Multi-stroke design of 2D continuum structures through topology optimization

• Introduces a multi-stroke design approach for fixed-width, closed-stroke 3D-printable structures. • Develops a three-field FPTO framework with a p-norm filter to enforce uniform stroke width. • Achieves printable, gap-free layouts with modest stiffness trade-offs. • Reveals volume fraction and stroke width effects on complexity, stiffness, and manufacturability. A multi-stroke design inspired by outlining the boundary of a character is proposed to generate an engineering structure with fixed-width closed annular strokes from the maternal structure, ensuring 3D-printing manufacturability and aesthetic harmony. For the first time, this paper develops a framework based on the three-field floating projection topology optimization (FPTO) method for designing stroke-based structures, ensuring a fixed stroke width via a p -norm-based filter scheme. The objective is to minimize the compliances of the stroke-based structure and its maternal structure simultaneously. Meanwhile, the minimal length scale of the maternal structure is controlled to avoid isolated strokes. Numerical results demonstrate that the optimized multi-stroke designs offer easy-to-implement printing paths with no unfilled or unprintable gaps with modest stiffness trade-offs compared to conventional solutions. Parametric studies reveal the influence of volume fraction and stroke width on structural complexity and manufacturability, with the proposed method showing the greatest advantages at higher volume fractions and smaller stroke widths. Overall, the framework provides an efficient, practical tool for directly designing printable, structurally efficient components.