Robust Design of Stochastic Dynamic Systems Based on Fatigue Damage

The design of engineering structures goes through several phases before arriving at a final concept or prototype. Comfort, safety and reliability are desirable characteristics to be achieved, but when it comes to obtaining lighter structures, this can be a problem as to the effects of mechanical vibration, such as fatigue in metals. Material properties related to fatigue are only obtained experimentally using standardized specimens and controlled environments. Results obtained by these tests present a statistical character and carry uncertainties and measurement errors that may significantly affect the final fatigue failure condition. In this context, the inclusion of uncertainties in a computational model becomes essential. This work presents a methodology for fatigue failure prediction by applying the Sines’ fatigue criterion and allowing fatigue analysis to be performed numerically during the design phase. Uncertainties are included in the model using the stochastic finite elements method, with random fields discretized by the so-called Karhunen-Loève expansion method. As stochastic analysis demands multiple function evaluations, the computational cost involved becomes high. Due to this, the application of a model condensation procedure is necessary. After presenting the theory, a robust multiobjective optimization procedure is performed to enhance fatigue life of a thin plate subjected to cyclic loads, which is directly in conflict with reducing its mass. This procedure seeks for not only one point in the search space, but a whole group of solutions where all are treated as optimal and are less susceptible to parameter fluctuations. Numerical results are presented in terms of FRF, stress responses in the frequency domain and Sines fatigue index for each finite element composing the plate.