Static model of a snowboard undergoing a
carved turn: validation by full-scale test
5th Workshop on structural analysis of lightweight structures
Benoit Caillaud, Johannes Gerstmayr
Department of Mechatronics, University of Innsbruck
Motivation
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• Observe and understand how a snowboard deforms and interacts with its environment
• Validate FE model predictions
• Correlate on-snow test feedback with structural analysis data
• Optimization of snowboard structures: demonstrate how the design can be steered by
the structural response under loading conditions
Outline
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Experimental Set-up
Finite Element Modeling
Model Validation
Numerical Results
Experimental Set-up (1)
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A static load bench was developed in-house to reproduce the in-situ conditions of a
snowboard undergoing a carved turn:
Fig. 1: CAD model of the static load bench
Fig. 2: Schematic 2-D representation of the external forces
and moments applied to the snowboard (side view)
Input parameters: Loading weight P Tilt angle θ
Benoit Caillaud – 18 Oct. 2018
Experimental Set-up (2)
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The tested prototype consisted of a simplified snowboard structure with a constant
thickness profile and sidecut radius:
Fig. 3: Geometrical parameters of the tested prototype Fig. 4: Stacking definition of the specimen
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Experimental Set-up (3)
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The Vicon motion tracking system1 captured the deformed shape of the snowboard.
29 retro-reflective markers were positioned on the structure and located by triangulation.
1 Merriaux P, Dupuis Y, Boutteau R, Vasseur P and Savatier X (2017) A study of vicon system positioning performance.
Sensors 17(7):1591
Fig. 5: Front view of the static load bench and the tested prototype
Fig. 6: A Vicon marker positioned on its support
12 measurement sets were defined with
symmetrical loading conditions:
Benoit Caillaud – 18 Oct. 2018
Absolute positioning error of the Vicon
system: 0.15mm for static measurements1
Finite Element Modeling (1)
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Snowboard
• General purpose shell elements
• Laminated composite sections
• Orthotropic material definition
The snowboard geometry and structure were idealized in a numerical model representing
the experimental conditions.
Fig. 7: FEM representation. The input loading and tilt angles are
introduced via the reference nodes RR and RF
Benoit Caillaud – 18 Oct. 2018
Contact plane
• Rigid body elements
• Hard contact formulation
• Friction coefficient
Analysis
• Reference nodes
• Static stress analysis
• Geometrical nonlinearities
• Contact pressure, displacement field
Finite Element Modeling (2)
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The structural deformations of the snowboard were assessed via the deformed FE
surface: successive lateral sections i of the snowboard were considered along with their
nodal X-coordinate.
Longitudinal bending
Lateral bending
Torsional deflections
Fig. 8: Representation of a deformed lateral section i of the
snowboard
Benoit Caillaud – 18 Oct. 2018
(1)
(2)
(3)
Model Validation (1)
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• Goal: compare experimental and numerical displacement fields
Least-square fit of all markers positions:
Fig. 9: Polynomial surface S interpolated from the experimental
marker positions
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(4)
(5)
Interpolation of measurements into polynomial surface S :
(k = total number of markers)
Model Validation (2)
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A and B are related with a translation and a 3D rotation by:
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Fig. 10: Interpolated measurements Fig. 11: Point cloud of deformed FE nodes
• Find the "best-fit" transformation that maps the interpolated measurements onto
the deformed FEM
n: total number of FE nodes
?
(8) (9)
(10)
Model Validation (3)
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If we translate the point clouds A and B from their respective centroid to the global origin:
with then:
The estimation of R results in the following minimization problem:
Using singular value decomposition2 :
2 Schöneman PH (1966) A generalized solution of the orthogonal Procrustes problem. Psychometrika 31(1):1-10
Benoit Caillaud – 18 Oct. 2018
The best-fit rotation matrix is given by:
And the corresponding translation becomes:
Fig. 12: Vertical positioning differences between the deformed
FEM and the interpolated surface after superimposition
(11)
(12) (13)
(14)
(15)
(16)
(17)
Model Validation (4)
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• Transform measured marker positions
Experimental point cloud:
Transformed point cloud:
k : total number of markers
Fig. 13: Final positioning differences between the
experiment and the FE deformed shapes
Over the 12 measurement sets:
Mean positioning difference:
Relative positioning error:
Positioning difference = normal absolute
distance from marker position to FE surface
(18)
Model Validation (5)
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• Goal: validate the distribution of the contact pressure along the snowboard‘s edge
Fig. 14: Experimental distribution of the contact pressure, measurement set A
Fig. 15: Numerical distribution of the contact pressure (FE results, simulation of set A)
Numerical Results (1)
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Assessment of structural deformations:
Longitudinal bending Lateral bending Torsional deflections
Numerical Results (2)
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Influence of different snow properties onto the contact pressure distribution:
RR
RF Contact plane
• Continuum elements
• Isotropic properties
• Contact formulation
d 3 E [MPa] 4 ν 5 μ 6 A [MPa mm-1]
Soft snow 0.3 15 0.23 0.3 0.001
Medium snow 0.4 70 0.25 0.25 0.01
Hard snow 0.5 320 0.27 0.2 0.05
Iced slope 0.6 1430 0.3 0.1 0.1
3 Scapozza C. (2004) Entwicklung eines dichte- und
temperaturabhängigen Stoffgesetzes zur Beschreibung des visko-
elastischen Verhaltens von Schnee. Dissertation, Swiss Federal
Institute of Technology Zurich 4 Mellor M. (1975) A review of basic snow mechanics. Snow
Mechanics, 114:251–291 5 Nachbauer W., Kaps P., Hasler M., Mössner M. (2016) The
Engineering Approach to Winter Sports, 2:17-32 6 Federolf P., JeanRichard F., Fauve M., Lüthi A., Rhyner H., Dual
J. (2005) Deformation of snow during a carved ski turn. Cold
Regions Science and Technology, 46(1):69-77
Numerical Results (3)
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Conclusion
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• Simulation suitable for predicting structural deformations and contact pressure
• Valid deformations ≡ correct stiffness representation: strain and stresses can be extracted
for strength analysis purposes (within the shell element formulation assumptions)
• RMSE of final positioning error qi suggested as a scalar indicator to be minimized for the
optimization of the model parameters
Further steps:
• Preliminary results with snow representation: validate with in-situ testing
• Implementation of a “real” snowboard structure (base, edges, sidewalls, topsheet)
• Establish a framework for solving the following inverse problem: which initial state
produces given structural outputs?
Thank you for your attention!
Feel free to ask questions…
Benoit Caillaud & Johannes Gerstmayr
Department of Mechatronics, University of Innsbruck, Austria