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

TL;DR

This paper introduces a computationally efficient closed-form method for calculating redundancy matrices in moderately redundant truss and frame structures, reducing effort compared to traditional approaches.

Contribution

It presents a novel closed-form expression derived via singular value decomposition, specifically optimized for moderately redundant structures.

Findings

Method reduces computational effort for redundancy matrices.

Effective for systems with increasing size and indeterminacy.

Demonstrated through several illustrative examples.

Abstract

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.