Mechanical properties of parts produced with polymer deposition additive manufacturing (AM) depend on the print bead direction, particularly when short carbon-fiber reinforcement is added to the polymer feedstock. This offers a unique opportunity in the design of these structures since the AM print path can potentially be defined in a direction that takes advantage of the enhanced stiffness gained in the bead and, therefore, fiber direction. This paper presents a topology optimization approach for continuous fiber angle optimization (CFAO), which computes the best layout and orientation of fiber reinforcement for AM structures. Statically loaded structures are designed for minimum compliance where the adjoint variable method is used to compute design derivatives, and a sensitivity filter is employed to reduce the checkerboard effect. The nature of the layer-by-layer approach in AM is given special consideration in the algorithm presented. Examples are provided to demonstrate the applicability of the method in both two and three dimensions. The solution to our two dimensional problem is then printed with a fused filament fabrication (FFF) desktop printer using the material distribution results and a simple infill method which approximates the optimal fiber angle results using a contour-parallel deposition strategy. Mechanical stiffness testing of the printed parts shows improved results as compared to structures designed without accounting for the direction of the composite structure. Results show that the mechanical properties of the final FFF carbon fiber/polymer composite printed parts are greatly influenced by the print direction, and optimized material orientation tends to align with the imposed force direction to minimize the compliance.
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