Statistical Optimization and Structural Analysis: Design of handmade custom Snowboards Benoit CAILLAUD 4th Workshop on Structural Analysis of Lightweight Structures Innsbruck, 02.06.2016 1
Agenda 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 2
Materials & Structure Wood Composite reinforcements Layup Edges Thickness profile Input parameters: Sidewalls - 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 {σ e }, {σ r } - Density, Toughness, Stability UD Roving UD Lin fiber ±45 fabric Basalte UD Roving 3
Geometry & Shape Dimensions Sidecut shape Camber profile Inserts positions Input parameters: - L, L m, L contact - L nose, L tail, L camber - W nose, W waist, W tail - Stance - Setback - H nose, H tail, H camber - Curvatures: sidecut, camber, rockers Sidecut Radius [m] 40 30 20 10 0-800 -600-400 -200 0 200 400 600 800 4
Portfolio 5
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 6
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 7
Calibration of test feedback Too Sinks short easily Floats Too easily long 8
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 6 5 4 3 2 1 0 Nose float = f(taper) Nose float = f(bindings Setback) Nose float = f(nose Rocker) 0 5 10 15 20 Taper [mm] 6 5 4 3 2 1 0 0 10 20 30 40 50 Bindings Setback [mm] 6 5 4 3 2 1 0 0 20 40 60 Nose Rocker [mm] CC = 0.258 CC = 0.135 CC = 0.061 Slope = 46,6.10-3 Slope = 8,3.10-3 Slope = 4,3.10-3 - Quantify parameter influence (slope of fitted numerical model) compare effects of different parameters input parameters must be standardized to their practical variation range 9
"Overall Stiffness" feedback Dx [N.mm] Correlation of test results 6 "Overall stiffness" = f(dx) 5 4 3 2 1 CC = 0.584 0 2.0E+05 4.0E+05 6.0E+05 8.0E+05 1.0E+06 Average Bending Stiffness Dx [N.mm] «Too soft» «Too stiff» Feedback parameter «Global Stiffness» 10
Dx [N.mm] Dx [N.mm] Structural Analysis Optimization Sensitivity Study: computation of average bending Stiffnesses for different layups Stacking sequence (symmetric) Material Orientation Thickness (mean value) Fiberglass ±45 t 45 = 0,4mm Fiberglass 0 t 0 = 0,4mm Wood core 0 t core = 6,8mm Fiberglass 0 t 0 = 0,4mm Fiberglass ±45 t 45 = 0,4mm Input parameters 3 (t core, t 0, t 45 ) Variation interval ±15% Number of samples 2197 (all combinations) Theory of thin laminates, [ABD] -1 matrix Average bending stiffness D x [N.mm] D x = f(t c ) 1200000 1100000 1000000 900000 800000 700000 600000 500000 400000 5.0 6.0 7.0 8.0 Core thickness tc [mm] CC = 0.980 CC = 0.130 Slope = 2,6.10 D x = f(t 0 ) 5 1400000 1200000 1000000 800000 600000 400000 200000 Slope = 9,2.10 5 0 0.32 0.37 0.42 0.47 UD Fiberglass, layer thickness t0 [mm] 11
Dx [N.mm] 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 900000 850000 Optimization of structural thickness according to output Mass [kg] 800000 750000 700000 650000 Deterministic sample 600000 2.8 2.85 2.9 2.95 3 3.05 3.1 M (0,35m²) [kg] Variation of CORE thickness only Variation of UD PLY thickness only Variation of 45 PLY thickness only 12
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 13
Thanks! www.baguetteboards.com