Static model of a snowboard undergoing a carved turn

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

[email protected]

Motivation

2 Benoit Caillaud – 18 Oct. 2018

• 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


Experimental Set-up

Finite Element Modeling

Model Validation

Numerical Results

Experimental Set-up (1)

4

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


5

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



6

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:


Absolute positioning error of the Vicon

system: 0.15mm for static measurements1

Finite Element Modeling (1)

7

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


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)

8

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


(1)

(2)

(3)

Model Validation (1)

9

• 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


(4)

(5)

Interpolation of measurements into polynomial surface S :

(k = total number of markers)


10

A and B are related with a translation and a 3D rotation by:


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)


11

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


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)



• 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)



• 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)


Assessment of structural deformations:

Longitudinal bending Lateral bending Torsional deflections



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



Conclusion


• 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

[email protected]

Documents

Static model of a snowboard undergoing a carved turn