This research proposes a robust design method incorporating with the topology optimization for coupled thermal and structural problem. For the robust optimization, the objective function is denned as a combination of maximizing total potential energy for the thermal and structural stiffness and minimizing variation in the total potential energy under uncertainties on design parameters such as conduction of heat, heat transfer coefficient, Young's modulus and applied load. The variation in the total potential energy is evaluated using the first-order derivation under assumption that the uncertainties are relatively small. As the topology optimization method, the formulation of a level set boundary expressions based on the concept of the phase field method is applied. This method allows topological changes with clearly boundary expressions during the optimization procedure. Furthermore, the geometrical complexity of the obtained optimal configurations can be controlled by adjusting a regularization factor, and the obtained optimal configurations are free of checkerboards and grayscales. Through numerical examples, the effect that uncertain conduction of heat, heat transfer, Young's modulus and applied load have upon the obtained configurations is investigated by comparing with deterministic optimum topology design results.
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