Heinrich Dieter, Mössner Martin, Kaps Peter, Nachbauer Werner
Department of Sport Science, University of Innsbruck, Innsbruck, Austria.
J Appl Biomech. 2011 Feb;27(1):81-6. doi: 10.1123/jab.27.1.81.
The deformation of skis and the contact pressure between skis and snow are crucial factors for carved turns in alpine skiing. The purpose of the current study was to develop and to evaluate an optimization method to determine the bending and torsional stiffness that lead to a given bending and torsional deflection of the ski. Euler-Bernoulli beam theory and classical torsion theory were applied to model the deformation of the ski. Bending and torsional stiffness were approximated as linear combinations of B-splines. To compute the unknown coefficients, a parameter optimization problem was formulated and successfully solved by multiple shooting and least squares data fitting. The proposed optimization method was evaluated based on ski stiffness data and ski deformation data taken from a recently published simulation study. The ski deformation data were used as input data to the optimization method. The optimization method was capable of successfully reproducing the shape of the original bending and torsional stiffness data of the ski with a root mean square error below 1 N m2. In conclusion, the proposed computational method offers the possibility to calculate ski stiffness properties with respect to a given ski deformation.
滑雪板的变形以及滑雪板与雪之间的接触压力是高山滑雪中刻滑转弯的关键因素。本研究的目的是开发并评估一种优化方法，以确定能使滑雪板产生给定弯曲和扭转挠度的弯曲和扭转刚度。应用欧拉 - 伯努利梁理论和经典扭转理论对滑雪板的变形进行建模。弯曲和扭转刚度近似为B样条的线性组合。为了计算未知系数，制定了参数优化问题，并通过多重打靶法和最小二乘数据拟合成功求解。基于从最近发表的模拟研究中获取的滑雪板刚度数据和滑雪板变形数据，对所提出的优化方法进行了评估。将滑雪板变形数据用作优化方法的输入数据。该优化方法能够成功再现滑雪板原始弯曲和扭转刚度数据的形状，均方根误差低于1 N·m²。总之，所提出的计算方法提供了根据给定的滑雪板变形来计算滑雪板刚度特性的可能性。
