1

Statistical Optimization and Structural Analysis: Design of handmade custom Snowboards

Benoit CAILLAUD

4th Workshop on Structural Analysis of Lightweight Structures Innsbruck, 02.06.2016

2

Introduction

Materials & Structure, Geometry & Shape

1. Calibration of test feedback

Elaboration of questionnaires Overview of first results

2. Correlation of test results with board parameters

Direct Sensitivity Study and ranking of significant parameters Application: optimization of custom handmade snowboards

3. Optimization under Structural analysis

Ranking of significant parameters according to certain target outputs Board parameters – Analysis results – Test results

Conclusions

Agenda

3

±45° fabric UD Roving Input parameters:

- Wood species combinations - Thickness profile - Reinforcement & Matrix types - Layup (orientation, thickness, stacking sequence) - Material properties (E Modulus {El Et Glt}, Poisson ratios) - Tensile, Compessive, Flexural Strength {σe}, {σr} - Density, Toughness, Stability

UD Lin fiber Basalte UD Roving

Wood

Sidewalls

Composite reinforcements

Edges Layup

Thickness profile

Materials & Structure

4

Input parameters:

- L, Lm, Lcontact

- Lnose, Ltail, Lcamber

- Wnose, Wwaist, Wtail

- Stance - Setback - Hnose, Htail, Hcamber

- Curvatures: sidecut, camber, rockers

Dimensions

Camber profile

Sidecut shape

Inserts positions

0

10

20

30

40

-800 -600 -400 -200 0 200 400 600 800

Sidecut Radius [m]

Geometry & Shape

Portfolio

5

6

Calibration of test feedback

→ 25 output parameters including:

- Board behaviour (discipline related) - Board aspect (graphics, weight) - Terrain conditions (weather, snow quality)

→ 35 feedback results gathered over Winter 15/16

7

Calibration of test feedback

I’m gonna die I’m loving it Boring A lot of fun!

Very slippery Very grippy Too stiff Too soft

8

Sinks easily Floats easily

Calibration of test feedback

Too short Too long

- Quantify parameter influence (slope of fitted numerical model) → compare effects of different parameters input parameters must be standardized to their practical variation range

9

Correlation of test results

Direct Sensitivity Study:

- Compute Correlation Coefficients between two sets of {Inputs} and {Outputs} → determine which parameters are significant to which outputs

0

1

2

3

4

5

6

0 5 10 15 20

Taper [mm]

0

1

2

3

4

5

6

0 10 20 30 40 50

Bindings Setback [mm]

0

1

2

3

4

5

6

0 20 40 60

Nose Rocker [mm]

Nose float = f(Taper) Nose float = f(bindings Setback) Nose float = f(Nose Rocker)

CC = 0.258 Slope = 46,6.10-3

CC = 0.135 Slope = 8,3.10-3

CC = 0.061 Slope = 4,3.10-3

10

Correlation of test results

0

1

2

3

4

5

6

2.0E+05 4.0E+05 6.0E+05 8.0E+05 1.0E+06

"Ove

rall

Stif

fne

ss"

fee

dbac

k

Average Bending Stiffness Dx [N.mm]

"Overall stiffness" = f(Dx)

CC = 0.584

Feedback parameter « Global Stiffness » D

x [N

.mm

]

« Too soft » « Too stiff »

0

200000

400000

600000

800000

1000000

1200000

1400000

0.32 0.37 0.42 0.47

Dx

[N.m

m]

UD Fiberglass, layer thickness t0 [mm]

Dx = f(t0)

400000

500000

600000

700000

800000

900000

1000000

1100000

1200000

5.0 6.0 7.0 8.0

Dx

[N.m

m]

Core thickness tc [mm]

Dx = f(tc)

11

Structural Analysis Optimization

Sensitivity Study: computation of average bending Stiffnesses for different layups

Stacking sequence (symmetric)

Material Orientation Thickness (mean value)

Fiberglass ±45° t45 = 0,4mm

Fiberglass 0° t0 = 0,4mm

Wood core 0° tcore = 6,8mm

Fiberglass 0° t0 = 0,4mm

Fiberglass ±45° t45 = 0,4mm

Input parameters 3 (tcore, t0, t45)

Variation interval ±15%

Number of samples 2197 (all combinations) Theory of thin laminates, [ABD]-1 matrix

Average bending stiffness Dx [N.mm]

CC = 0.980 Slope = 2,6.105

CC = 0.130 Slope = 9,2.105

600000

650000

700000

750000

800000

850000

900000

2.8 2.85 2.9 2.95 3 3.05 3.1

Dx

[N.m

m]

M (0,35m²) [kg]

Optimization of structural thickness according to output Mass [kg]

Variation of CORE thickness only

Variation of UD PLY thickness only

Variation of 45° PLY thickness only

12

Structural Analysis Optimization

- Define optimization target parameter (Mass, Material Cost, Time…) - Assess variation of single parameters around the deterministic sample - Sort the parameters by influence ranking

Deterministic sample

13

Conclusions

Design of a custom snowboard:

1) Define the board specifications: for whom? for which activity?

2) Pick up the best fit among all existing shapes, based on rider profile and feedback results

3) Run sensitivity study with the chosen existing board as "mean value"

4) Optimization of geometrical and structural parameters using the study results:

- sort significant input parameter by influence level (descending) - define priorities and « best compromise »

Further steps: - Expand number of samples and feedback results - Structural analysis via FE modelization: consideration of field inputs and selected load cases

- Qualification of material data - Consideration of physical inputs correlation - Fitting of nonlinear numerical models

Thanks!

www.baguetteboards.com