Structural topological optimization with dynamic fatigue constraints subject to dynamic random loads

More attention has been attracted to engineering structural design on fatigue failure, while few works are devoted to topology optimizations considering dynamic fatigue failure under random vibrations. In this paper, a new layout optimization method is proposed to consider high-cycle dynamic fatigue constraints which are caused by periodic random dynamic loads. Being incorporated with the rational approximation for material properties (RAMP), the optimization model is built, where the objective function is the structural weight, and the dynamic fatigue failure constraints are applied in the structure. According to the Crossland's criterion, the dynamic fatigue constraints can be formulated by the peak value of the period fluctuating dynamic stress that never exceed the threshold. Then, the Kreisselmeier–Steinhauser (KS) aggregation function is introduced to reduce the number of dynamic fatigue failure constraints. To overcome stress concentration phenomenon, the P-norm aggregation function is introduced to the objective function as a penalty term. Moreover, a new penalty approach is introduced to solve stress singularity, and a constraint-limit-variant method is adopted to obtain stable convergent topologies. The sensitivity of the dynamic fatigue constraints with respect to the design variables is derived so as to form the approximate functions for the dynamic fatigue constraint functions and the objective function. Finally, based on the sensitivity and dual theory, the defined optimization problem is solved by the aforementioned algorithm. The results of several numerical examples are given to demonstrate the validity and effectiveness of the proposed approach.