レベルセット法に基づく熱構造連成問題のトポロジー最適設計に対する不確定性を考慮したロバスト設計法

概要

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In this paper, a robust design method is applied to the topology optimization for coupled thermal and structural problem. For the robust topology optimization, the objective function is defined 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, Youngs modulus and applied load. The variation in the total potential energy is evaluated using the first-order derivation under assumption that 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, Youngs modulus and applied load have upon the obtained configurations is investigated by comparing with deterministic optimum topology design results.