Recent progress of self-supported air electrodes for flexible Zn-air batteries

Smart wearable devices are regarded to be the next prevailing technology product after smartphones and smart homes,and thus there has recently been rapid development in flexible electronic energy storage devices.Among them,flexible solid-state zinc-air batteries have received widespread attention because of their high energy density,good safety,and stability.Efficient bifunctional oxygen electrocatalysts are the primary consideration in the development of flexible solid-state zinc-air batteries,and self-supported air cathodes are strong candidates because of their advantages including simplified fabrication process,reduced interfacial resistance,accelerated electron transfer,and good flexibility.This review outlines the research progress in the design and construction of nanoarray bifunctional oxygen electrocatalysts.Starting from the configuration and basic principles of zinc-air batteries and the strategies for the design of bifunctional oxygen electrocatalysts,a detailed discussion of self-supported air cathodes on carbon and metal substrates and their uses in flexible zinc-air batteries will follow.Finally,the challenges and opportunities in the development of flexible zinc-air batteries will be discussed.

Recent advances of carbon fiber-based self-supported electrocatalysts in oxygen electrocatalysis

Oxygen reduction reaction(ORR) and oxygen evolution reaction(OER) are the key reactions in numerous renewable energy devices. Unlike conventional powdered catalysts, self-supported catalysts are extensively employed in oxygen electrocatalysis because of the enhanced electron-transfer rate, high specific surface area, and superior mechanical flexibility. Among the self-supported conductive substrates, carbon fiber usually exhibits several distinctive advantages, such as a straightforward preparation process, relatively low cost, good stability, and excellent conductivity. Against this background,carbon fiber-based self-supported electrocatalysts have been widely applied and studied in oxygen electrocatalysis, indicating a promising development direction in oxygen electrocatalyst research.Thus, it is essential to offer an overall summary of the research progress in this field to facilitate its subsequent development. Taking the regulatory mechanisms and modification methods as a starting point, this review comprehensively summarizes recent research on carbon fiber-based self-supported electrocatalysts in recent years. Firstly, a brief overview of the synthesis methods and regulatory mechanisms of carbon fiber-based self-supported electrocatalysts is given. Furthermore, the view also highlights the modification methods and research progress of self-supported electrocatalysts synthesized on carbon fiber-based substrates in recent years in terms of different dopant atoms. Finally, the prospects for the application of self-supported electrocatalysts based on carbon fiber in oxygen electrocatalysis and the possible future directions of their development are presented. This review summarizes recent developments and applications of self-supported bi-functional electrocatalysts with carbon fiber-based materials as the conducting substrate in oxygen electrocatalysis. It also lays a robust scientific foundation for the subsequent reasonable design of highly effective carbon fiber-based self-supported electrocatalysts.

Self-supported metal(Fe, Co, Ni)-embedded nitrogen-doping carbon nanorod framework as trifunctional electrode for flexible Zn-air batteries and switchable water electrolysis

To meet the practical demand of wearable/portable electronics, developing high-efficiency and durable multifunctional catalyst and in-situ assembling catalysts into electrodes with flexible features are urgently needed but challenging. Herein, we report a simple route to fabricate bendable multifunctional electrodes by in-situ carbonization of metal ion absorbed polyaniline precursor. Alloy nanoparticles encapsulated in graphite layer are uniformly distributed in the N-doping carbon nanorod skeleton. Profiting from the favorable free-standing structure and the cooperative effect of metallic nanoparticles, graphitic layer and N doped-carbon architecture, the trifunctional electrodes exhibit prominent activities and stability toward HER, OER and ORR. Notably, due to the protection of carbon layer, the electrocatalysts show the reversible catalytic HER/OER properties. The overall water splitting device can continuously work for 12 h under frequent exchanges of cathode and anode. Importantly, the bendable metal air batteries fabricated by self-supported electrode not only displays the outstanding battery performance,achieving a decent peak power density(125 mW cm^(-2)) and exhibiting favorable charge-discharge durability of 22 h, but also holds superb flexible stability. Specially, a lightweight self-driven water splitting unit is demonstrated with stable hydrogen production.

Bioinspired Nanostructured Superwetting Thin-Films in a Self-supported form Enabled“Miniature Umbrella”for Weather Monitoring and Water Rescue

Two-dimensional(2D)soft materials,especially in their self-supported forms,demonstrate attractive properties to realize biomimetic morphing and ultrasensitive sensing.Although extensive efforts on design of self-supported functional membranes and integrated systems have been devoted,there still remains an unexplored regime of the combination of mechanical,electrical and surface wetting properties for specific functions.Here,we report a self-supported film featured with elastic,thin,conductive and superhydrophobic characteristics.Through a well-defined surface modification strategy,the surface wettability and mechanical sensing can be effectively balanced.The resulted film can function as a smart umbrella to achieve real-time simulated raining with diverse frequencies and intensity.In addition,the integrated umbrella can even response sensitively to the sunlight and demonstrate a positively correlation of current signals with the intensity of sun illumination.Moreover,the superhydrophobic umbrella can be further employed to realize water rescue,which can take the underwater object onto water surface,load and rapidly transport the considerable weight.More importantly,the whole process of loaded objects and water flow velocity can be precisely detected.The self-supported smart umbrella can effectively monitor the weather and realize a smart water rescue,demonstrating significant potentials in multifunctional sensing and directional actuation in the presence of water.

Synergistic integration of self-supported 1T/2H-WS_(2) and nitrogendoped rGO on carbon cloth for pH-universal electrocatalytic hydrogen evolution

Hydrogen economy based on electrochemical water splitting exemplified one of the most promising means for overcoming the rapid consumption of fossil fuels and the serious deterioration of global climate.The development of earth-abundant,efficient,and durable electrocatalysts for hydrogen evolution reaction(HER)plays a vital role in the commercialization of water electrolysis.Regard,the self-supported electrode with unique nitrogen-doped reduced graphene oxide(N-rGO)nanoflakes and WS_(2) hierarchical nanoflower that were grown directly on carbon cloth(CC)substrate(WS_(2)/N-rGO/CC)was successfully synthesized using a facile dual-step hydrothermal approach.The as-synthesized 50%1T/2H-WS_(2)/N-rGO/CC(WGC),which possessed high metallic 1T phase of 57%not only efficiently exposed more active sites and accelerated mass/charge diffusion,but also endowed excellent structural lustiness,robust stability,and durability at a high current density.As a result,the 50%WGC exhibited lower overpotentials and Tafel slopes of 21.13 mV(29.55 mV∙dec^(-1))and 80.35 mV(137.02 mV∙dec^(-1))as compared to 20%Pt-C/CC,respectively for catalyzing acidic and alkaline hydrogen evolution reactions.Pivotally,the as-synthesized 50%WGC also depicted long-term stability for more than 8 h in the high-current-density regions(100 and 220 mA∙cm^(-2)).In brief,this work reveals a self-supported electrode as an extraordinary alternative to Pt-based catalysts for HER in a wide pH range,while paving a facile strategy to develop advanced electrocatalysts with abundant heterointerfaces for practical applications in energy-saving hydrogen production.

Scalable production of self-supported WSe/CNFs by electrospinning as the anode for high-performance lithium-ion batteries

WS2/carbon nanofibers （WS2/CNFs） are obtained by a simple electrospinning method in which few-/ single-layer WS2 is uniformly embedded in carbon fibers. When used as the active anode material for Li-ion cells, these nanofibers exhibit a first-cycle discharge/charge capacity of 941/756 mAh/g at 100 mAJg and maintain a capacity of 458 mAh/g after 100 cycles at 1 A/g. The evolution of size and crystallinity of WS2 with heating treatment are system- atically studied, which are found to strongly influence the final electrochemical performance. Interestingly, the WS2 samples of lowest crystallinity show the highest performance among all studied samples, which could result from the large interfacial capacity for Li ions due to their large specific surface area. More interestingly, the inherent flexible attribute of electrospun nanofibers renders them a great potential in the utilization of binder-flee anodes. Similar high discharge/charge capacity of 761/604 mAh/g with a first coulombic efficiency of 79.4 % has been achieved in these binder-flee anodes. Considering the universal of such simple and scalable preparation strategy, it is very likely to extend this method to other similar two-dimensional layered materials besides WS2 and provides a promising candidate elec- trode for developing flexible battery devices.

Robust self-supported anode by integrating Sb2S3 nanoparticles with S,N-codoped graphene to enhance K-storage performance

Developing high-performance anode materials for potassium-ion batteries is significantly urgent. We here demonstrate Sb_2S_3 nanoparticles(~20 nm) homogeneously dispersed in porous S,N-codoped graphene framework(Sb_2S_3-SNG) as a self-supported anode material for potassium-ion batteries. The rational structure design of integrating Sb_2S_3 nanoparticles with S,N-codoped graphene contributes to high reactivity, strong affinity, good electric conductivity, and robust stability of the composite, enabling superior K-storage performance. Moreover, the self-supported architecture significantly decreases the inactive weight of the battery, resulting in a high energy density of a Sb_2S_3-SNG/KVPO_4 F-C full cell to ~166.3 W h kg^(-1).

Self-supported transition metal phosphide based electrodes as high-efficient water splitting cathodes

Electrolytic water splitting has been considered as a promising technology to produce highly pure H2 by using electrical power produced from wind, solar energy or other fitful renewable energy resources. Combining novel self-supporting structure and high-performance transition metal phosphides （TMP） shows substantial promise for practical application in water splitting. In this review, we try to provide a comprehensive analysis of the design and fabrication of various self-supported TMP electrodes for hydrogen evolution reaction, which are divided into three categories： catalysts growing on carbon-based substrates, catalysts growing on metal-based substrates and free- standing catalyst films. The material structures together with catalytic performances of self-supported electrodes are presented and discussed. We also show the specific strategies to further improve the catalytic performance by elemental doping or incorporation of nanocarbons. The simple and one-step methods to fabricate self-supported TMP electrodes are also highlighted. Finally, the chal- lenges and perspectives for self-supported TMP electrodes in water splitting application are briefly discussed.

Self-supported ternary Co0.5Mn0.5P/carbon cloth （CC） as a high-performance hydrogen evolution electrocatalyst

Scalable production of earth-abundant, easy-to-prepare, and cost-effective electrocatalysts for the hydrogen evolution reaction （HER） is essential for sustainable energy-based systems. Herein, we systematically studied the electrocatalytic HER performance of a self-supported ternary Co0.5Mn0.5P/carbon cloth （CC） nanomaterial prepared using a hydrothermal reaction and phosphorizafion process. Electrochemical tests demonstrated that the ternary Co0.5Mn0.5P/CC nanomaterial could be a highly active electrocatalyst in acidic media, with overpotentials of only 41 and 89 mV, affording current densities of 10 and 100 mA.cm-2, respectively, and a Tafel slope of 41.7 mV.dec-1. Furthermore, the electrocatalyst exhibited superior stability, with 3,000 cycles of cyclic voltammetry from -0.2 to 0.2 V at a scan rate of 100 mV.s-1 and 40 h of static polarization at a fixed overpotential of large-scale hydrogen production. 83 mV, indicating its potential for

Self-supported transition metal chalcogenides for oxygen evolution

Owing to stable spatial framework and large electrochemical interface,self-supported transition metal chalcogenides have been actively explored in renewable energy fields,especially in oxygen evolution reaction(OER).Here,we review the research progress of self-supported transition metal chalcogenides(including sulfides,selenides,and tellurides)for the OER in recent years.The basic principle and evaluation parameters of OER are first introduced,and then the preparation methods of transition metal chalcogenides on various self-supporting substrates(including Ni foam(NF),carbon cloth(CC),carbon fiber paper(CFP),metal mesh/plate,etc.)are systematically summarized.Subsequently,advanced optimization strategies(including interface and defect engineering,heteroatom doping,edge engineering,surface morphology engineering,and construction of heterostructure)are introduced in detail to improve the inherent catalytic activity of self-supported electrocatalysts.Finally,the challenges and prospects of developing more promising self-supported chalcogenide electrocatalysts are proposed.

Advance in 3D self-supported amorphous nanomaterials for energy storage and conversion

The advancement of next-generation energy technologies calls for rationally designed and fabricated electrode materials that have desirable structures and satisfactory performance.Three-dimensional(3D)self-supported amorphous nanomaterials have attracted great enthusiasm as the cornerstone for building high-performance nanodevices.In particular,tremendous efforts have been devoted to the design,fabrication,and evaluation of self-supported amorphous nanomaterials as electrodes for energy storage and conversion devices in the past decade.However,the electrochemical performance of devices assembled with 3D self-supported amorphous nanomaterials still remains to be dramatically promoted to satisfy the demands for more practical applications.In this review,we aim to outline the achievements made in recent years in the development of 3D self-supported amorphous nanomaterials for a broad range of energy storage and conversion processes.We firstly summarize different synthetic strategies employed to synthesize 3D nanomaterials and to tailor their composition,morphology,and structure.Then,the performance of these 3D self-supported amorphous nanomaterials in their corresponding energy-related reactions is highlighted.Finally,we draw out our comprehensive understanding towards both challenges and prospects of this promising field,where valuable guidance and inspiration will surely facilitate further development of 3D self-supported amorphous nanomaterials,thus enabling more highly efficient energy storage and conversion devices that play a key role in embracing a sustainable energy future.

Self-supported transition metal oxide electrodes for electrochemical energy storage

Electrode materials are of decisive importance in determining the performance of electrochemical energy storage(EES)devices.Typically,the electrode materials are physically mixed with polymer binders and conductive additives,which are then loaded on the current collectors to function in real devices.Such a configuration inevitably reduces the content of active species and introduces quite some undesired interfaces that bring down the energy densities and power capabilities.One viable solution to address this issue is to construct self-supported electrodes where the active species,for example transition metal oxides(TMOs),are directly integrated with conductive substrates without polymer binders and conductive additives.In this review,the recent progress of self-supported TMO-based electrodes for EES devices including lithium-ion batteries(LIBs),sodium-ion batteries(SIBs),aluminum-ion batteries(AIBs),metal-air batteries,and supercapacitors(SCs),is discussed in great detail.The focused attention is firstly concentrated on their structural design and controllable synthesis.Then,the mechanism understanding of the enhanced electrochemical performance is presented.Finally,the challenges and prospects of self-supported TMO-based electrodes are summarized to end this review.

Self-supported porous heterostructure WC/WO_(3−x)ceramic electrode for hydrogen evolution reaction in acidic and alkaline media

Tungsten carbide(WC)-based materials are widely considered as the hydrogen evolution reaction(HER)process catalysts due to their“Pt-like”electronic structure.Nonetheless,traditional powder electrodes have a high cost,and display problems related to the process itself and the poor stability over operation time.This paper presented a self-supported asymmetric porous ceramic electrode with WO_(3-x)whiskers formed in situ on the walls of the finger-like holes and membrane surface,which was prepared by combining phase inversion tape-casting,pressureless sintering,and thermal treatment in a CO_(2) atmosphere.The optimized ceramic electrode displayed good catalytic HER activity and outstanding stability at high current densities.More specifically,it demonstrated the lowest overpotentials of 107 and 123 mV and the lowest Tafel slopes of 59.3 and 72.4 mV·dec^(-1)at 10 mA·cm^(-2)in acidic and alkaline media,respectively.This superior performance was ascribed to the structure of the ceramic membrane and the charge transfer efficiency,which was favored by the in situ developed WC/WO_(3-x)heterostructure and the oxygen vacancies.

g-C_(3)N_(4) encapsulated ZrO_(2) nanofibrous membrane decorated with CdS quantum dots: A hierarchically structured, self-supported electrocatalyst toward synergistic NH3 synthesis

The advancement of electrocatalytic N2 reduction reaction (NRR) toward ambient NH3 synthesis lies in the development of more affordable electrocatalysts than noble metals. Recently, various nanostructures of transition metal compounds have been proposed as effective electrocatalysts;however, they exist in the form of loose powders, which have to be immobilized on a matrix before serving as the electrode for electrolysis. The matrix, being it carbon paper, carbon cloth or metal foam, is electrocatalytically inactive, whose introduction inevitably raises the invalid weight while sacrificing the active sites of the electrode. Herein, we report on the fabrication of a flexible ZrO2 nanofibrous membrane as a novel, self-supported electrocatalyst. The heteroatom doping can not only endow the nanofibrous membrane with excellent flexibility, but also induce oxygen vacancies which are responsible for easier adsorption of N2 on the ZrO2 surface. To improve the electrocatalytic activity, a facile SILAR approach is employed to decorate it with CdS quantum dots (QDs), thereby tuning its Fermi level. To improve the conductivity, a g-C3N4 nanolayer is further deposited which is both conductive and active. The resulting hierarchically structured, self-supported electrocatalyst, consisting of g-C3N4 encapsulated ZrO2 nanofibrous membrane decorated with CdS QDs, integrates the merits of the three components, and exhibits a remarkable synergy toward NRR. Excellent NH3 yield of 6.32 × 10−10 mol·s−1cm−2 (−0.6 V vs. RHE) and Faradaic efficiency of 12.9% (−0.4 V vs. RHE) are attained in 0.1 M Na2SO4.

Self-supported Ni6MnO8 3D mesoporous nanosheet arrays with ultrahigh lithium storage properties and conversion mechanism by in-situ XAFS

Murdochite-type Ni6MnO8 three-dimensional mesoporous nanosheet arrays grown on carbon cloth （NMO-SA/CC） are synthesized using an in-situ growth strategy. As self-supported binder-free anodes for LIBs, the NMO-SA/CC hierarchical nanostructures exhibit ultrahigh capacity, excellent cycling stability, and good rate capability. The excellent lithium storage performance can be ascribed to the perfect electrical contact between NMO-SA and CC. The mesopores in the thin nanosheet can maximize the electrode contact with the electrolyte by decreasing the Li＋ diffusion path. Moreover, these effects relieve the pulverization and agglomeration that originate from the large volume variations during the Li＋ intercalation/deintercalation cycles. The in-situ X-ray absorption fine structure （XAFS） spectrum recorded during the initial lithiation/delithiation processes reveals the conversion reaction process.

Carbon-based flexible self-supporting cathode for lithium-sulfur batteries:Progress and perspective

The flexible self-supporting electrode can maintain good mechanical and electrical properties while retaining high specific capacity,which meets the requirements of flexible batteries.Lithium-sulfur batteries(LSBs),as a new generation of energy storage system,hold much higher theoretical energy density than traditional batteries,and they have attracted extensive attention from both the academic and industrial communities.Selection of a proper substrate material is important for the flexible self-supporting electrode.Carbon materials,with the advantages of light weight,high conductivity,strong structural plasticity,and low cost,provide the electrode with a large loading space for the active material and a conductive network.This makes the carbon materials meet the mechanical and electrochemical requirements of flexible electrodes.In this paper,the commonly used fabrication methods and recent research progresses of the flexible self-supporting cathode with a carbon material as the substrate are introduced.Various sulfur loading methods are summarized,which provides useful information for the structural design of the cathode.As the first review article of the carbon-based flexible self-supporting LSB cathodes,it provides valuable guidance for the researchers working in the field of LSB.

Deciphering the lithium storage chemistry in flexible carbon fiber-based self-supportive electrodes

Flexible carbon fiber cloth(CFC)is an important scaffold and/or current collector for active materials in the development of flexible self-supportive electrode materials(SSEMs),especially in lithium-ion batteries.However,during the intercalation of Li ions into the matrix of CFC(below 0.5 V vs.Li/Li+),the incompatibility in the capacity of the CFC,when used directly as an anode material or as a current collector for active materials,leads to difficulty in the estimation of its actual contribution.To address this issue,we prepared Ni_(5)P_(4)nanosheets on CFC(denoted CFC@Ni_(5)P_(4))and investigated the contribution of CFC in the CFC@Ni_(5)P_(4)by comparing to the powder Ni_(5)P_(4)nanosheets traditionally coated on a copper foil(CuF)(denoted P-Ni_(5)P_(4)).At a current density of 0.4 mA cm^(−2),the as-prepared CFC@Ni_(5)P_(4)showed an areal capacity of 7.38 mAh cm^(−2),which is significantly higher than that of the PNi_(5)P_(4)electrode.More importantly,theoretical studies revealed that the CFC has a high Li adsorption energy that contributes to the low Li-ion diffusion energy barrier of the Ni_(5)P_(4)due to the strong interaction between the CFC and Ni_(5)P_(4),leading to the superior Li-ion storage performance of the CFC@Ni_(5)P_(4)over the pristine Ni_(5)P_(4)sample.This present work unveils the underlying mechanism leading to the achievement of high performance in SSEMs.

Self-supporting and hierarchically porous Ni_(x)Fe-S/NiFe_(2)O_(4) heterostructure as a bifunctional electrocatalyst for fluctuating overall water splitting

Stable non-noble metal bifunctional electrocatalysts are one of the challenges to the fluctuating overall water splitting driven by re-newable energy.Herein,a novel self-supporting hierarchically porous Ni_(x)Fe-S/NiFe_(2)O_(4) heterostructure as bifunctional electrocatalyst was constructed based on porous Ni-Fe electrodeposition on three-dimensional(3D)carbon fiber cloth,in situ oxidation,and chemical sulfuration.Results showed that the Ni_(x)Fe-S/NiFe_(2)O_(4) heterostructure with a large specific surface area exhibits good bifunctional activity and stability for both hydrogen evolution reaction(HER)and oxygen evolution reaction(OER)because of the abundance of active sites,synergistic effect of the heterostructure,superhydrophilic surface,and stable,self-supporting structure.The results further confirmed that the Ni_(x)Fe-S phase in the heterostructure is transformed into metal oxides/hydroxides and Ni_(3)S_(2) during OER.Compared with the commercial 20wt%Pt/C||IrO_(2)-Ta_(2)O_(5) electrolyzer,the self-supporting Ni1/5Fe-S/NiFe_(2)O_(4)||Ni1/2Fe-S/NiFe_(2)O_(4) electrolyzer exhibits better stability and lower cell voltage in the fluctu-ating current density range of 10-500 mA/cm^(2).Particularly,the cell voltage of Ni1/5Fe-S/NiFe_(2)O_(4)||Ni1/2Fe-S/NiFe_(2)O_(4) is only approximately 3.91 V at an industrial current density of 500 mA/cm^(2),which is lower than that of the 20wt%Pt/C||IrO_(2)-Ta_(2)O_(5) electrolyzer(i.e.,approximately 4.79 V).This work provides a promising strategy to develop excellent bifunctional electrocatalysts for fluctuating overall water splitting.

Self-supporting NiFe LDH-MoS_(x) integrated electrode for highly efficient water splitting at the industrial electrolysis conditions

Developing effective and practical electrocatalyst under industrial electrolysis conditions is critical for renewable hydrogen production.Herein,we report the self-supporting NiFe LDH-MoS_(x) integrated electrode for water oxidation under normal alkaline test condition(1 M KOH at 25℃)and simulated industrial electrolysis conditions(5 M KOH at 65℃).Such optimized electrode exhibits excellent oxygen evolution reaction(OER)performance with overpotential of 195 and 290 mV at current density of 100 and 400 mA·cm^(-2) under normal alkaline test condition.Notably,only over-potential of 156 and 201 mV were required to achieve the current density of 100 and 400mA·cm^(-2) under simulated industrial electrolysis conditions.No significant degradations were observed after long-term durability tests for both conditions.When using in two-electrode system,the operational voltages of 1.44 and 1.72 V were required to achieve a current density of 10 and 100 mA·cm^(-2) for the overall water splitting test(NiFe LDH-MoS_(x)/INF||20%Pt/C).Additionally,the operational voltage of employing NiFe LDH-MoS_(x)/INF as both cathode and anode merely require 1.52 V at 50mA·cm^(-2) at simulated industrial electrolysis conditions.Notably,a membrane electrode assembly(MEA)for anion exchange membrane water electrolysis(AEMWEs)using NiFe LDH-MoS_(x)/INF as an anode catalyst exhibited an energy conversion efficiency of 71.8%at current density of 400 mA·cm^(-2)in 1 M KOH at 60℃.Further experimental results reveal that sulfurized substrate not only improved the conductivity of NiFe LDH,but also regulated its electronic configurations and atomic composition,leading to the excellent activity.The easy-obtained and cost-effective integrated electrodes are expected to meet the large-scale application of industrial water electrolysis.

Topology Optimization of Self-Supporting Structures for Additive Manufacturing with Adaptive Explicit Continuous Constraint

The integration of topology optimization(TO)and additive manufacturing(AM)technologies can create significant synergy benefits,while the lack of AM-friendly TO algorithms is a serious bottleneck for the application of TO in AM.In this paper,a TO method is proposed to design self-supporting structures with an explicit continuous self-supporting constraint,which can be adaptively activated and tightened during the optimization procedure.The TO procedure is suitable for various critical overhang angles(COA),which is integrated with build direction assignment to reduce performance loss.Besides,a triangular directional self-supporting constraint sensitivity filter is devised to promote the downward evolution of structures and maintain stability.Two numerical examples are presented;all the test cases have successfully converged and the optimized solutions demonstrate good manufacturability.In the meanwhile,a fully self-supporting design can be obtained with a slight cost in performance through combination with build direction assignment.