レベルセット法に基づく境界表現を用いた形状・トポロジー最適化

抄録

A simultaneous shape and topology optimisation method based on the level set method is presented. In most of structural optimisation methods which have been proposed so far, either shape or topological derivative is used to update both shape and topology of the design object. In this study, configuration of the design object is expressed as a distribution of a level set function (LSF). By using both shape and topological derivatives, the variation of the objective functional due to shape deformation and topological change can approximately be expanded into a quadratic function of the variations of the LSF. This expansion of the objective functional makes it possible to treat shape and topological derivatives simultaneously. The LSF at each point is updated in a way to maximise or minimise the variation of the expanded objective functional iteratively. Through an example of optimisation problem of cloaking devices, it is shown that the proposed method can optimise both shape and topology simultaneously.