Optimization Problem of Material Composition in Nonhomogeneous Hollow Sphere Which has Two Dimensionally Distributed Nonhomogeneous Material Property Subjected to Axisymmetric Heat Supply

Abstract

This study is intended as an optimization of material composition in nonhomogeneous hollow sphere which has two-dimensional nonhomogeneous material properties in the radial and meridian directions and is subjected to an axisymmetric heat supply. Numerical solutions of temperature change and axisymmetric thermal stress under the steady state are obtained for nonhomogeneous hollow sphere which has two-dimensional nonhomogeneous material properties by making use of finite element method. As an illustrative numerical result, optimal two-dimensional material composition is found for the functionally graded hollow sphere so as to minimize the ratio of thermal stress under the steady state to strength of material.