Structural topology optimization through implicit boundary evolution based on the Allen–Cahn equation

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.