This review paper provides an overview of different level-set methods for structural topology optimization. Level-set methods can be categorized with respect to the level-set-function parameterization, the geometry mapping, the physical/mechanical model, the information and the procedure to update the design and the applied regularization. Different approaches for each of these interlinked components are outlined and compared. Based on this categorization, the convergence behavior of the optimization process is discussed, as well as control over the slope and smoothness of the level-set function, hole nucleation and the relation of level-set methods to other topology optimization methods. The importance of numerical consistency for understanding and studying the behavior of proposed methods is highlighted. This review concludes with recommendations for future research.

Level-set methods for structural topology optimization: a review

This paper first reviews manufacturing technologies for realizing air-filled metal-pipe rectangular waveguides (MPRWGs) and 3-D printing for microwave and millimeter-wave applications. Then, 3-D printed MPRWGs are investigated in detail. Two very different 3-D printing technologies have been considered: low-cost lower-resolution fused deposition modeling for microwave applications and higher-cost high-resolution stereolithography for millimeter-wave applications. Measurements against traceable standards in MPRWGs were performed by the U.K.’s National Physical Laboratory. It was found that the performance of the 3-D printed MPRWGs were comparable with those of standard waveguides. For example, across X-band (8–12 GHz), the dissipative attenuation ranges between 0.2 and 0.6 dB/m, with a worst case return loss of 32 dB; at W-band (75–110 GHz), the dissipative attenuation was 11 dB/m at the band edges, with a worst case return loss of 19 dB. Finally, a high-performance W-band sixth-order inductive iris bandpass filter, having a center frequency of 107.2 GHz and a 6.8-GHz bandwidth, was demonstrated. The measured insertion loss of the complete structure (filter, feed sections, and flanges) was only 0.95 dB at center frequency, giving an unloaded quality factor of 152—clearly demonstrating the potential of this low-cost manufacturing technology, offering the advantages of lightweight rapid prototyping/manufacturing and relatively very low cost when compared with traditional (micro)machining.

3-D Printed Metal-Pipe Rectangular Waveguides

Additive manufacturing (AM), also known as three-dimensional (3D) printing, has boomed over the last 30 years, and its use has accelerated during the last 5 years AM is a materials-oriented manufacturing technology, and printing resolution versus printing scalability/speed trade-off exists among various types of materials, including polymers, metals, ceramics, glasses, and composite materials Four-dimensional (4D) printing, together with versatile transformation systems, drives researchers to achieve and utilize high dimensional AM Multiple perspectives of the AM of structural materials have been raised and illustrated in this review, including multi-material AM (MMa-AM), multi-modulus AM (MMo-AM), multi-scale AM (MSc-AM), multi-system AM (MSy-AM), multi-dimensional AM (MD-AM), and multi-function AM (MF-AM) The rapid and tremendous development of AM materials and methods offers great potential for structural applications, such as in the aerospace field, the biomedical field, electronic devices, nuclear industry, flexible and wearable devices, soft sensors, actuators, and robotics, jewelry and art decorations, land transportation, underwater devices, and porous structures

Additive manufacturing of structural materials

3D printing is used extensively in product prototyping and continues to emerge as a viable option for the direct manufacture of final parts. It is known that dielectric materials with relatively high real permittivity—which are required in important technology sectors such as electronics and communications—may be 3D printed using a variety of techniques. Among these, the fused deposition of polymer composites is particularly straightforward but the range of dielectric permittivities available through commercial feedstock materials is limited. Here we report on the fabrication of a series of composites composed of various loadings of BaTiO3 microparticles in the polymer acrylonitrile butadiene styrene (ABS), which may be used with a commercial desktop 3D printer to produce printed parts containing user-defined regions with high permittivity. The microwave dielectric properties of printed parts with BaTiO3 loadings up to 70 wt% were characterised using a 15 GHz split post dielectric resonator and had real relative permittivities in the range 2.6–8.7 and loss tangents in the range 0.005–0.027. Permittivities were reproducible over the entire process, and matched those of bulk unprinted materials, to within ~1%, suggesting that the technique may be employed as a viable manufacturing process for dielectric composites.

/pdf/microwave-dielectric-characterisation-of-3d-printed-batio3-33i6t5qf4l.pdf

Microwave dielectric characterisation of 3D-printed BaTiO3/ABS polymer composites.

The electromagnetic (EM) spectrum is becoming more crowded, and it is densely populated with various wireless signals and parasitic interferers in connection with communication and sensing services. Increasingly sophisticated radio-frequency (RF), microwave, and millimeter-wave filters are required to enable the selection and/or rejection of specific frequency channels. This will occur in future generations of the wireless system, such as the current hotly debated fifth-generation communication systems, where the spectral channelization of a heterostructured wide-band signals will be critical in support of a host of coexisting bandwidths or speeds and applications. Bandpass filters have been the most useful and popular types for such applications and are the most difficult to design and develop in practice. Other types of filters such as notch (stopband) and lowpass filters have also been widely used in many systems, and their design is generally perceived less critical with respect to band-pass filters. This article will focus on the presentation and discussion of bandpass filters. Design factors or parameters of filters, such as selectivity, cost, miniaturization, sensitivity to environmental effects (temperature and humidity, for example), and power handling, combined with predefined in-band and out-of-band performance metrics, are critical specifications of the design with respect to the development of RF and microwave front ends. This is indispensable for the efficient utilization of frequency spectrum resources and the cost-effective enhancement of wireless system performances.

Substrate Integrated Waveguide Filter: Basic Design Rules and Fundamental Structure Features

Three-dimensional (3-D) ceramic stereolithography has been developed and used to manufacture RF devices using periodic structures. To our knowledge, it is the first time that zirconia and high-performance Ba3ZnTa2O9 ceramics are used with that process to manufacture high unloaded quality factor resonant structures and bandpass filters working in the Ka-band. A theoretical study on the performances of periodic arrangements of high-permittivity structures has been carried out and has led to the manufacture of a high unloaded quality factor cavity and narrow three-pole filter (1% bandwidth) measured at a working frequency of 33 GHz

Ceramic Layer-By-Layer Stereolithography for the Manufacturing of 3-D Millimeter-Wave Filters

This letter presents a compact design of a shielded high unloaded Q dielectric resonator. The main interest of this work is the use of the three-dimensional stereolithography process to manufacture innovative ceramic radio frequency devices. Thus, a resonator, its support, and the surrounding cavity is manufactured in one part out of alumina by that process. The measured structure exhibits an unloaded Q of 3900 at 11.88GHz and is free of spurious modes over a 3-GHz range

Innovative Shielded High $Q$ Dielectric Resonator Made of Alumina by Layer-by-Layer Stereolithography

An original waveguide located in a woodpile (layer-by-layer) crystal is presented in this paper. Its geometrical sizes, shape and location have been optimized in order to maximize its bandwidth and the matching between this guide and the input/ouput feeding WR waveguides. The 3D electromagnetic band gap (EBG) crystal has been designed, optimized and manufactured in one monolithic piece with zirconia (epsivr=31.2 at 30 GHz) by the 3D ceramic stereolithography process. It experimentally exhibits a large complete bandgap superior to 20% and the waveguide located in such woodpile provides a measured 20% bandwidth around 26 GHz while keeping a return loss inferior to -10dB.

Large experimental bandpass waveguide in 3D EBG woodpile manufactured by layer-by-layer ceramic stereolithography

The finite element method is coupled with the topology gradient (TG) and level-set (LS) methods for optimizing the shape of microwave components using a computer-aided design model. On the one hand, the LS approach is based on the classical shape derivative; while on the other hand, the TG method is precisely designed for introducing new perturbations in the optimization domain. These two approaches, which consist in minimizing a cost function related to the component behavior, are first described. Regarding given electrical specifications, these techniques are applied to optimize the distribution of ceramic parts of a dual-mode resonator in order to improve its behavior. The optimized dielectric resonators result in a wide spurious-free stop band. A comparison between classical and optimized dual mode resonator is presented. Theoretical results are then validated by careful measurements. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE 2010.

Shape optimized design of microwave dielectric resonators by level-set and topology gradient methods

Electromagnetic BandGap (EBG) concept is used to create cavity by dimensioning a variant cell (or defect) inside a 2D EBG material. Compact high unloaded Q cavity (Qu ~ 2500) and narrow two and three pole filters are designed in Ka band. They are manufactured by layer-by-layer stereolithography and made out of high permittivity yttria-stabilized Zirconia. Measurements of the three pole filter working at 33.45GHz exhibits an 1.05% bandwidth and an insertion loss of 1.7dB. These specifiations are close to the theoretical values of 33GHz (1.5% shift in central working frequency) and 0.95% bandwidth.

C. Delage

Papers

Ceramic Layer-By-Layer Stereolithography for the Manufacturing of 3-D Millimeter-Wave Filters

Innovative Shielded High $Q$ Dielectric Resonator Made of Alumina by Layer-by-Layer Stereolithography

Large experimental bandpass waveguide in 3D EBG woodpile manufactured by layer-by-layer ceramic stereolithography

Shape optimized design of microwave dielectric resonators by level-set and topology gradient methods

Narrow Ka Bandpass Filters Made Of High Permittivity Ceramic By Layer-By-Layer Polymer Stereolithography