A Problem in Applied Topology: on the Selection of Cycles for the Flexibility Analysis of Skeletal Structures
A Problem in Applied Topology: on the Selection of Cycles for the Flexibility Analysis of Skeletal Structures
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应用拓扑学中的一个问题：骨骼结构柔度分析中循环的选择
DOI：
10.1093/imamat/5.2.254
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发表时间：
1969
影响因子：
1.2
通讯作者：
E. Maunder
中科院分区：
文献类型：
--
作者：
J. C. Henderson;E. Maunder
发展了广义静态基础理论，用于应用于骨骼结构问题的柔性方法。结果表明，结构的线性图模型的积分循环组的任何最大线性独立循环组都可以用于形成静态基础。通过将该图嵌入到二维多面体中可以找到这样一组简单的循环。细胞复合体的形成使得限制 2 细胞的简单循环对应于可以构建静态基础的子结构。给出了两种构建嵌入的方法。其中一个可折叠复合体是由一组圆盘的联合形成的；而在另一种情况下，嵌入到可定向流形中，该流形被修改以形成可接受的复合体。
A theory of generalized statical bases is developed for use in the flexibility methods as applied to skeletal structural problems. It is shown that any maximal linearly independent set of cycles of the integral cycle group of a linear graph model of the structure may be used in the formation of a statical basis. Such a set of simple cycles is found by embedding this graph into a two-dimensional polyhedron. Cell complexes are formed so that the simple cycles bounding the 2-cells correspond to substructures on which a statical basis may be constructed. Two methods are given for the construction of the embeddings. In one a collapsible complex is formed from a union of a set of disks; while in the other the embedding is into an orientable manifold which is modified to form an admissible complex.