  This work provides a numerical calculation of shape gradients of failure
probabilities for mechanical components using a first discretize, then adjoint
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 adjoint methods in the design for mechanical integrity. In
this work we propose, implement and validate a method for the numerical
calculation of the shape gradients of failure probabilities for the failure
mechanism low cycle fatigue (LCF), which applies to polycrystalline metal.
Numerical examples range from a bended rod to a complex geometry from a turbo
charger in 3D.
