Redundancy matrices provide insights into the load carrying behavior of statically indeterminate structures. This information can be employed for the design and analysis of structures with regard to certain objectives, for example reliability, robustness, or adaptability. In this context, the structure is often iteratively examined with the help of slight adjustments. However, this procedure generally requires a high computational effort for the recalculation of the redundancy matrix due to the necessity of costly matrix operations. This paper addresses this problem by providing generic algebraic formulations for efficiently updating the redundancy matrix (and related matrices). The formulations include various modifications like adding, removing, and exchanging elements and are applicable to truss and frame structures. With several examples, we demonstrate the interaction between the formulas and their mechanical interpretation. Finally, a performance test for a scaleable structure is presented.
翻译:冗余矩阵可深入了解静态不确定结构的负载行为。这种信息可用于设计和分析与某些目标有关的结构,例如可靠性、稳健性或适应性。在这方面,通常在稍作调整的情况下对结构进行迭代审查。然而,由于需要花费昂贵的矩阵操作,这一程序一般需要大量计算重新计算冗余矩阵。本文件通过提供通用的代数公式来解决这一问题,以便有效地更新冗余矩阵(及相关矩阵)。这些公式包括各种修改,如添加、删除和交换要素,并适用于三角体和框架结构。我们用几个例子展示了公式及其机械解释之间的相互作用。最后,介绍了一个可缩放结构的性能测试。