Shape design sensitivity analysis of an axisymmetric turbine disk using the boundary element method

Abstract

A method of design sensitivity analysis for shape optimization of an axisymmetric turbine disk using the boundary element method is developed. In this method, an optimization problem is defined in functional form. The material derivative concept in continuum mechanics and an adjoint variable method are employed for the shape design sensitivity analysis. Then the variational adjoint equation is transformed to an equivalent adjoint system in the form of a partial differential equation with boundary conditions in a systematic way. The state and adjoint system equations are finally formulated in the form of boundary integral equations for numerical calculation, which is confirmed by the fact that, for axisymmetric elasticity problems, boundary integral expression is valid for the variational solution even when the classical solution does not exist. Accuracy of shape design sensitivity using the suggested method is compared with that using FEM. It is found that the method is not only reliable but also generally effective in various shape optimization of axisymmetric elasticity problems.