Efficient Update of Redundancy Matrices for Truss and Frame Structures

Abstract

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.

Efficient Computation of Redundancy Matrices for Moderately Redundant Truss and Frame Structures

“…Thus, the behavior of the proposed algorithm may differ for frames with curved members. Finally, a new update algorithm for the full redundancy matrix based on our proposed decomposition can be developed and compared with the existing update algorithm from Krake et al (2022). The implementation of the update should be straightforward, e.g., it profits from existing algorithms for dense and sparse matrices (Reichel and Gragg 1990;Andrew and Dingle 2014).…”

“…In both cases, a fast calculation of the redundancy matrix is essential. Recently, an algorithm for efficient updates of redundancy matrices in truss and frame structures is proposed in Krake et al (2022). Therein, in distinction to the present contribution, generic algebraic formulations due to various modifications like adding, removing, and exchanging elements are employed.…”