AXISYMMETRICAL THERMOELASTIC SHAPE SENSITIVITY ANALYSIS AND ITS APPLICATION TO TURBINE DISK DESIGN

Abstract

A general method for shape design sensitivity analysis (SDSA) as applied to an axisymmetric thermoelasticity problem is presented using the material derivative concept and the adjoint variable method. The sensitivity of a general functional composed of thermal and mechanical quantities is considered. The method for deriving the sensitivity formula is based on standard direct thermal and elastic boundary integral equation formulation. It is then applied to obtain explicit formulas for a representative displacement and stress constraint imposed on a sector of the boundary. Results of numerical implementation are presented for weight minimization of a turbine disc under thermomechanical loading. The sensitivities of the displacement and stress constraint calculated by the formulas are compared with those by finite differences. Optimum shape obtained under the thermomechanical loading is discussed with that under the mechanical loading only, clearly showing the practical importance of the SDSA of thermoelastic systems.