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首页> 外文期刊>Scandinavian journal of statistics >What is the shape of a bundle? An analysis of Rosen's fibrous composites experiments using the chain-of-bundles model
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What is the shape of a bundle? An analysis of Rosen's fibrous composites experiments using the chain-of-bundles model

机译：束的形状是什么？使用束状链模型分析Rosen的纤维复合材料实验

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摘要

In the 1960s, W. B. Rosen conducted some remarkable experiments on unidirectional fibrous composites that gave seminal insights into their failure under increasing tensile load. These insights led him to a grid system where the nodes in the grid were ineffective length fibers and to model the composite as something he called a chain-of-bundles model (i.e., a series system of parallel subsystems of horizontal nodes that he referred to as bundles), where the chain fails when one of the bundles fails. A load-sharing rule was used to quantify how the load is borne among the nodes. Here, Rosen's experiments are analyzed to determine the shape of a bundle. The analysis suggests that the bundles are not horizontal collection of nodes but rather small rectangular grid systems of nodes where the load-sharing between nodes is local in its form. In addition, a Gibbs measure representation for the joint distribution of binary random variables is given. This is used to show how the system reliability for a reliability structure can be obtained from the partition function for the Gibbs measure and to illustrate how to assess the risk of failure of a bundle in the chain-of-bundle model.
机译：在1960年代，W。B. Rosen对单向纤维复合材料进行了一些出色的实验，从而对在增加拉伸载荷下的破坏提供了开创性的见识。这些见解使他建立了一个网格系统，其中网格中的节点是长度无效的纤维，并将复合材料建模为他称为捆绑链模型的模型（即，他所指的水平节点的并行子系统的串联系统） （例如bundle），其中一个bundle发生故障时链失败。使用负载共享规则来量化节点之间如何承担负载。在这里，分析罗森的实验以确定束的形状。分析表明，束不是节点的水平集合，而是节点的小型矩形网格系统，其中节点之间的负载分担以其形式局部存在。另外，给出了二进制随机变量联合分布的吉布斯测度表示。这用于说明如何从Gibbs度量的分区函数中获得可靠性结构的系统可靠性，并说明如何在捆绑链模型中评估捆绑失败的风险。

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