受荷索杆机构的运动分析
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摘要
本文以索杆张力结构的施工成形、攀达穹顶的顶升施工等问题为背景,将这些体系抽象为受荷杆系或索杆机构,重点对其运动形态解析理论进行研究。主要工作包括以下四个方面内容：
(1)提出了一种基于有限元法的杆系机构运动路径分析方法。以驱动杆长度为控制变量,建立了受荷杆系机构运动的基本方程,并引入弧长法实现运动路径的自动求解。
(2)将运动形态的稳定判别引入到受荷杆系机构运动分析的有限元法中。通过考察系统切线刚度矩阵最小特征值的变化,来跟踪机构运动形态的稳定性。提出了精确定位运动路径上奇异点的牛顿法求解策略,并对奇异点的分岔条件进行了严谨的理论解释。通过引入由切线刚度矩阵零空间基底组成的干扰力,来实现分岔路径的跟踪。
(3)在传统动力松弛法中引入弧长法,提出了一种改进的受荷索杆机构运动解析方法。该方法不仅保留了动力松弛法计算效率高的特点,且结合弧长法可实现索杆结构运动路径的自动跟踪。更重要的,通过在动力松弛法中引入与切向刚度矩阵零空间基底相关的初始干扰速度,也可实现受荷索杆机构运动分岔路径的跟踪。
(4)结合实际工程,对一种新型的月牙形索桁罩棚结构施工成形过程进行了分析。针对建议的施工方案,采用本文提出的方法对体系的成形过程进行了数值模拟,并分析了体系提升过程中的形态变化特征。基于该罩棚结构的1：15模型,进一步对其施工成形过程进行了试验,验证了建议施工方法的可行性。通过测试值和理论值的比较,也验证了本文提出的运动形态分析方法的正确性。
Based on the background of the problems such as construction of cable-strut tensile structures and jacking process of Panta Dome, these systems are abstracted to be load-bearing mechanisms consisting of cables and bar elements, and the theoretical kinematic analysis of the mechanism is focused in this paper. The main work includes:
(1) A kinematic path analysis method for the pin-bar mechanism is presented based on the finite element method. The basic kinematic equations of the load-bearing pin-bar mechanism are established and the elongations of the driving bars are taken as the control parameters. The arc-length method is employed so the kinematic path can be traced automatically.
(2) The kinematic configuration stability criterion is introduced into the kinematic analysis of the load-bearing pin-bar mechanism. The minimal eigenvalue of the tangent stiffness matrix is employed to determinate the stability of the equilibrium configuration on the kinematic path. The method for pinpointing the singular point on the kinematic path based on the Newton method is presented. The bifurcation conditions of the singular point are explained theoretically. In order to trace the bifurcation paths, the disturbing force depend on the zero space vector of the tangent stiffness matrix is introduced.
(3) The arc-length method is introduced into the traditional dynamic relaxation method, and a modified method for the load-bearing cable-bar mechanism kinematic analysis is presented. The high computational efficiency of the dynamic relaxation method is preserved, and the automatic path tracing can be realized combined with the arc-length method. More importantly, the bifurcation path can be traced by introducing the initial disturbing velocity depended on the zero space vector of the tangent stiffness matrix into the modified method.
(4) The construction process of the novel crescent-shaped cable-strut tensile structure is analyzed based on a practical application. Numerical simulation of the recommended construction process is carried out by the proposed method, and the characteristics of the structure during the construction are analyzed. Based on the1:15experimental model of the tensile structure, the hoisting experiment of the construction process is conducted to verify the recommended construction scheme. The results of the experiment are compared with the numerical simulation and the proposed method is verified.
(1)提出了一种基于有限元法的杆系机构运动路径分析方法。以驱动杆长度为控制变量,建立了受荷杆系机构运动的基本方程,并引入弧长法实现运动路径的自动求解。
(2)将运动形态的稳定判别引入到受荷杆系机构运动分析的有限元法中。通过考察系统切线刚度矩阵最小特征值的变化,来跟踪机构运动形态的稳定性。提出了精确定位运动路径上奇异点的牛顿法求解策略,并对奇异点的分岔条件进行了严谨的理论解释。通过引入由切线刚度矩阵零空间基底组成的干扰力,来实现分岔路径的跟踪。
(3)在传统动力松弛法中引入弧长法,提出了一种改进的受荷索杆机构运动解析方法。该方法不仅保留了动力松弛法计算效率高的特点,且结合弧长法可实现索杆结构运动路径的自动跟踪。更重要的,通过在动力松弛法中引入与切向刚度矩阵零空间基底相关的初始干扰速度,也可实现受荷索杆机构运动分岔路径的跟踪。
(4)结合实际工程,对一种新型的月牙形索桁罩棚结构施工成形过程进行了分析。针对建议的施工方案,采用本文提出的方法对体系的成形过程进行了数值模拟,并分析了体系提升过程中的形态变化特征。基于该罩棚结构的1：15模型,进一步对其施工成形过程进行了试验,验证了建议施工方法的可行性。通过测试值和理论值的比较,也验证了本文提出的运动形态分析方法的正确性。
Based on the background of the problems such as construction of cable-strut tensile structures and jacking process of Panta Dome, these systems are abstracted to be load-bearing mechanisms consisting of cables and bar elements, and the theoretical kinematic analysis of the mechanism is focused in this paper. The main work includes:
(1) A kinematic path analysis method for the pin-bar mechanism is presented based on the finite element method. The basic kinematic equations of the load-bearing pin-bar mechanism are established and the elongations of the driving bars are taken as the control parameters. The arc-length method is employed so the kinematic path can be traced automatically.
(2) The kinematic configuration stability criterion is introduced into the kinematic analysis of the load-bearing pin-bar mechanism. The minimal eigenvalue of the tangent stiffness matrix is employed to determinate the stability of the equilibrium configuration on the kinematic path. The method for pinpointing the singular point on the kinematic path based on the Newton method is presented. The bifurcation conditions of the singular point are explained theoretically. In order to trace the bifurcation paths, the disturbing force depend on the zero space vector of the tangent stiffness matrix is introduced.
(3) The arc-length method is introduced into the traditional dynamic relaxation method, and a modified method for the load-bearing cable-bar mechanism kinematic analysis is presented. The high computational efficiency of the dynamic relaxation method is preserved, and the automatic path tracing can be realized combined with the arc-length method. More importantly, the bifurcation path can be traced by introducing the initial disturbing velocity depended on the zero space vector of the tangent stiffness matrix into the modified method.
(4) The construction process of the novel crescent-shaped cable-strut tensile structure is analyzed based on a practical application. Numerical simulation of the recommended construction process is carried out by the proposed method, and the characteristics of the structure during the construction are analyzed. Based on the1:15experimental model of the tensile structure, the hoisting experiment of the construction process is conducted to verify the recommended construction scheme. The results of the experiment are compared with the numerical simulation and the proposed method is verified.
引文
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