Multidisciplinary topology optimization solved as a Nash game

In the present work, multidisciplinary optimization is formulated in the game theory framework. We choose a coupled heat transfer—thermoelastic system as the case study for which a topology design approach is developed. The multidisciplinary optimization problem is solved as a non-cooperative game and we determine a Nash equilibrium. The game has two players and the parameterization of the design domain is such that the design variables describe the material density and a parameter which influences the heat flow by convection to the surrounding fluid. The first player controls the structure and the second player controls the temperature distribution in the structure. For the second player, we present mathematical proof of existence of a discrete valued optimal solution and it is concluded that no regularization of the suboptimization problem is needed. We present two numerical examples which illustrate the proposed methodology. One of the examples is also solved by weighting the objectives to a scalar valued objective function and the result is compared with the Nash game solution