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

TL;DR

This paper introduces a numerical method for calculating shape gradients of failure probabilities in mechanical components under cyclical loading, enabling more efficient design optimization through probabilistic life prediction models.

Contribution

It proposes and validates a novel adjoint-based approach for shape gradient computation of failure probabilities in low cycle fatigue of metals, applicable to complex geometries.

Findings

Effective shape gradient computation for LCF failure probabilities.

Validated method on complex 3D geometries.

Facilitates design optimization in mechanical integrity.

Abstract

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.