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

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.