the file cs_param_study_results.txt.

Table 4 Partial correlations (I/O)#

$$GJ$$

$$EI_f$$

$$EI_c$$

$$a^{wl}_2$$

9.9931687970e-01

9.9778765807e-01

9.9718993466e-01

$$a^{wt}_2$$

-9.9933614526e-01

-9.9787290438e-01

-9.1880696915e-01

Table 5 Partial rank correlations (I/O)#

$$GJ$$

$$EI_f$$

$$EI_c$$

$$a^{wl}_2$$

9.4672926241e-01

9.3704257133e-01

1.0000000000e+00

$$a^{wt}_2$$

-9.7026934103e-01

-9.5257934442e-01

-1.0000000000e+00

Table 6 Simple correlations (All)#

$$a^{wl}_2$$

$$a^{wt}_2$$

$$GJ$$

$$EI_f$$

$$EI_c$$

$$a^{wl}_2$$

1.0000000000e+00

0.0000000000e+00

7.0179013104e-01

6.9934359720e-01

9.8236434169e-01

$$a^{wt}_2$$

0.0000000000e+00

1.0000000000e+00

-7.1191083397e-01

-7.1326523789e-01

-1.7179552901e-01

$$GJ$$

7.0179013104e-01

-7.1191083397e-01

1.0000000000e+00

9.9976390358e-01

8.1008496932e-01

$$EI_f$$

6.9934359720e-01

-7.1326523789e-01

9.9976390358e-01

1.0000000000e+00

8.0653484855e-01

$$EI_c$$

9.8236434169e-01

-1.7179552901e-01

8.1008496932e-01

8.0653484855e-01

1.0000000000e+00

Table 7 Simple rank correlations (All)#

$$a^{wl}_2$$

$$a^{wt}_2$$

$$GJ$$

$$EI_f$$

$$EI_c$$

$$a^{wl}_2$$

1.0000000000e+00

0.0000000000e+00

5.7975090436e-01

6.3245553203e-01

9.4868329805e-01

$$a^{wt}_2$$

0.0000000000e+00

1.0000000000e+00

-7.9056941504e-01

-7.3786478737e-01

-3.1622776602e-01

$$GJ$$

5.7975090436e-01

-7.9056941504e-01

1.0000000000e+00

9.8333333333e-01

8.0000000000e-01

$$EI_f$$

6.3245553203e-01

-7.3786478737e-01

9.8333333333e-01

1.0000000000e+00

8.3333333333e-01

$$EI_c$$

9.4868329805e-01

-3.1622776602e-01

8.0000000000e-01

8.3333333333e-01

1.0000000000e+00

## Files for this example#

### Input files#

airfoil_gbox_uni.xml.tmp

This is the design template for the type of cross-section having an airfoil profile with a main box-type spar. Depending on the problem, one or more design templates might be needed. More details on design templates can be found in Section Cross-sectional Design Templates.

material_database_us_ft.xml

This is the local material database used by the cross-section. There is also an global database (MaterialDB.xml) located in ivabs/bin. Users can add more contents in both files. More details on the material inputs can be found in Section Materials and layups.

SC1095.dat

This is the airfoil data file for the cross-section. Depending on the problem, one or more airfoil data files might be needed.

cs_param_study.yml

This is the main input file required for all cases. It contains most of the information needed. More details on the main input file can be found in Section Guide to Main Input File.

run.py

This is the startup script. It is required for all cases, but no changes needed and can be directly copied to a different working directory.

### Output files#

Current version of iVABS uses Dakota as the driver. Hence, most output files are related to Dakota.

cs_param_study.dakota

This is the Dakota input generated by iVABS from cs_param_study.yml.

cs_param_study.out

This is the Dakota main output file including a summary of the process.

cs_param_study.results.txt

This is the Dakota result file. Contents could be different for different Dakota methods.

cs_param_study_tabular.dat

This contains a table of inputs and outputs of each evaluation/iteration.

cs_param_study.rst

This is the Dakota restart file. If the Dakota process stops for some reason, you can try to continue the process from the stopping point, using the following command:

dakota -i cs_param_study.dakota -read_restart cs_param_study.rst
cs_param_study.err

This is the Dakota error file.

evals/eval.#/

Each directory contains all input and output files for each evaluation/iteration. Links for the five input files are also generated in these directories.