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"Fatigue has been played a key role into the design process of structures, since many failures of them are attributed to repeated loading and unloading conditions. Crack growth due to fatigue, represents a critical issue for the integrity and resistance of structures and several numerical methods mainly based on fracture mechanics have been proposed in order to address this issue. Apart from loading, the shape of the structures is directly attributed to their service life. In this study, the extended finite element is integrated into a shape design optimization framework aiming to improve the service life of structural components subject to fatigue. The relation between the geometry of the structural component with the service life is also examined. This investigation is extended into a probabilistic design framework considering both material properties and crack tip initialization as random variables. The applicability and potential of the formulations presented are demonstrated with a characteristic numerical example. It is shown that with proper shape changes, the service life of structural component can be enhanced significantly. Comparisons with optimized shapes found for targeted service life are also addressed, while the choice of initial imperfection position and orientation was found to have a significant effect on the optimal shapes."
<https://link.springer.com/chapter/10.1007/978-3-319-18320-6_24?error=cookies_not_supported&code=1ae57456-0bcc-48a1-b0c1-89394f4edf83>