一种空间悬索的几何非线性计算方法

doi:10.3901/JME.2022.09.147

机械工程学报 ›› 2022, Vol. 58 ›› Issue (9): 147-156.doi: 10.3901/JME.2022.09.147

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一种空间悬索的几何非线性计算方法

徐金帅^1,2, 齐朝晖^1,2, 卓英鹏^1,2, 赵天骄^1,2, 滕儒民³

1. 大连理工大学工程力学系大连 116023;
2. 大连理工大学工业装备结构分析国家重点实验室大连 116023;
3. 大连理工大学机械工程学院大连 116023

收稿日期:2021-06-18 修回日期:2021-12-10 出版日期:2022-05-05 发布日期:2022-06-23
通讯作者: 齐朝晖(通信作者)，男，1964年出生，博士，教授，博士研究生导师。主要研究方向为计算动力学、复杂机械系统动力学和结构几何非线性。E-mail：zhaohuiq@dlut.edu.cn E-mail:zhaohuiq@dlut.edu.cn
作者简介:徐金帅，男，1982年出生，博士研究生。主要研究方向为结构几何非线性、机械系统动力学。E-mail：xujinshuai@mail.dlut.edu.cn
基金资助:
国家自然科学基金资助项目(11872137)

A Geometric Nonlinear Calculation Method for Spatial Suspension Cable

XU Jinshuai^1,2, QI Zhaohui^1,2, ZHUO Yingpeng^1,2, ZHAO Tianjiao^1,2, TENG Rumin³

1. Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023;
2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023;
3. School of Mechanical Engineering, Dalian University of Technology, Dalian 116023

Received:2021-06-18 Revised:2021-12-10 Online:2022-05-05 Published:2022-06-23

摘要/Abstract

摘要： 以单元两节点的矢径与切矢量作为描述变量，对空间悬索进行单元离散，采用Hermite插值建立悬索单元。基于空间悬索曲率连续这一物理事实，单元公共节点处矢径的二阶导数连续，将悬索中间节点的切矢量用两端节点矢径与切矢量表达，实现系统自由度缩减。依据虚功率原理，建立空间悬索非线性平衡方程，对平衡方程求时间导数，得到系统方程的雅可比矩阵。采用三点抛物线近似悬链线的方式建立悬索初始形状，得到非线性方程的初值。对于仅承受重力且已知无应变原长的悬索，采用端部载荷与重力平衡的方式，计算出悬索两端的载荷。在此基础上，实现在已知悬索一端载荷大小的情况下，计算悬索无应变原长。提出了一种空间柔性悬索的几何非线性计算方法，通过数值算例，验证了方法的可靠性，为空间静态悬索计算，提供一种新的计算途径。

关键词: 空间悬索, 几何非线性, 虚功率原理, 无应变原长

Abstract: The radius vector and tangent vector of the two nodes of the element are used as the description variables to discretize the spatial suspension cable, and the Hermite interpolation is used to establish the suspension cable element. Based on the physical fact that the curvature of the suspension cable is continuous, the second derivative of the radius vector of the common node is continuous. The tangent vector of the middle nodes is expressed by the radius vector and tangent vector of the two ending nodes, which reduces the system freedom. According to the principle of virtual power, the nonlinear equilibrium equation of spatial suspension cable is established. The time derivative of the equation and the Jacobian matrix of the system equation are obtained. The initial shape of suspension cable is established by using three-point parabola to approximate catenary, and the initial value of nonlinear equation is obtained. For the suspension cable with only gravity and known initial length without strain, the load at both ends of suspension cable is calculated by balancing the ending load and gravity. On this basis, the initial length of the suspension without strain can be calculated under the condition of the load at one end of the cable. A geometric nonlinear method of spatial flexible suspension cable is proposed. The reliability of the method is verified by numerical examples. A new method is provided for the calculation of spatial static suspension cable.

Key words: spatial suspension cable, geometric nonlinear, principle virtual power, initial length without strain

中图分类号:

TH213

徐金帅, 齐朝晖, 卓英鹏, 赵天骄, 滕儒民. 一种空间悬索的几何非线性计算方法[J]. 机械工程学报, 2022, 58(9): 147-156.

XU Jinshuai, QI Zhaohui, ZHUO Yingpeng, ZHAO Tianjiao, TENG Rumin. A Geometric Nonlinear Calculation Method for Spatial Suspension Cable[J]. Journal of Mechanical Engineering, 2022, 58(9): 147-156.

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一种空间悬索的几何非线性计算方法

A Geometric Nonlinear Calculation Method for Spatial Suspension Cable

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