This paper describes a study of three-dimensional braids produced by a four-step 1 × 1 method. An analytical approach is employed in conjunction with experimental investigations to establish the relationship betw...This paper describes a study of three-dimensional braids produced by a four-step 1 × 1 method. An analytical approach is employed in conjunction with experimental investigations to establish the relationship between the braid structure and braiding parameters. Based on microscopic observations, we divide a three-dimensional braid structure into three representative regions, i.e., the interior, surface and corner, and treat the three regions, respectively. Three types of microstructural unit-cell models are then established. The surface characteristics and the relationship between the interior and surface unit-cells have been derived. Good agreement has been obtained between the calculated and measured values of fiber volume fraction of the braided composite samples.展开更多
Hybrid braids of polyglycolide （PGA） and chitosan were prepared by the three-yarn braiding method from PGA and chitosan fiber bundles. These braids were in vitro degraded by incubating them in phosphate buffered sal...Hybrid braids of polyglycolide （PGA） and chitosan were prepared by the three-yarn braiding method from PGA and chitosan fiber bundles. These braids were in vitro degraded by incubating them in phosphate buffered saline （ PBS ） at pH 7.4 and 37℃ for 5 weeks. Results suggested that PGA/chitosan hybrid braids degraded significantly. Scanning electron micrographs showed that chitosan fibers in the PGA/chitosan hybrid braid with about 75% PGA in weight （ PGA75/chitosan ）were shaped into gel-like after 5 weeks, but those in the hybrid braid with about 25% PGA in weight（PGA25/chitosan） did not change. After 5 weeks, the ultimate tensile loads of PGA and PGA75/chitosan braids lost almost completely, but those of chitosan and PGA25/chitosan braids remained around 14 N. The PGA/chitosan hybrid braids with higher initial ultimate tensile load would have potential applications in tendon/ligament tissue reconstruction.展开更多
The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra,...The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra, which is an approach similar to Jones' s original construction.展开更多
Currently,there are a limited number of dynamic models available for braided composite plates with large overall motions,despite the incorporation of three-dimensional(3D)braided composites into rotating blade compone...Currently,there are a limited number of dynamic models available for braided composite plates with large overall motions,despite the incorporation of three-dimensional(3D)braided composites into rotating blade components.In this paper,a dynamic model of 3D 4-directional braided composite thin plates considering braiding directions is established.Based on Kirchhoff's plate assumptions,the displacement variables of the plate are expressed.By incorporating the braiding directions into the constitutive equation of the braided composites,the dynamic model of the plate considering braiding directions is obtained.The effects of the speeds,braiding directions,and braided angles on the responses of the plate with fixed-axis rotation and translational motion,respectively,are investigated.This paper presents a dynamic theory for calculating the deformation of 3D braided composite structures undergoing both translational and rotational motions.It also provides a simulation method for investigating the dynamic behavior of non-isotropic material plates in various applications.展开更多
Three-dimensional(3D)braided composites have significant potential for use in engineering structural materials.However,conventional 3D braiding machines are insufficient for designing composites with complex geometrie...Three-dimensional(3D)braided composites have significant potential for use in engineering structural materials.However,conventional 3D braiding machines are insufficient for designing composites with complex geometries.This paper proposes a programmable design methodology for 3D rotary braiding machines using circle-cutting and combination strategies.By introducing varying numbers of incisions on the circle,a diverse range of horn gears can be designed.Different combinations of these cut-circles allow the horn gears to be assembled into various 3D rotary braiders.The parametric equation for the braider plate is derived,showing that a combination strategy involving two cut-circles is feasible for braider design,whereas integrating three cut-circles simultaneously is impossible for a single machine.The construction of an automatic 6-3 type 3D braiding machine demonstrates the effectiveness of the proposed design strategy.This flexible braider design approach provides a practical solution for producing 3D braided composites with complex geometries.展开更多
This paper aims to experimentally and numerically probe fatigue behaviours and lifetimes of 3D4D(three-dimensional four-directional)braided composite I-beam under four-point flexure spectrum loading.New fatigue damage...This paper aims to experimentally and numerically probe fatigue behaviours and lifetimes of 3D4D(three-dimensional four-directional)braided composite I-beam under four-point flexure spectrum loading.New fatigue damage models of fibre yarn,matrix and fibre–matrix interface are proposed,and fatigue failure criteria and PFDA(Progressive Fatigue Damage Algorithm)are thus presented for meso-scale fatigue damage modelling of 3D4D braided composite I-beam.To validate the aforementioned model and algorithm,fatigue tests are conducted on the 3D4D braided composite I-beam under four-point flexure spectrum loading,and fatigue failure mechanisms are analyzed and discussed.Novel global–local FE(Finite Element)model based on the PFDA is generated for modelling progressive fatigue failure process and predicting fatigue life of 3D4D braided composite I-beam under four-point flexure spectrum loading.Good agreement has been achieved between experimental results and predictions,demonstrating the effective usage of new model.It is shown that matrix cracking and interfacial debonding initially initiates on top surface of top flange of I-beam,and then gradually propagates from the side surface of top flange to the intermediate web along the braiding angle,and considerable fiber breakage finally causes final fatigue failure of I-beam.展开更多
Sandy braided river deposits are widely preserved in ancient stratigraphic records and act as a significant type of hydrocarbon reservoir.Due to the frequent and rapid migration of channels within the riverbed,the sed...Sandy braided river deposits are widely preserved in ancient stratigraphic records and act as a significant type of hydrocarbon reservoir.Due to the frequent and rapid migration of channels within the riverbed,the sedimentary architecture is highly complex.In this paper,a flume experiment was conducted to reveal the detailed depositional process and establish a fine sedimentary architecture model for sandy braided rivers.The result showed that(1)Three types of braid channels,including the lateral migration channel,the confluence channel,and the deep incised channel,were recognized based on geometry,scale,distribution,and spatial patterns;they are interconnected,forming a complex channel network.(2)Braid channels were characterized by lateral migration,abandonment,filling,and chute cutoff.Lateral migration of channels shaped the braid bars and dominated the formation,growth,and reworking of braid bars.(3)Controlled by the fast and frequent variations of the braid channel network,braid bars were continuously formed,reworked,reshaped,and composited of multiple accretions with different types,orientations,scales,and preservation degrees.Symmetrical and asymmetrical braid bars pre-sented significantly different composition patterns.(4)Dominated by the continuous reworking of braid channels,temporary deposits were limited preserved,braid channel deposits account for 54.3 percent of the eventually preserved braided river deposits,and four types of amalgamate patterns were recognized.Braid bars were cut and limited preserved,only accounting for 45.7 percent of the eventually preserved braided river deposits.(5)During the experiment,only 28 percent of near-surface temporary deposits were eventually preserved in fragmented forms with the final experimental braided river;the shape,spatial patterns,and most of the deposits observed during the depositional process were largely reworked and poorly preserved.(6)The scale of eventually preserved braid bars and braid channels is significantly smaller than the temporary deposits from geomorphic observations.The aspect ratio of the eventually preserved braid bars and the width-to-depth ratio of the eventually preserved braid channel are also significantly different from that of the temporary ones measured from topography data.展开更多
In this paper, we focus our attention on the connections between the braid group and Nielsen fixed point theory. A new forcing relation between braids is introduced, and we show that it can be fulfilled by using Niels...In this paper, we focus our attention on the connections between the braid group and Nielsen fixed point theory. A new forcing relation between braids is introduced, and we show that it can be fulfilled by using Nielsen fixed point theory.展开更多
In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤n - 2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnect...In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤n - 2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnected. We also prove that the graph has one major component.展开更多
Motivated by the work in Li et al.(2019),this paper deals with the theory of the braids from chromatic configuration spaces.These kinds of braids possess the property that some strings of each braid may intersect toge...Motivated by the work in Li et al.(2019),this paper deals with the theory of the braids from chromatic configuration spaces.These kinds of braids possess the property that some strings of each braid may intersect together and can also be untangled,so they are quite different from the ordinary braids in the sense of Artin(1925).This enriches and extends the theory of ordinary braids.展开更多
In this paper,the authors systematically discuss orbit braids in M×I with regards to orbit configuration space FG(M,n),where M is a connected topological manifold of dimension at least 2 with an effective action ...In this paper,the authors systematically discuss orbit braids in M×I with regards to orbit configuration space FG(M,n),where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G.These orbit braids form a group,named orbit braid group,which enriches the theory of ordinary braids.The authors analyze the substantial relations among various braid groups associated to those configuration spaces FG(M,n),F(M/G,n)and F(M,n).They also consider the presentations of orbit braid groups in terms of orbit braids as generators by choosing M=C with typical actions of Zpand(Z_(2))^(2).展开更多
In order to solve the problem of oily wastewater,the poly(m-phenyleneisophthalamide)(PMIA)braided tube reinforced(PBR)poly(tetrafluoroethylene-co-perfluoropropyl vinyl ether)(PFA)hollow fiber membrane with thermal and...In order to solve the problem of oily wastewater,the poly(m-phenyleneisophthalamide)(PMIA)braided tube reinforced(PBR)poly(tetrafluoroethylene-co-perfluoropropyl vinyl ether)(PFA)hollow fiber membrane with thermal and solvent resistant property was prepared via no-solvent green method.The membrane surface and pore structure was optimized by changing the sintering temperature and graphene(GE)content.The morphologies showed that the spherical surface with good lipophilicity was formed,and the excellent mechanical strength with a favorable interface bonding state could be obtained due to the PFA melts permeating into the supporting layer.The doping of GE produced synergistic effects with the sintering temperature owing to its good thermal conductivity and pore formation.The PBR-PFA/GE hollow fiber membrane exhibited good hydrophobicity and lipophilicity with more than 97%separation efficiency for different oil products at-0.02 MPa.With the addition of GE,the average pore size first increases and then decreases,and the porosity gradually decreases.In addition,the hollow fiber membrane showed high separation ability to the water-in-oil emulsion,and maintained a stable flux recovery rate after recycling,making it possible to apply in the field of oily wastewater treatment.展开更多
The increasing demand for sustainable and environmentally friendly materials has driven research towards the development of green composites.In this work,the flax/polylactic acid(PLA)braided yarns were fabricated by b...The increasing demand for sustainable and environmentally friendly materials has driven research towards the development of green composites.In this work,the flax/polylactic acid(PLA)braided yarns were fabricated by braiding PLA filaments with 4 to 24 spindles on flax yarns.After curing at different temperatures(180℃and 190℃),the core/sheath structural flax/PLA composite yarns were manufactured.According to the results of the tensile test,the flax/PLA composite yarn with 4-spindle PLA yarns as a sheath layer and at a curing temperature of 180℃reached the maximum elastic modulus of about(5.79±0.65)GPa and the maximum tensile strength of about(162.17±18.18)MPa.This flax/PLA composite yarn with good mechanical properties would be suitable for green composites in the automobile manufacturing industry and building materials.展开更多
Variable-diameter deployable carbon fiber reinforced polymer(CFRP)composites possess deformation and load-bearing functions and are composed of stiff-flexible coupled preforms and matrix.The stiff-flexible coupled pre...Variable-diameter deployable carbon fiber reinforced polymer(CFRP)composites possess deformation and load-bearing functions and are composed of stiff-flexible coupled preforms and matrix.The stiff-flexible coupled preform,serving as the reinforcing structure,directly determines the deployable properties,and its forming technology is currently a research challenge.This paper designs a braiding and needle-punching(BNP)composite preform forming technology suitable for stiff-flexible coupled preforms.Before forming,the preform is partitioned into flexible and rigid zones,with braiding and needle-punching performed layer by layer in the respective zones.A retractable rotating device is developed to form the stiff-flexible coupled preform,achieving a diameter variation rate of up to 26.6%for the BNP preform.A structural parameter model is also established to describe the geometric parameter changes in the deformation and load-bearing areas of the preform during deployment as a function of the braiding angle.Based on experiments,this paper explains the performance changes of BNP composites concerning the structural parameters of the preform.Experimental analysis shows that as the braiding angle increases,the tensile performance of BNP composites significantly decreases,with the change rate of tensile strength first decreasing and then increasing.Additionally,when the braiding angle is less than 21.89°,the impact toughness of BNP composites remains within the range of 83.66±2 kJ/m^(2).However,when the braiding angle exceeds 21.89°,the impact toughness of BNP composites gradually decreases with increasing braiding angle.Furthermore,a hybrid agent model based on Latin hypercube sampling and error back-propagation neural network is developed to predict the tensile and impact properties of BNP composites with different structural parameters,with maximum test relative errors of 1.89%for tensile strength and 2.37%for impact toughness.展开更多
Topological methods are rapidly developing and are becoming more used in physics, biology and chemistry. One area of topology has showed its immense potential in explaining potential financial contagion and financial ...Topological methods are rapidly developing and are becoming more used in physics, biology and chemistry. One area of topology has showed its immense potential in explaining potential financial contagion and financial crisis in financial markets. The aforementioned method is knot theory. The movement of stock price has been marked and braids and knots have been noted. By analysing the knots and braids using Jones polynomial, it is tried to find if there exists an untrivial knot equal to unknot? After thorough analysis, possible financial contagion and financial crisis prediction are analysed by using instruments of knot theory pertaining in that sense to Jones, Laurent and Alexander polynomial. It is proved that it is possible to predict financial disruptions by observing possible knots in the graphs and finding appropriate polynomials. In order to analyse knot formation, the following approach is used: “Knot formation in three-dimensional space is considered and the equations about knot forming and its disentangling are considered”. After having defined the equations in three-dimensional space, the definition of Brownian bridge concerning formation of knots in three-dimensional space is defined. Using analogy method, the notion of Brownian bridge is translated into 2-dimensional space and the foundations for the application of knot theory in 2-dimensional space have been set up. At the same time, the aforementioned approach is innovative and it could be used in accordance with stochastic analysis and quantum finance.展开更多
D braiding technology has stimulated a great deal of interest in the world at large and been widely used in aerospace, military, civil construction and medical fields. Although 3 D braided composites have many good f...D braiding technology has stimulated a great deal of interest in the world at large and been widely used in aerospace, military, civil construction and medical fields. Although 3 D braided composites have many good features, their features are very complicated. Optic fiber sensors can be multi braided into 3 D braided composites to fulfill a new kind of 3 D smart composites to monitor RTM process, study mechanical behaviors and damage states after molding, and monitor its own condition during service life. Since optic performances of optic fibers have direct and important relation to the performances of optic fiber sensors, experimental research is done to devise a method to incorporate the optic fiber into a 3 D structure. The optical performances of the braided optic fibers are tested and compared with the original one to study the optic performances of optic fibers, before their being braided into composites and after the RTM process.展开更多
This paper aims to find the relationship between the structural parameters and the radial stiffness of the braided stent and to understand the stress distribution law of the wires. According to the equation of the spa...This paper aims to find the relationship between the structural parameters and the radial stiffness of the braided stent and to understand the stress distribution law of the wires. According to the equation of the space spiral curve, a three-dimensional parametrical geometrical model is constructed. The finite element model is built by using the beam-beam contact elements and 3D beam elements. The constituent nitinol wires are assumed to be linear elastic material. The finite element analysis figures out that the radial stiffness of the stent and the stress distribution of the wires are influenced by all the structural parameters. The helix pitch of the wires is the most important factor. Under the condition of the same load and other structural parameters remaining unchanged, when the number of wires is 24, the stress of the wire crosssection is at the minimum. A comparison between the vitro experimental results and the analytical results is conducted, and the data is consistent, which proves that the current finite element model can be used to appropriately predict the mechanical performance of the braided esophageal stents.展开更多
As an advanced composite material, the 3D braided composite has received more and more attention in foreign countries. However, it has received less attention in China. The geometric unit cell which can describe the b...As an advanced composite material, the 3D braided composite has received more and more attention in foreign countries. However, it has received less attention in China. The geometric unit cell which can describe the basic structure and the relationship between the braiding angle and geometric parameters of the fabric and fiber volume ratio are given in this paper based on two 3D braiding processes, namely, the four-step and the twostep ones. Several existing mechanical models to predict groperties of the 3D braided comPOsites are discussed and their shortcomings are pointed out herein. Then a new model called the inclined laminal combination model is proposed, which is based on the classical laminated plate theory and can predict the basic mechanical behavior of the two 3D braided composites with four-step or two-step braid. In the model, each yarn in the unit cell is regarded as an inclined laminate and then a 3D analysis is performed. It is found that the predicted mechanical properties of the 3D braided composites by the proposed model are compared well with the experimental data.展开更多
文摘This paper describes a study of three-dimensional braids produced by a four-step 1 × 1 method. An analytical approach is employed in conjunction with experimental investigations to establish the relationship between the braid structure and braiding parameters. Based on microscopic observations, we divide a three-dimensional braid structure into three representative regions, i.e., the interior, surface and corner, and treat the three regions, respectively. Three types of microstructural unit-cell models are then established. The surface characteristics and the relationship between the interior and surface unit-cells have been derived. Good agreement has been obtained between the calculated and measured values of fiber volume fraction of the braided composite samples.
基金Supported by the Cooperative Project Between Nankai University and Tianjin University, Ministry of EducationScientific Research Starting Fund for Homecoming Scholars, Ministry of Education.
文摘Hybrid braids of polyglycolide （PGA） and chitosan were prepared by the three-yarn braiding method from PGA and chitosan fiber bundles. These braids were in vitro degraded by incubating them in phosphate buffered saline （ PBS ） at pH 7.4 and 37℃ for 5 weeks. Results suggested that PGA/chitosan hybrid braids degraded significantly. Scanning electron micrographs showed that chitosan fibers in the PGA/chitosan hybrid braid with about 75% PGA in weight （ PGA75/chitosan ）were shaped into gel-like after 5 weeks, but those in the hybrid braid with about 25% PGA in weight（PGA25/chitosan） did not change. After 5 weeks, the ultimate tensile loads of PGA and PGA75/chitosan braids lost almost completely, but those of chitosan and PGA25/chitosan braids remained around 14 N. The PGA/chitosan hybrid braids with higher initial ultimate tensile load would have potential applications in tendon/ligament tissue reconstruction.
基金supported by the National Natural Sciences Foundation of China(Nos.11329101,11431009,11301135,11201314,11302136,A2014210062)the Excellent Young Scientist Fund of Shijiazhuang Tiedao University
文摘The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra, which is an approach similar to Jones' s original construction.
基金Project supported by the National Natural Science Foundation of China(Nos.12372071 and 12372070)the Aeronautical Science Fund of China(No.2022Z055052001)the Foundation of China Scholarship Council(No.202306830079)。
文摘Currently,there are a limited number of dynamic models available for braided composite plates with large overall motions,despite the incorporation of three-dimensional(3D)braided composites into rotating blade components.In this paper,a dynamic model of 3D 4-directional braided composite thin plates considering braiding directions is established.Based on Kirchhoff's plate assumptions,the displacement variables of the plate are expressed.By incorporating the braiding directions into the constitutive equation of the braided composites,the dynamic model of the plate considering braiding directions is obtained.The effects of the speeds,braiding directions,and braided angles on the responses of the plate with fixed-axis rotation and translational motion,respectively,are investigated.This paper presents a dynamic theory for calculating the deformation of 3D braided composite structures undergoing both translational and rotational motions.It also provides a simulation method for investigating the dynamic behavior of non-isotropic material plates in various applications.
基金funded by the Shanghai Natural Science Foundation of Shanghai Municipal Science and Technology Commission(20ZR1400600)the Fundamental Research Funds for the Central Universities(2232023G-06)through collaborative research with the Advanced Fibrous Materials Lab(AFML)at the University of British Columbia.
文摘Three-dimensional(3D)braided composites have significant potential for use in engineering structural materials.However,conventional 3D braiding machines are insufficient for designing composites with complex geometries.This paper proposes a programmable design methodology for 3D rotary braiding machines using circle-cutting and combination strategies.By introducing varying numbers of incisions on the circle,a diverse range of horn gears can be designed.Different combinations of these cut-circles allow the horn gears to be assembled into various 3D rotary braiders.The parametric equation for the braider plate is derived,showing that a combination strategy involving two cut-circles is feasible for braider design,whereas integrating three cut-circles simultaneously is impossible for a single machine.The construction of an automatic 6-3 type 3D braiding machine demonstrates the effectiveness of the proposed design strategy.This flexible braider design approach provides a practical solution for producing 3D braided composites with complex geometries.
基金supported by the National Natural Science Foundation of China(No.12472340).
文摘This paper aims to experimentally and numerically probe fatigue behaviours and lifetimes of 3D4D(three-dimensional four-directional)braided composite I-beam under four-point flexure spectrum loading.New fatigue damage models of fibre yarn,matrix and fibre–matrix interface are proposed,and fatigue failure criteria and PFDA(Progressive Fatigue Damage Algorithm)are thus presented for meso-scale fatigue damage modelling of 3D4D braided composite I-beam.To validate the aforementioned model and algorithm,fatigue tests are conducted on the 3D4D braided composite I-beam under four-point flexure spectrum loading,and fatigue failure mechanisms are analyzed and discussed.Novel global–local FE(Finite Element)model based on the PFDA is generated for modelling progressive fatigue failure process and predicting fatigue life of 3D4D braided composite I-beam under four-point flexure spectrum loading.Good agreement has been achieved between experimental results and predictions,demonstrating the effective usage of new model.It is shown that matrix cracking and interfacial debonding initially initiates on top surface of top flange of I-beam,and then gradually propagates from the side surface of top flange to the intermediate web along the braiding angle,and considerable fiber breakage finally causes final fatigue failure of I-beam.
基金funded by two projects of the National Natural Science Foundation of China(No.41802123,42130813).
文摘Sandy braided river deposits are widely preserved in ancient stratigraphic records and act as a significant type of hydrocarbon reservoir.Due to the frequent and rapid migration of channels within the riverbed,the sedimentary architecture is highly complex.In this paper,a flume experiment was conducted to reveal the detailed depositional process and establish a fine sedimentary architecture model for sandy braided rivers.The result showed that(1)Three types of braid channels,including the lateral migration channel,the confluence channel,and the deep incised channel,were recognized based on geometry,scale,distribution,and spatial patterns;they are interconnected,forming a complex channel network.(2)Braid channels were characterized by lateral migration,abandonment,filling,and chute cutoff.Lateral migration of channels shaped the braid bars and dominated the formation,growth,and reworking of braid bars.(3)Controlled by the fast and frequent variations of the braid channel network,braid bars were continuously formed,reworked,reshaped,and composited of multiple accretions with different types,orientations,scales,and preservation degrees.Symmetrical and asymmetrical braid bars pre-sented significantly different composition patterns.(4)Dominated by the continuous reworking of braid channels,temporary deposits were limited preserved,braid channel deposits account for 54.3 percent of the eventually preserved braided river deposits,and four types of amalgamate patterns were recognized.Braid bars were cut and limited preserved,only accounting for 45.7 percent of the eventually preserved braided river deposits.(5)During the experiment,only 28 percent of near-surface temporary deposits were eventually preserved in fragmented forms with the final experimental braided river;the shape,spatial patterns,and most of the deposits observed during the depositional process were largely reworked and poorly preserved.(6)The scale of eventually preserved braid bars and braid channels is significantly smaller than the temporary deposits from geomorphic observations.The aspect ratio of the eventually preserved braid bars and the width-to-depth ratio of the eventually preserved braid channel are also significantly different from that of the temporary ones measured from topography data.
基金supported by National Natural Science Foundation of China(Grant No.11326077)
文摘In this paper, we focus our attention on the connections between the braid group and Nielsen fixed point theory. A new forcing relation between braids is introduced, and we show that it can be fulfilled by using Nielsen fixed point theory.
文摘In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤n - 2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnected. We also prove that the graph has one major component.
基金supported by National Natural Science Foundation of China(Grant No.11971112)。
文摘Motivated by the work in Li et al.(2019),this paper deals with the theory of the braids from chromatic configuration spaces.These kinds of braids possess the property that some strings of each braid may intersect together and can also be untangled,so they are quite different from the ordinary braids in the sense of Artin(1925).This enriches and extends the theory of ordinary braids.
基金supported by the National Natural Science Foundation of China(No.11971112)。
文摘In this paper,the authors systematically discuss orbit braids in M×I with regards to orbit configuration space FG(M,n),where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G.These orbit braids form a group,named orbit braid group,which enriches the theory of ordinary braids.The authors analyze the substantial relations among various braid groups associated to those configuration spaces FG(M,n),F(M/G,n)and F(M,n).They also consider the presentations of orbit braid groups in terms of orbit braids as generators by choosing M=C with typical actions of Zpand(Z_(2))^(2).
基金funding provided by the National Natural Science Foundation of China(52103035,52173038).
文摘In order to solve the problem of oily wastewater,the poly(m-phenyleneisophthalamide)(PMIA)braided tube reinforced(PBR)poly(tetrafluoroethylene-co-perfluoropropyl vinyl ether)(PFA)hollow fiber membrane with thermal and solvent resistant property was prepared via no-solvent green method.The membrane surface and pore structure was optimized by changing the sintering temperature and graphene(GE)content.The morphologies showed that the spherical surface with good lipophilicity was formed,and the excellent mechanical strength with a favorable interface bonding state could be obtained due to the PFA melts permeating into the supporting layer.The doping of GE produced synergistic effects with the sintering temperature owing to its good thermal conductivity and pore formation.The PBR-PFA/GE hollow fiber membrane exhibited good hydrophobicity and lipophilicity with more than 97%separation efficiency for different oil products at-0.02 MPa.With the addition of GE,the average pore size first increases and then decreases,and the porosity gradually decreases.In addition,the hollow fiber membrane showed high separation ability to the water-in-oil emulsion,and maintained a stable flux recovery rate after recycling,making it possible to apply in the field of oily wastewater treatment.
基金National Natural Science Foundation of China(No.52273054)Shanghai Natural Science Foundation,China(No.20ZR1402200)。
文摘The increasing demand for sustainable and environmentally friendly materials has driven research towards the development of green composites.In this work,the flax/polylactic acid(PLA)braided yarns were fabricated by braiding PLA filaments with 4 to 24 spindles on flax yarns.After curing at different temperatures(180℃and 190℃),the core/sheath structural flax/PLA composite yarns were manufactured.According to the results of the tensile test,the flax/PLA composite yarn with 4-spindle PLA yarns as a sheath layer and at a curing temperature of 180℃reached the maximum elastic modulus of about(5.79±0.65)GPa and the maximum tensile strength of about(162.17±18.18)MPa.This flax/PLA composite yarn with good mechanical properties would be suitable for green composites in the automobile manufacturing industry and building materials.
基金Supported by Jiangsu Provincial Frontier Leading Technology Basic Research Project(Grant No.BK20212007)Aero-Engine and Gas Turbine Basic Science Center(Grant No.P2022-B-IV-014-001)+1 种基金China Postdoctoral Program Fund(Grant No.1005/YBA23044)China Postdoctoral Assistance Fund(Grant No.1005/YBA23031)。
文摘Variable-diameter deployable carbon fiber reinforced polymer(CFRP)composites possess deformation and load-bearing functions and are composed of stiff-flexible coupled preforms and matrix.The stiff-flexible coupled preform,serving as the reinforcing structure,directly determines the deployable properties,and its forming technology is currently a research challenge.This paper designs a braiding and needle-punching(BNP)composite preform forming technology suitable for stiff-flexible coupled preforms.Before forming,the preform is partitioned into flexible and rigid zones,with braiding and needle-punching performed layer by layer in the respective zones.A retractable rotating device is developed to form the stiff-flexible coupled preform,achieving a diameter variation rate of up to 26.6%for the BNP preform.A structural parameter model is also established to describe the geometric parameter changes in the deformation and load-bearing areas of the preform during deployment as a function of the braiding angle.Based on experiments,this paper explains the performance changes of BNP composites concerning the structural parameters of the preform.Experimental analysis shows that as the braiding angle increases,the tensile performance of BNP composites significantly decreases,with the change rate of tensile strength first decreasing and then increasing.Additionally,when the braiding angle is less than 21.89°,the impact toughness of BNP composites remains within the range of 83.66±2 kJ/m^(2).However,when the braiding angle exceeds 21.89°,the impact toughness of BNP composites gradually decreases with increasing braiding angle.Furthermore,a hybrid agent model based on Latin hypercube sampling and error back-propagation neural network is developed to predict the tensile and impact properties of BNP composites with different structural parameters,with maximum test relative errors of 1.89%for tensile strength and 2.37%for impact toughness.
文摘Topological methods are rapidly developing and are becoming more used in physics, biology and chemistry. One area of topology has showed its immense potential in explaining potential financial contagion and financial crisis in financial markets. The aforementioned method is knot theory. The movement of stock price has been marked and braids and knots have been noted. By analysing the knots and braids using Jones polynomial, it is tried to find if there exists an untrivial knot equal to unknot? After thorough analysis, possible financial contagion and financial crisis prediction are analysed by using instruments of knot theory pertaining in that sense to Jones, Laurent and Alexander polynomial. It is proved that it is possible to predict financial disruptions by observing possible knots in the graphs and finding appropriate polynomials. In order to analyse knot formation, the following approach is used: “Knot formation in three-dimensional space is considered and the equations about knot forming and its disentangling are considered”. After having defined the equations in three-dimensional space, the definition of Brownian bridge concerning formation of knots in three-dimensional space is defined. Using analogy method, the notion of Brownian bridge is translated into 2-dimensional space and the foundations for the application of knot theory in 2-dimensional space have been set up. At the same time, the aforementioned approach is innovative and it could be used in accordance with stochastic analysis and quantum finance.
文摘D braiding technology has stimulated a great deal of interest in the world at large and been widely used in aerospace, military, civil construction and medical fields. Although 3 D braided composites have many good features, their features are very complicated. Optic fiber sensors can be multi braided into 3 D braided composites to fulfill a new kind of 3 D smart composites to monitor RTM process, study mechanical behaviors and damage states after molding, and monitor its own condition during service life. Since optic performances of optic fibers have direct and important relation to the performances of optic fiber sensors, experimental research is done to devise a method to incorporate the optic fiber into a 3 D structure. The optical performances of the braided optic fibers are tested and compared with the original one to study the optic performances of optic fibers, before their being braided into composites and after the RTM process.
基金The National Natural Science Foundation of China(No.51005124)the Opening Foundation of Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments(No.JS-NB-2009-1-1)
文摘This paper aims to find the relationship between the structural parameters and the radial stiffness of the braided stent and to understand the stress distribution law of the wires. According to the equation of the space spiral curve, a three-dimensional parametrical geometrical model is constructed. The finite element model is built by using the beam-beam contact elements and 3D beam elements. The constituent nitinol wires are assumed to be linear elastic material. The finite element analysis figures out that the radial stiffness of the stent and the stress distribution of the wires are influenced by all the structural parameters. The helix pitch of the wires is the most important factor. Under the condition of the same load and other structural parameters remaining unchanged, when the number of wires is 24, the stress of the wire crosssection is at the minimum. A comparison between the vitro experimental results and the analytical results is conducted, and the data is consistent, which proves that the current finite element model can be used to appropriately predict the mechanical performance of the braided esophageal stents.
文摘As an advanced composite material, the 3D braided composite has received more and more attention in foreign countries. However, it has received less attention in China. The geometric unit cell which can describe the basic structure and the relationship between the braiding angle and geometric parameters of the fabric and fiber volume ratio are given in this paper based on two 3D braiding processes, namely, the four-step and the twostep ones. Several existing mechanical models to predict groperties of the 3D braided comPOsites are discussed and their shortcomings are pointed out herein. Then a new model called the inclined laminal combination model is proposed, which is based on the classical laminated plate theory and can predict the basic mechanical behavior of the two 3D braided composites with four-step or two-step braid. In the model, each yarn in the unit cell is regarded as an inclined laminate and then a 3D analysis is performed. It is found that the predicted mechanical properties of the 3D braided composites by the proposed model are compared well with the experimental data.
