杆系结构拓扑找力分析  

Topological force finding analysis of bar structure

作　　者：张志宏[1] 赵恺 ZHANG Zhi-hong;ZHAO Kai(Department of Civil Engineering,College of Civil Engineering,Shanghai Normal University,Shanghai 201418,China)

机构地区：[1]上海师范大学建筑工程学院土木系,上海201418

出　　处：《计算力学学报》2024年第6期1124-1129,共6页Chinese Journal of Computational Mechanics

基　　金：上海市自然科学基金(13ZR1430500)资助项目.

摘　　要：首先,对杆系结构多种类型的线性图表示方法进行了讨论.其次,引入关联矩阵显式来组装平衡矩阵,推导出独立于体系具体形状几何的平衡矩阵新形式即关联矩阵,并基于该形式的平衡矩阵提出了拓扑找力分析的概念.最后,通过杆系结构算例,对比不同情况下的平衡矩阵及其零空间,进一步验证了杆系结构多种类型的线性图表示和拓扑找力的正确性与适用性.Firstly,the paper studied various types of linear graph representations of a bar-type structure.Secondly,the incidence matrix is introduced to assemble the equilibrium matrix,and a new form of equilibrium matrix independent of the specific shape geometry of the structure is derived.The concept of topological force finding analysis is proposed based on this form of equilibrium matrix.Finally,the equilibrium matrices and their null spaces in different cases of a bar-type structure are compared.The correctness and applicability of linear graph representation and topological force finding for various types of bar structures are further verified.

关 键 词：杆系结构 线性图 平衡矩阵 拓扑找力 

分 类 号：O189.1[理学—数学]