A rapid path‐length searching procedure for multi‐axial fatigue cycle counting

Abstract

In this paper, a series of advanced searching algorithms have been examined and implemented for accelerating multi‐axial fatigue cycle counting efforts when dealing with large time histories. In a computerized calculation of the path‐length dependent cycle counting method, most of the central processor unit's (CPU) time is spent on searching for the maximum range or distance in a stress or strain space. A brute‐force search is the simplest to implement, and will always find a solution if it exists. However, its cost, in many practical problems, tends to grow exponentially as the size of the loading spectrum increases with a search time measured in the order of O(n2), where n is the number of spectrum data points. In contrast, a form of Andrew's monotone chain algorithm, as demonstrated in this paper, can remarkably reduce the solution time to the order of O(n log n). The effectiveness of the new path‐length searching procedure is demonstrated by a series of worked examples with a varying degree of non‐proportionality in multi‐axial loading history.

Multiaxial fatigue assessment of welded joints in marine structures

“…Two sets of characteristics were determined depending on a dominant Mode I or Mode III [35,52]. PDMR cycle counting has been validated in various studies and was applied succesfully in the multiaxial fatigue assessment of welded joints [36,[133][134][135].…”

Comparative study of multiaxial fatigue methods applied to welded joints in marine structures

“…The authors used their own multiaxial cycle counting algorithm developed based on publications of the PDMR cycle counting method [52,57,58]. This algorithm was used to process time traces of normal and shear nominal stress which were generated with the two considered wave spectra.…”

Uncertainty Characterization of Engineering Failure Data

“…Convex hull searching algorithm is considered one of the first sophisticated algorithms in the discipline of computational geometry. Convex hull algorithms have been recently used in multi-axial fatigue analysis and numerical implementation to accelerate the calculation speed [10]. The complexity of computational time for convex hull search with the traditional brute-force algorithm is…”