On non‐parametric fatigue optimization

• Published in: International journal for numerical methods in engineering Vol. 124; no. 5; pp. 1168 - 1192
• Main Authors: Sartorti, Roman, Möcker, Torsten, Kriegesmann, Benedikt, Pedersen, Claus B.W.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 15.03.2023; Wiley Subscription Services, Inc
• Subjects: critical planes; Damage; damage parameters; Design optimization; fatigue damage; Fatigue failure; Fatigue life; Nonparametric statistics; non‐parametric optimization; Numerical analysis; Numerical differentiation; Parameters; rainflow counting; Search algorithms; semi‐analytical adjoint sensitivities; Sensitivity analysis; Stiffness; Tensors
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.7158

The present work presents a novel approach for semi‐analytic adjoint sensitivity‐based design optimization for nonproportional fatigue damage. In order to apply fatigue damage in sensitivity‐based design optimizations, an essential part is to calculate correct sensitivities. However, this is not straight forward since fatigue damage calculation typically include rainflow counting and critical plane search algorithms. Therefore, no derivatives are directly available for the fatigue damage calculation, only functional values given by numerical computation. In existing literature the considered fatigue damage calculation is simplified until a closed‐form differentiability is satisfied. However, these simplifications are not applicable for industrial examples where accurate fatigue life estimates are required. In the present work numerical differentiation of the fatigue damage values with respect to the stress tensor is applied to calculate semi‐analytical adjoint sensitivities at material points for multiple load cases. The proposed method is verified and demonstrated using different damage parameter types including critical plane analysis. Additionally, different academic and industrial numerical examples are compared to stress and stiffness optimized designs. The fatigue damage optimized designs show improved fatigue damage results for both the specific damage parameter types and when comparing to stress and stiffness optimized designs. Furthermore, it is successfully applied for different design variables (sizing, non‐parametric shape and bead) as well as different optimization formulations using fatigue damage either as objective or constraint.