J. W. Lee, G. H. Yoon, and S. H. Jeong. Computers & Mathematics with Applications 70, no. 8 (2015): 1852-1877.

This research develops a new topological optimization (TO) method to assess dynamic fatigue failure in the frequency domain for random excitation forces. Besides static failure, fatigue life (or fatigue failure) is an important design criterion for the safety of mechanical and building structures. Therefore, many assessment theories and computational approaches have been proposed, and they can be divided into two categories: time domain and frequency domain. Although both approaches have been successfully applied for engineering purposes, they are rarely considered in structural TO. To consider fatigue failure caused by stochastic mechanical loads in structural TO, this research adopts fatigue assessment approaches in the frequency domain, such as narrow band solution, the Wirsching and Light method, the Ortiz and Chen method, and Dirlik method. For TO, we perform an adjoint sensitivity analysis with those fatigue assessment methods. We consider some two-dimensional benchmark problems and show that the present design method successfully constrains fatigue.