An Improvement to Exact Reanalysis Algorithm for Local Non-topological Structural Modifications

Abstract

A new direct reanalysis algorithm for local high-rank structural modifications, based on triangular factorization, has recently been developed. In this work, an improvement is proposed for further reduction of the workload so that the algorithm becomes more efficient and also suitable for low-rank modifications. Compared to the original algorithm, firstly, an alternative formula for updating the triangular factors is derived to avoid repetitive calculations for certain low-rank cases. Secondly, to maximize the efficiency, a combined algorithm is proposed that estimates the workloads of the original and alternative algorithms for each row individually before numerical calculations and selects the one with smaller workload. Numerical experiments show that compared with full factorization, the combined algorithm is significantly more efficient and expected to save up to 75% of execution time in our numerical examples. The new method can be easily implemented and applied to engineering problems, especially to local and step-by-step modification of structures.