Topology Optimization for Local Fatigue Constraints Using the Augmented Lagrangian Method in Orthotropic Materials

Resumo

Fatigue is a phenomenon that causes failures in structures subjected to cyclic loading, compromising integrity, safety and possibly generating fissures and cracks. Orthotropic materials, such as fiber composites in the case of fiberglass, are designed to resist this type of failure and the development and manufacture of these materials are designed to achieve high performance. Topology optimization emerges as an efficient alternative for structural design, allowing the distribution of the material intelligently and exploiting the anisotropy of the material with lower cost and greater efficiency. In addition, optimizing the fibers with the main loading directions helps to reduce stress concentrations, control the propagation of fatigue damage and avoid fractures. Apply topology optimization in the design of structures composed of orthotropic materials, considering fatigue constraints to extend their structural life. Minimizing the volume of the structure and optimizing the orientation of the fibers, in order to maximize resistance, ensuring safety and durability under loading conditions. Fatigue modeling is performed considering the phenomenon as a local process, allowing the precise capture of stress concentrators in critical regions different from the P-norm. The formulation is based on the Basquin equation for estimating fatigue life, combined with the Hashin fatigue failure criterion, adapted for orthotropic materials. The optimization is conducted via the Augmented Lagrangian method, and the sensitivities of the constraints and the objective function are obtained by automatic differentiation. The problem is solved numerically using the finite element method implemented in the FEniCS, with the quasi-Newton solver employed to update the design variables. Numerical examples will be presented demonstrating the effectiveness of the proposed methodology in obtaining optimized structures in terms of volume, fiber orientation and fatigue resistance. Volumetric reduction of approximately 50% is expected, with fibers efficiently distributed to reinforce the matrix in the most stressed regions, resulting in lighter, stronger and more durable structures. The proposed approach should demonstrate its effectiveness as an advanced structural design tool, promoting optimized solutions in terms of structural performance. Hoping to contribute to the development of safe, adapted structures following structural fatigue standards.