Structural topology optimization through implicit boundary evolution based on the Allen–Cahn equation. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Gao, Jiawen; Song, Baowei; Mao, Zhaoyong
• Is Part Of: Engineering optimization. Volume 53:Issue 1(2021)
• Page Start: 125
• Page End: 144
• Publication Date: 2021-01-02
• Subjects: Topology optimization -- phase-field method -- Allen–Cahn equation -- characteristic function -- sensitivity; Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2019.1705288
• Languages: English
• ISSNs: 0305-215X

Abstract

ABSTRACT: An improved phase-field method based on the Allen–Cahn (AC) equation is proposed for topology optimization to obtain the optimized structure with a smooth and clear boundary. In the proposed method, the design structure is represented by the phase-field function, and the structural boundary is implicitly represented by the 0.5 contour of the phase-field function. The characteristic function is used in finite element analysis. As the design variable, the phase-field function is updated by the AC equation. In this framework, a modified sensitivity is used to make the structural boundary smooth. Several numerical examples are studied to demonstrate the effectiveness of this method.