Fatigue-based topology optimization with non-proportional loads

Abstract

Fatigue resistance is an important structural design criterion. In this work, we present a method for the topology optimization of structures subject to non-proportional cyclic loading with regard to fatigue criteria. The non-proportionality of the loading leads to a significant increase in computational cost with respect to topology optimization methods that only consider proportional loading, as a count of stress reversals must be performed for each point where fatigue damage is to be computed. To alleviate this expense, we take advantage of the common situation where the loading history can be expressed as a linear combination of a set of unit loads. Since we employ stresses to compute damage, the fatigue-driven problem shares the same difficulties as stress-based topology optimization problems, namely the onset of singular optima, the high non-linearity of damage with respect to the design variables, and a large number of points where damage is to be evaluated. We employ similar strategies to those of stress-based topology optimization to circumvent these difficulties. We demonstrate our method through several numerical examples, including a realistic-size 3-dimensional component.