Multi-material and thickness optimization of laminated composite structures subject to high-cycle fatigue

Laminated composite structures have a distinct inherent potential for optimization due to their tailorability and their associated complex failure mechanisms that makes intuitive design remarkably difficult. Optimization of such is a maturing technology with many criteria and manufacturing constraints having been successfully demonstrated. An approach for high-cycle fatigue is however yet to be developed in a gradient-based context. Thus, the objective of this work is to introduce a novel framework that allows for effective high-cycle fatigue optimization of laminated composite structures.Offset is taken in the Discrete Material and Thickness Optimization parametrization, which allows for simultaneous material and thickness selection for each layer that constitute a laminate. The fatigue analysis approach is based on accumulating damage from all variable-amplitude cycles in an arbitrary spectrum. As high-cycle fatigue behavior is highly nonlinear, it is difficult to handle in optimization. To stabilize the problem, damage is scaled using an inverse P-mean norm formulation that reduces the nonlinearity and provides an accurate measure of the damage. These scaled damages are then aggregated using P-norm functions to reduce the number of constraints. This is convenient, as it allows sensitivities to be efficiently calculated using analytical adjoint design sensitivity analysis. The effectiveness of this approach will be demonstrated on both benchmark examples and a more complicated main spar structure.