Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal entries are required. The standard computation procedure has a high computational effort. Many structures fall in the category of moderately redundant, i.e., the ratio of the statical indeterminacy to the number of all load-carrying modes of all elements is less one half. This paper proposes a closed-form expression for redundancy contributions that is computationally efficient for moderately redundant systems. The expression is derived via a factorization of the redundancy matrix that is based on singular value decomposition. Several examples illustrate the behavior of the method for increasing size of systems and, where applicable, for increasing degree of statical indeterminacy.

翻译：大型超静定桁架与框架结构展现出复杂的承载行为，冗余矩阵对其分析与设计具有重要价值。根据具体任务需求，可能需要完整的冗余矩阵或仅需其对角线元素。标准计算方法存在计算量大的问题。许多结构属于中等冗余范畴，即其静不定次数与所有构件承载模态数量之比小于二分之一。本文提出一种闭式冗余贡献表达式，该方法对中等冗余系统具有显著的计算效率。该表达式基于奇异值分解的冗余矩阵分解法推导得出。通过多个算例展示了该方法在系统规模递增情况下的性能表现，并在适用条件下验证了静不定次数增加时的算法特性。