Optimization of thermal conductivities of isotropic and orthotropic solids is treated as a steady-state optimal control problem. Nonlinear necessary optimum conditions are first derived for the so-called material optimization problem, and a general numerical method of solution is then proposed. The iterative numerical procedure solves the linearized state and co-state equations by the finite element method and minimizes the performance index by the conjugate gradient method. Numerical solutions, checked with exact results when possible, are given for an isotropic infinite plate and a cylinder.

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