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| 杆系结构拓扑找力分析 |
| Topological force finding analysis of bar structure |
| 投稿时间：2023-06-16 修订日期：2023-09-07 |
| DOI： |
| 中文关键词: 杆系结构；线性图 平衡矩阵 拓扑找力 |
| 英文关键词:Bar structure Linear graphs Equilibrium matrices Topological force finding |
| 基金项目:上海市自然科学基金(NO: 13ZR1430500)资助项目. |
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| 中文摘要: |
| 首先，本文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。 |
| 英文摘要: |
| Firstly, based on the bar structure, the paper discussed various types of linear graph representations. 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 system is deduced. The concept of topological force finding analysis is proposed based on this form of equilibrium matrix. Finally, the equilibrium matrix and its zero space in different cases are compared by the bar structure arithmetic example. The correctness and applicability of linear graph representation and topological force finding for various types of bar structures are further verified. |
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