A branch and bound algorithm for evaluation of the Findley fatigue criterion

• A new method for evaluation of the Findley critical plane criterion is described.
• The critical plane is the plane maximizing a function f of the stress history.
• The method uses derived bounds on the variation of f to find the critical plane.
• The method converges to within a user specified tolerance of the global maximum of f.
• The method evaluates fewer planes, reducing execution time compared to known methods.

In this manuscript, a new algorithm for evaluation of the Findley fatigue criterion is proposed. The algorithm uses a branch and bound technique to limit the number of investigated planes in the search for the critical one. The algorithm has two major advantages over currently existing methods. Firstly, for a given tolerance on the error of the evaluation, it needs to investigate fewer planes on average, thereby reducing the execution time compared to state of the art methods. Secondly, the algorithm is guaranteed to give results within a tolerance of the global maximum, and this tolerance may be freely chosen by the analyst.