Abstract
The topology optimization method is one of the most flexible structural optimization method that allows not only shape changes but also topological changes during the optimization process. However, due to its high flexibility, the utility of topology optimization results is often spoiled by a preponderance of impractical designs such as structures contains many grayscales. To mitigate this problem, a type of structural optimization method using the level set boundary expression has been proposed, in which the boundary of the optimal configuration are implicitly represented using the level set function. This paper proposes a topology optimization based on the level set method using mathematical programming. In the proposed method, the level set function is updated using a mathematical programming. The optimization problem which has many constraint functionals can be easily formulated using the proposed method. We apply it to the minimum mean compliance problem to verify the proposed method.
