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六种平衡矩阵及其零空间与列空间力学意义研究
Study on six forms of equilibrium matrices and physical meaning of their zero space and column space
投稿时间:2024-04-19  修订日期:2024-07-01
DOI:
中文关键词:  平衡矩阵  零空间与列空间  找力分析  找形分析  形态生成
英文关键词:Equilibrium matrix  Zero space and column space  Force finding analysis  Form finding analysis  Morphogenesis
基金项目:
作者单位邮编
张志宏* 上海师范大学 201418
赵恺 上海师范大学 
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中文摘要:
      本文在矩阵力法基本列式的基础上,首先引入关联矩阵显式组装平衡矩阵,推导出平衡矩阵的六种不同形式。其次,本文对六种平衡矩阵的零空间和列空间的力学意义进行了初步讨论。最后,结合不同类型的索杆体系算例,对六种平衡矩阵在形态生成分析中可能的应用进行探讨,拓扑几何未知,可采用平衡矩阵进行体系的拓扑找力分析;拓扑几何已知,可采用平衡矩阵进行找力分析与找形分析。本文工作对进一步促进索杆体系找形与找力混合形态分析有一定的帮助。
英文摘要:
      On the basis of the fundamental formulas of matrix force method, firstly, this paper first introduces the explicit assembly of the equilibrium matrix using the incidence matrix, deriving six different forms of the equilibrium matrix. Subsequently, the mechanical significance of the null space and column space of these six equilibrium matrices is preliminarily discussed. Finally, through examples of different types of cable-bar systems, the potential applications of these six equilibrium matrices in form-finding analysis are explored. When the topological geometry is unknown, the equilibrium matrix can be used for topological force analysis of the system; when the topological geometry is known, the equilibrium matrix can be employed for both force-finding and form-finding analysis. This work contributes to advancing the hybrid analysis of form-finding and force-finding in cable-strut systems.
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