Topology Optmization Applied to Problems with Local Fatigue Constraints Based on Augmented Lagrangian Method

Resumo

Fatigue is the most usual failure mode of any mechanical structure subject to loading. There are several methods to predict the structure life, and different approaches can be applied to extend this life. From the point of view of materials engineering, new materials can be proposed to deal with this issue. However, developing and producing these materials can be expensive. A different approach consists of optimizing the design using some optimization algorithm, determining the optimized material distribution that ensures a higher fatigue life. This work proposes to use topology optimization to design structures subjected to permanent loads to increase the component life. The objective is to minimize the volume, considering fatigue constraints. The works in the literature deal with fatigue constraints using aggregate methods, which are common in problems considering stress constraints. Our proposed approach uses a norm of the stress field to represent the stress constraint. However, stress and fatigue are local phenomena. Thus, in this work, the Augmented Lagrangian method is used to deal with the large number of constraints in the problem. This approach, previously used in stress-constraints problems, makes treating fatigue as a local phenomenon. The Modified Goodman method is used to measure local fatigue. This method considers a sensitivity factor that accurately estimates fatigue life. Numerical examples show the efficiency of the proposed method.