دانلود رایگان مقاله اثرات مرزی در رویکرد میدان فازی برای توپولوژی بهینه سازی

Abstract

A phase-field based topology optimization approach is considered for the maximum stiffness or minimum compliance problem. The objective functional to be minimized consists in addition to the compliance a cost for gray solutions and a cost for interfaces between void and full material. Since the interfaces between void and full material are penalized via a volume integral in the original phase-field formulation there is no penalty associated with interfaces along the external boundaries. In the present contribution, an additional term representing the cost of interfaces at external boundaries is added to the functional subject to minimization. It is shown that the new boundary term enters the optimization as a Robin boundary condition. The method is implemented in a finite element setting and numerical simulations of typical structures are considered. The results indicate that the optimal designs are influenced by the cost of interfaces to a large extent.

8. Conclusions

A phase-field approach for topology optimization has been considered for the situation of maximizing the stiffness for a given amount of material. In the usual phase-field approach there is no penalty for interfaces forming at design domain boundaries and special emphasis was here devoted to associate costs to the interfaces forming at the design boundaries. Thus an augmented functional including costs for material located at the design domain boundaries has been proposed. It was shown that stationarity of the functional leads to Robin boundary condition instead of the usual Neumann boundary conditions used in a phase-field approach. In addition it was shown that adopting a Ginzburg–Landau approach for the evolution laws together with the Robin boundary conditions minimizes the functional.