Towards Manufacturing-Friendly Shapes in Discrete Topology Optimization

TL;DR

This work addresses manufacturing irregularities in discrete topology optimization for antennas by introducing a graph-based regularity framework. It represents the design domain as a graph and defines triangle- and basis-function–level shape parameters (e.g., $r_{area}$, $r_{point}$, $r_{hom}$, $r_{slot}$) to quantify islands, point connections, and rapid material changes, incorporating them into the optimization objective. The approach yields Pareto-frontier descriptions of trade-offs between electromagnetic performance, embodied by $Q/Q_{lb}$, and manufacturability metrics, and demonstrates applicability to discrete memetic algorithms with potential extension to 3D. The findings offer a practical, computationally inexpensive way to generate more manufacturable antenna designs while preserving general applicability to other discrete optimization schemes.

Abstract

This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate regularity measures for any discrete optimization algorithm. Shape regularity is quantified by scalar figures ready to evaluate design choices in the form of Pareto-frontiers. Developed metrics deal with information concerning material usage, problematic distribution, and features that complicate manufacturing. The theory is verified by several examples demonstrating the treatment of isolated islands of materials, point connections between material segments, or homogeneity.

Figures (21)

• Figure 1: A solution to problem \ref{['eq:TopoOptUnrestricted']} found by the algorithm from art:Capek2021MemeticSchemeTopoOptI. The electrical size of the design domain is $ka=0.7$. The orange line represents the position of the feeding point. The value $r_\mathrm{point}$ quantifies the presence of point connections.
• Figure 2: A sketch of the most salient issues related to discrete topology optimization. The depicted features are taken from Fig. \ref{['pic:TopoOptExampleUnrestricted']}. (a) Isolated metal island, (b) point connection, (c) rapidly changing material distribution.
• Figure 3: Solution to problem \ref{['eq:TopoOptRestricted']} at $ka=0.7$. The orange line represents the position of the feeding point.
• Figure 4: A comparison of the absolute value of the reflection coefficient of two designs resulting from problems \ref{['eq:TopoOptUnrestricted']} and \ref{['eq:TopoOptRestricted']}, respectively. The black solid line highlights the $-10\,$dB return loss level considered for the fractional bandwidth calculation. The bandwidth performance of both designs is included for direct comparison.
• Figure 5: Trade-off between the Q-factor and a relative number of point connections $r_\mathrm{point}$. Red and green insets represent two designs at the extremes of the Pareto frontier which is highlighted by a dashed line.