Optimal three-dimensional design of functionally graded parts for additive manufacturing using Tamura–Tomota–Ozawa model

Although some conventional manufacturing technologies are capable of producing functionally graded materials, only a few additive manufacturing processes are able to build functionally graded materials with complex distribution of material composition. To exploit this unique advantage, we have developed a new methodology capable of optimization of material distribution for three-dimensional parts for any given conditions. Representation of material distribution was done through a new technique by extending the nonuniform rational basis spline surfaces to four-dimensional space. Mori–Tanaka, Levin, and Tamura–Tomota–Ozawa models were employed for the estimation of effective material properties of functionally graded structures. Subroutines were developed in a commercial finite element software to enable the analysis of parts made from functionally graded material. A constrained particle swarm optimization method was selected and implemented to optimize the material composition distribution taking into account the additive manufacturing limitations. As a case study, the material distribution optimization of a functionally graded femur bone plate under thermomechanical loading was considered. The objective was to maximize the safety factor; i.e. the ratio of local yield strength of the functionally graded plate over the von Mises stress. The results showed significant improvement compared to nonoptimal part and demonstrated the efficacy of the proposed methodology.