マルチプルフェイズプロジェクション法によるトポロジー最適化（設計変数の低減のための新しいプロジェクション関数の定式化）

概要

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The topology optimization method is the most flexible optimization method that allows both shape and 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 that are difficult or impossible to manufacture, such as structures with numerous extremely thin members and tiny holes. This paper proposes a new structural optimization methodology that reduces the number of design variables in a multiple phase projection method, which advantageously reduces computational time and benefits manufacturability. The multiple phase projection method is a geometrical contraint method that imposes a minimum length scale on both solid and void phases. Normally, two design variables are associated with each of these phases at each node in the finite element analysis, resulting in an undesirable increase in the number of design variables. To mitigate this problem, we develop a new methodology that requires only one design variable at each node. An optimum design example for a minimum compliance problem is provided to confirm that the new methodology provides reasonable solutions that achieve the given minimum length scale using a reduced number of design variables.