Nonlinear dynamics analysis of beveled flexible beam with a high length-diameter ratio in medium

Obstacle avoidance in medicine or engineering can be achieved by utilizing the property of high length- diameter ratio beveled-angle flexible beams that undergo self deflection in interaction with the medium. In this paper, anew method for modeling and analyzing the dynamics of beveled-angle flexible beams in viscoelastic medium is proposed, which greatly improves the accuracy of the model. First, it is proposed to use the absolute nodal coordinate method (ANCF) based on quintic Hermite interpolation to model the dynamics of flexible beams, which improves the computational accuracy in comparison with other models. Secondly, the puncture force calculation method with the addition of type-II inclined tip fracture force is proposed for the first time, which is more in line with the actual situation and improves the accuracy at the same time. Once again, through experimental data and theoretical analysis, the principle of constant cross-section pressure is proposed as a way to calculate the friction force of the beam more accurately. Insertion experiments were carried out using NiTi beveled needles and agar gel. By comparing the actual paths and the paths calculated by the method of this paper, the root mean square error (RMSE) of the method proposed in this paper is less than 0.549 mm in all control groups. The correctness of the above model is verified.