Element-based connectivity approach for topology optimization of rib layout design
摘要
Topology optimization is a powerful tool for designing high-performance structures, but its practicality is often constrained by manufacturability requirements. Among these, the extrusion constraint plays a crucial role by enforcing all elements aligned along a specified direction to share the same material density, thereby producing components with a constant cross-section suitable for extrusion-based fabrication. In this context, the extrusion constraint is employed as an effective strategy to generate ribbed or stiffened layouts directly within the optimization process. Additionally, maximum size control is introduced to prevent the formation of excessively large or impractical features. This paper presents a connectivity-based approach to simultaneously enforce extrusion and maximum size constraints in topology optimization problems for structured mesh. By leveraging element connectivity, the method ensures a consistent material layout along extrusion directions while controlling feature size, without requiring extensive preprocessing or a complex mathematical formulation. Integrated into a compliance minimization framework and implemented using PyMAPDL, the approach seamlessly interacts with finite element analysis. Numerical test cases, including plate, cylinder, spherical dome, s-shape shell, and cycloid-shape shell validate the effectiveness of the proposed method in producing manufacturable ribbed designs. However, this improvement in manufacturability is achieved with only a limited increase in structural compliance approximately 20% for the plate, 6% for the cylinder, 1% for the spherical dome, 11% for the s-shape, and 18% for the cycloid-shape shell. This demonstrates the effectiveness of the proposed method in producing ribbed designs with minimal loss in structural performance.