Multi-objective Design Optimization of Functionally Graded Materials

In this paper, we present a methodology for the simulation and multi- objective optimization of material distribution of functionally graded materials (FGMs). The proposed approach focuses on metal/ceramic and metal/metal functionally graded materials, which oer great promise in high temperature and high heat flux applications. The spatial dis- tribution of the volume fraction is defined using piecewise cubic interpolation of volume fractions at a finite number of control points. The eective material properties are estimated from the local volume fractions of the material constituents us- ing the Mori-Tanaka and self-consistent homoge- nization schemes. Functionally graded rectangu- lar structures that are graded in two-dimensions are analyzed using the element-free Galerkin method to obtain the temperature and stress fields. An exact solutions to the heat conduc- tion and thermoelasticity problems has also been developed for functionally graded thick shells that are graded in the radial direction. The volume fraction distribution is optimized using an elitist, non-dominated sorting multi-objective genetic algorithm. Results for two model prob- lems demonstrate that the proposed methodol- ogy provides a useful design tool for tailoring the material composition of functionally graded components for multiple, often conflicting, ob- jectives.

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