A Spatial Geometric Nonlinearity Spline Beam Element With Nodal Parameters Containing Strains北大核心CSCD

Many slender rods in engineering can be modeled as Euler-Bernoulli beams. For the analysis of their dynamic behaviors, it is necessary to establish the dynamic models for the flexible multi-body systems. Geometric nonlinear elements with absolute nodal coordinates help solve a large number of dynamic problems of flexible beams, but they still face such problems as shear locking, nodal stress discontinuity and low computation efficiency. Based on the theory of large deformation beams’ virtual power equations, the functional formulas between displacements and rotation angles at the nodes were established, which can satisfy the deformation coupling relationships. The generalized strains to describe geometric nonlinear effects in this case were derived. Some parameters of boundary nodes were replaced by axial strains and sectional curvatures to obtain a more accurate and concise constraint method for applying external forces. To improve the numerical efficiency and stability of the system’s motion equations, a model-smoothing method was used to filter high frequencies out of the model. The numerical examples verify the rationality and effectiveness of the proposed element. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

滑轮绳索系统中动态节点绳索单元

解除了传统有限元方法中单元节点与物质点固结的假设, 建立了空间点的速度和加速度与相应物质点的速度和加速度之间的数学关系, 强调了虚功率原理中出现的速度和加速度皆为物质速度和物质加速度. 在此基础上构造了单元节点既不与空间坐标固定也不与物质坐标固定的动态节点绳索单元. 根据滑轮绳索系统的特点, 选取绳索出入绳点的弧长坐标、出入绳角、面外摆角以及拉伸应变等空间参数描述了滑轮绳索系统的运动. 将绳索与滑轮以及绳索与卷筒之间的相互作用合理简化为物质速度间的约束条件, 避免了传统方法中接触力计算不收敛、效率低等缺点. 所提方法可精细求解绳索与滑轮间接触边界点位置和卷筒入绳点在卷筒上的运动、滑轮的中心和其连体基的运动、绳索出入滑轮和卷筒时空间方位的变化以及绳索上任意点的拉力变化等细节. 可为含绳索机械系统的力学分析提供新的理论基础. 所用的解除单元节点与物质点绑定的理论具有一定的普适性, 可为有限元方法的理论和应用提供参考.