Shape gradients for the failure probability of a mechanic component under cyclic loading: a discrete adjoint approach

This work provides a numerical calculation of shape gradients of failure probabilities for mechanical components using a first discretize, then adjoin approach. While deterministic life prediction models for failure mechanisms are not (shape) differentiable, this changes in the case of probabilistic life prediction. The probabilistic, or reliability based, approach thus opens the way for efficient adjoin methods in the design for mechanical integrity. In this work we propose, implement and verify a method for the numerical calculation of the shape gradients of failure probabilities for the failure mechanism low cycle fatigue, which applies to polycrystalline metal. Numerical examples range from a bended rod to a complex geometry from a turbo charger in 3D.