Shape design sensitivity analysis and optimization for nonlinear heat and electric conduction problems

In this article, the shape optimization for the Joule heating of solid bodies is investigated. nz, conductivity coefficients are permitted to vary with temperature. The shape design sensitivity analysis is performed for a general objective function using the adjoint variable method and the material derivative technique. The Kirchhoff's transformation or the Newton-Ralpson method is utilized during the Galerkin finite-element discretizations. The minimization of the objective function is achieved through the conjugate gradient method. After analytical verifications, two two-dimensional example problems are numerically investigated by the present method.