不稳定结构形态的广义逆矩阵创构研究  

Research on the construction of generalized inverse matrix of unstable structures

作　　者：田东霞 Tian Dongxia(Fenyang Normal School of Lvliang University,Fenyang 032200,China)

机构地区：[1]吕梁学院汾阳师范分校,山西汾阳032200

出　　处：《湖南文理学院学报（自然科学版）》2022年第3期10-15,29,共7页Journal of Hunan University of Arts and Science(Science and Technology)

摘　　要：不稳定结构在受到外力作用时其形状会持续改变至势能达到下限的零弯矩平衡状态。本文基于这一定律,同时引用广义逆矩阵理论提出了一种杆件结构的创构方法。首先对杆单元进行分类,以每个类别所有杆件长度之和不变为前提,建立限制杆形态改变的移形方程,然后基于势能改变梯度与广义逆矩阵理论来寻找势能降幅最大的位置,对节点位置进行渐进式调整指导该点势能降至下限。通过单元类和临时单元使该方法对不同形态的创构具有普适性。实证结果表明,所提出的方法具有很强的实效性。When an unstable structure is subjected to external force,its shape will continue to change until the potential energy reaches the zero-moment equilibrium state of the lower limit.Based on this law and the generalized inverse matrix theory,this paper presents a method for the construction of bar structures.Firstly,the bar elements are classified.On the premise that the sum of the lengths of all members in each category remains unchanged,the displacement equation limiting the change of the bar shape is established.Based on the gradient of potential energy change and the theory of generalized inverse matrix,the position of the node is adjusted gradually to guide the potential energy to the lower limit.Through unit class and temporary unit,this method has universality for different forms of creation.The empirical results show that the proposed method has strong effectiveness.

关 键 词：不稳定结构 广义逆矩阵 最大弯矩 最大位移 杆件结构 

分 类 号：O151.21[理学—数学]