Efficient Update of Redundancy Matrices for Truss and Frame Structures

TL;DR

This paper introduces algebraic methods for efficiently updating redundancy matrices in truss and frame structures, reducing computational effort during iterative structural analysis and design.

Contribution

It provides generic algebraic formulations for fast updates of redundancy matrices, applicable to various modifications in truss and frame structures.

Findings

Formulations enable efficient matrix updates for structural modifications.

Examples demonstrate mechanical interpretation of the formulas.

Performance testing shows scalability and efficiency improvements.

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.