Thickness filters for gradient based multi-material and thickness optimization of laminated composite structures

This paper presents a new gradient based method for performing discrete material and thickness optimization of laminated composite structures. The novelty in the new method lies in the application of so-called casting constraints, or thickness filters in this context, to control the thickness variation throughout the laminate. The filters replace the layerwise density variables with a single continuous through-the-thickness design variable. Consequently, the filters eliminate the need for having explicit constraints for preventing intermediate void through the thickness of the laminate. Therefore, the filters reduce both the number of constraints and design variables in the optimization problem. Based upon a continuous approximation of a unit step function, the thickness filters are capable of projecting discrete 0/1 values to the underlying layerwise or ”physical” density variables which govern the presence of material in each layer through the thickness of the laminate. Combined with an in-plane density filter, the method enables manufacturers to control the length scale of the geometry while obtaining near discrete designs. Together with the applied manufacturing constraints it is now possible for manufacturers to steer the design towards a higher level of manufacturability. The method is demonstrated for mass minimization with displacement and manufacturing constraints. The results show that the method indeed is capable of obtaining near discrete designs which obey the governing constraints.