フェーズフィールド法に基づく構造最適化(ペリメータ制約効果の検証とコンプライアントメカニズム創生問題・固有振動数最大化問題への拡張)

摘要

This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. Since the proposed method does not require extra operations such as re initialization of the level set function or smoothing of sensitivities, the computational cost is lower than that of typical level set methods. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double-well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective function and the effect that perimeter control has on the optimal configurations.%ある条件下における機械構造物の最適設計案を考えrnることは，機械設計者及び研究者にとって非常に重要rnな課題である．このような構造最適化問題を数値計算rnで解く際の一般的な方法として，対象となる領域の境rn界形状の最適化を行う形状最適化と，対象の形状のみrnならず形態も最適化可能なトポロジー最適化とが挙げrnられる．