Multi-objective optimization of functionally graded thick shells for thermal loading

Presented herein is a methodology for the multi-objective optimization of material distribution of functionally graded cylindrical shells for steady thermomechanical processes. The proposed approach focuses on isotropic metal/ceramic and metal/metal functionally graded materials, which offer great promise in high temperature and high heat flux applications. The material composition is assumed to vary only in the thickness direction. The volume fractions of the constituent material phases at a point are obtained through piecewise cubic interpolation of volume fractions defined at a finite number of evenly spaced control points. The effective material properties are estimated using the self-consistent homogenization scheme. The volume fractions at the control points, which are chosen as the design variables, are optimized using an elitist, non-dominated sorting multi-objective genetic algorithm. Candidate designs are evaluated using an exact power-series solution to the two-dimensional quasi-static heat conduction and plane strain thermoelasticity problems. The formulation, which is applicable to both thin and thick functionally graded shells, can also be used to analyze and optimize functionally graded plates in the limit that the midsurface radius of the shell approaches infinity. The proposed methodology is illustrated by optimizing the material composition profile for two model problems. In the first model problem, both the mass and the peak hoop stress of Zirconia/Titanium alloy plates and shells are simultaneously minimized for a prescribed temperature load with a constraint on the maximum temperature experienced by the metal. The goal of the second model problem is to simultaneously minimize the mass and maximize the factor of safety of Tungsten/Copper alloy functionally graded plates and shells under an applied heat flux, subject to a constraint on the factor of safety.