Efficient topology optimization of large dynamic finite element systems using fatigue

The present paper modifies and extends the recently developed equivalent static load method for the optimization of dynamically loaded linear elastic finite element systems with a huge number of degrees of freedom. In the equivalent static load method, dynamic loads have been transformed into equivalent static loads. This leads to an equivalent static response optimization with multiple loading conditions instead of a dynamic optimization problem. In the present paper, the equivalent static load algorithm is modified and extended by introducing a fatigue analysis in the iterative optimization procedure, where damage is used as suitable termination criterion of the iteration, as well as for the determination of a single and meaningful equivalent static load that leads to maximal damage in the structure. During the evolution process the structure is systematically stiffened by using the solid isotropic microstructure with penalization approach until a user-defined damage level is reached. Three standard examples from literature and an industrial application with a large number of degrees of freedom (600,000) demonstrate the computational efficiency of the proposed method.