Abstract The degree of statical indeterminacy as a fundamental property in structural mechanics is today mainly known as a property of a complete system without any information about its spatial distribution. The redundancy matrix provides information about the distribution of statical indeterminacy in the system and by this gives an additional valuable insight into the load-bearing behaviour. The derivation and definition of the redundancy matrix are presented based on truss systems and its mathematical properties and their mechanical interpretations are provided. The definition of the redundancy matrix is extended to other discrete systems like beam structures and a definition of the redundancy density is given for the continuous 1D case. Potential applications of the concept include robust design of structures, quantification of imperfection sensitivity as well as assessment of optimal actuator placement in adaptive structures.

中文翻译：

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桁架和梁结构中冗余分布的量化

摘要 作为结构力学中的一个基本属性的静态不确定度今天主要被称为完整系统的属性，而没有关于其空间分布的任何信息。冗余矩阵提供了有关系统中静态不确定性分布的信息，从而为承载行为提供了额外的宝贵见解。给出了基于桁架系统的冗余矩阵的推导和定义，并提供了其数学特性及其力学解释。冗余矩阵的定义扩展到其他离散系统，如梁结构，并为连续一维情况给出了冗余密度的定义。该概念的潜在应用包括结构的稳健设计、