Modeling, Minimizing and Managing the Risk of Fatigue for Mechanical Components

TL;DR

This paper reviews recent advances in probabilistic modeling of fatigue failure in mechanical components, focusing on shape design optimization and service scheduling to enhance reliability.

Contribution

It provides a comprehensive review of probabilistic failure models, shape optimization techniques, and applications in service scheduling for fatigue risk management.

Findings

Existence results for optimal shapes

Application of shape derivatives in design

Integration of stochastic models in reliability analysis

Abstract

Mechanical components that are exposed to cyclic mechanical loading fail at loads that are well below the ultimate tensile strength. This process is known as fatigue. The failure time, that is the time when a first crack forms, is highly random. In this work we review some recent developments in the modelling of probabilistic failure times, understood as the time to the formation of a fatigue crack. We also discuss the how probabilistic models can be used in shape design with the design intent of optimizing the component's reliability. We give review a recent existence result for optimal shapes and we discuss continuous and discrete shape derivatives. Another application is optimal service scheduling. The mathematical fields involved range from reliability statistics over stochastic point processes, multiscale modeling, PDEs on variable geometries, shape optimization and numerical analysis to operations research.