Several additive manufacturing processes are capable of fabricating three-dimensional parts with complex distribution of material composition to achieve desired local properties and functions. This unique advantage could be exploited by developing and implementing methodologies capable of optimizing the distribution of material composition for one-, two-, and three-dimensional parts. This paper is the first effort to review the research works on developing these methods. The underlying components (i.e., building blocks) in all of these methods include the homogenization approach, material representation technique, finite element analysis approach, and the choice of optimization algorithm. The overall performance of each method mainly depends on these components and how they work together. For instance, if a simple one-dimensional analytical equation is used to represent the material composition distribution, the finite element analysis and optimization would be straightforward, but it does not have the versatility of a method which uses an advanced representation technique. In this paper, evolution of these methods is followed; noteworthy homogenization approaches, representation techniques, finite element analysis approaches, and optimization algorithms used/developed in these studies are described; and most powerful design methods are identified, explained, and compared against each other. Also, manufacturing techniques, capable of producing functionally graded materials with complex material distribution, are reviewed; and future research directions are discussed.

Additive manufacturing enables the fabrication of lightweight composite structures with complex geometries; however, accurately predicting their structural response remains challenging when topology optimization introduces multiple thin load-bearing members and complex deposition paths. This study evaluated the end-to-end accuracy of a simplified engineering workflow that combines coupon-derived anisotropic material properties, isotropic topology generation, laminate shell analysis, geometry reconstruction, FDM fabrication, and component testing for short-carbon-fiber-reinforced PLA structures. In-plane elastic properties were characterized using ASTM D3039 tensile and ASTM D3518 shear tests and implemented in ANSYS Mechanical and ACP (Pre). Baseline and topology-derived brackets with different retained-mass targets were manufactured and tested under tensile loading. Experimental stiffness was determined using linear regression over the 25–60% range of each specimen’s maximum load, which provided highly linear fits across all specimens. The simulations systematically overpredicted experimental stiffness, with errors of approximately 14–52% for the baseline and minimum-compliance configurations. Mesh refinement and variations in the assumed out-of-plane elastic properties produced changes substantially smaller than the largest simulation–experiment discrepancies. The results therefore quantify the limitations of transferring coupon-calibrated homogeneous properties through a simplified topology-optimization and FDM workflow and show that the observed disagreement cannot be attributed to mesh density or the investigated out-of-plane material assumptions alone. The workflow is best interpreted as a preliminary engineering assessment rather than as validation of a high-fidelity constitutive or component model.