Evolutionary topology optimization of continuum structures considering fatigue failure

A simplified topology optimization was developed to prevent fatigue failure in this paper. It is based on the bi-directional evolutionary structural optimization (BESO) approach where the modified Goodman fatigue failure criterion was applied directly in the sensitivity analysis. The high-cycle fatigue under proportional loadings with constant amplitude was considered in fatigue analysis. To reduce the computational cost, the modified p-norm approach of the fatigue constraint was applied by assembling the contribution of the local fatigue failure criterion in one function. For the finite element analysis, the sensitivity number of the elements was calculated based on the results from the equivalent linear static analysis while the sensitivity number is based on the Goodman fatigue criterion. The optimization problem was defined as maximizing the stiffness of a structure with a volume constraint and a fatigue failure constrain to prevent fatigue within the prescribed life cycles. The effectiveness of the proposed optimization approach was confirmed through comparison between the new approach results and those from the traditional compliance minimization problem using several traditional examples with obvious stress concentration.