OPTIMIZATION OF MATERIAL COMPOSITION TO MINIMIZE THERMAL STRESSES IN A FUNCTIONALLY GRADED HOLLOW SPHERE WITH PIECEWISE POWER LAW

摘要

The optimization problem of material design making use of a FGM hollow sphere by a piecewise-power model is discussed due to axisymmetric surface heating.The thermal conductivity,the Young's modulus,and the coefficient of linear thermal expansion are assumed to be expressed as power functions of the radial coordinate,and their values continue on the interfaces.The two-dimensional temperature is analyzed exactly by the method of separation of variables.Solving the Navier's equations,the two dimensionalsolution for the thermoelastic response of a functionally graded sphere with piecewise power law nonhomogeneity is obtained herein under the boundary condition that the inner and outer surfaces are traction free.As an example,numerical calculations are carried out for a functionally graded hollow sphere made of aluminum alloy and alumina subjected to uniform heating or axisymmetrical heating.The optimum material compositions are determined using the nonlinear programming method to minimize theratio of the thermal stress to strength.