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This work provides a numerical calculation of shape gradients of failureprobabilities for mechanical components using a first discretize, then adjointapproach. While deterministic life prediction models for failure mechanisms arenot (shape) differentiable, this changes in the case of probabilistic lifeprediction. The probabilistic, or reliability based, approach thus opens theway for efficient adjoint methods in the design for mechanical integrity. Inthis work we propose, implement and validate a method for the numericalcalculation of the shape gradients of failure probabilities for the failuremechanism low cycle fatigue (LCF), which applies to polycrystalline metal.Numerical examples range from a bended rod to a complex geometry from a turbocharger in 3D.

Shape gradients for the failure probability of a mechanical component under cyclical loading