Spline interpolation method based on arc length parameterization and its application in stress field interpolation for flexible plates

Abstract

This paper proposes a method of curve interpolation based on the parameters of arc length that is used to interpolate the stress field of the wind tunnel flexible plate. The quotient of the arc length from the starting point to the interpolation point divided by the total arc length is the parameter corresponding to this point. The researchers calculated the optimum combination of parameters with the help of the particle swarm optimization algorithm. The optimization computation aims to find the combination of parameters corresponding to the shortest arc length of the interpolation curve. The simulated strain data of the flexible plate are collected by researchers to verify the performance of the algorithm. The experimental results show that the error of this method is small and that the increase in the error in the computation of the higher-order interpolation is not significant. This paper introduces fiber Bragg grating to the multipoint strain measurement of a wind tunnel flexible plate. The authors interpolated the stress measured from FBGs by the interpolation method proposed in this paper. Then, the stress distribution law and the maximum stress point of the flexible plate were found. The maximum one-dimensional stress is -193.21 MPa, and the position is 623.55 mm and 149.5 mm.