A review of the design methods of complex topology structures for 3D printing

As a matter of fact,most natural structures are complex topology structures with intricate holes or irregular surface morphology.These structures can be used as lightweight infill,porous scaffold,energy absorber or micro-reactor.With the rapid advancement of 3D printing,the complex topology structures can now be efficiently and accurately fabricated by stacking layered materials.The novel manufacturing technology and application background put forward new demands and challenges to the current design methodologies of complex topology structures.In this paper,a brief review on the development of recent complex topology structure design methods was provided;meanwhile,the limitations of existing methods and future work are also discussed in the end.

A Simple and Efficient Structural Topology Optimization Implementation Using Open-Source Software for All Steps of the Algorithm:Modeling, Sensitivity Analysis and Optimization

This work analyzes the implementation of a continuous method of structural topology optimization(STO)using open-source software for all stages of the topology optimization problem:modeling,sensitivity analysis and optimization.Its implementation involves three main components:numerical analysis using the Finite Element Method(FEM),sensitivity analysis using an Adjoint method and an optimization solver.In order to allow the automated numerical solution of Partial Differential Equations(PDEs)and perform a sensitivity analysis,FEniCS and Dolfin Adjoint software are used as tools,which are open-source code.For the optimization process,Ipopt(Interior Point OPTimizer)is used,which is a software package for nonlinear optimization scale designed to find(local)solutions of mathematical optimization problems.The topological optimization method used is based on the SIMP-Solid IsotropicMaterial with Penalization interpolation.The considered problem is the minimization of compliance/maximization of stiffness,considering the examples of recurrent structures in the literature in 2D and 3D.A density filtering algorithm based on Helmholtz formulation is used.The complete code involves 51 lines of programming and is presented and commented in detail in this article.

Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

Three-dimensional spatial structure of the macro-pores and flow simulation in anthracite coal based on X-ray μ-CT scanning data

The three-dimensional(3 D) structures of pores directly affect the CH4 flow.Therefore,it is very important to analyze the3 D spatial structure of pores and to simulate the CH4 flow with the connected pores as the carrier.The result shows that the equivalent radius of pores and throats are 1-16 μm and 1.03-8.9 μm,respectively,and the throat length is 3.28-231.25 μm.The coordination number of pores concentrates around three,and the intersection point between the connectivity function and the X-axis is 3-4 μm,which indicate the macro-pores have good connectivity.During the single-channel flow,the pressure decreases along the direction of CH4 flow,and the flow velocity of CH4 decreases from the pore center to the wall.Under the dual-channel and the multi-channel flows,the pressure also decreases along the CH4 flow direction,while the velocity increases.The mean flow pressure gradually decreases with the increase of the distance from the inlet slice.The change of mean flow pressure is relatively stable in the direction horizontal to the bedding plane,while it is relatively large in the direction perpendicular to the bedding plane.The mean flow velocity in the direction horizontal to the bedding plane(Y-axis) is the largest,followed by that in the direction horizontal to the bedding plane(X-axis),and the mean flow velocity in the direction perpendicular to the bedding plane is the smallest.

Topological Structure of Vortex Solution in Jackiw-Pi Model

By using φ-mapping method,we discuss the topological structure of the self-duality solution in Jackiw-Pimodel in terms of gauge potential decomposition.We set up relationship between Chern-Simons vortex solution andtopological number,which is determined by Hopf index and Brouwer degree.We also give the quantization of flux inthis ease.Then,we study the angular momentum of the vortex,which can be expressed in terms of,the flux.

Topological structure bifurcation of temperature field of deformable drop in Marangoni migration

The unsteady processes of the Marangoni migration of deformable liquid drops are simulated numerically in a wider range of Marangoni number(up to Ma = 500) in the present work.A steady terminal state can always be reached,and the scaled terminal velocity is a monotonic function decreasing with increasing Marangoni number,which is generally in agreement with corresponding experimental data.The topological structure of flow field in the steady terminal state does not change as the Marangoni number increase...

Syntheses and Crystal Structures of Two Coordination Polymers Based on a Flexible Ligand N,N'-Diacetic Acid Imidazolium

Two coordination compounds with a flexible ligand N,N?-diacetic acid imidazolium(HDAM),{[Co(trans-DAM)(bipy)(H2O)2](OH)·4H2O}n 1 and {[Cd(trans-DAM)(bipy)(H2O)](NO3)?2H2O}n 2(bipy = 4,4'-bipyridine),were prepared and characterized by single-crystal X-ray diffraction.Compound 1 crystallizes in monoclinic,space group P2/n with a = 7.589(6),b = 11.444(2),c = 12.894(3),β = 90.99(3)°,V = 1119.8(4)3,Z = 4,C8.5H14N2O5.5Co0.5,Mr = 261.68,Dc = 1.552 g/cm3,F(000) = 546,μ = 0.832 mm-1,the final R = 0.0657 and wR = 0.1958.Compound 2 crystallizes in the monoclinic C2 space group with a = 17.479(4),b = 11.689(2),c = 11.670(2),β = 117.13(3)°,V = 2121.9(7)3,Z = 4,C17H21N5O10Cd,Mr = 567.79,Dc = 1.777 g/cm3,F(000) = 1144,μ = 1.096 mm-1,the final R = 0.0233 and wR = 0.0638.In 1,the Co(II) ions are linked by μ2-trans-DAM-and bipy ligands to build a 2D(4,4) rectangular grid layer,exhibiting a 4-connected sql net.As for 2,μ3-trans-DAM-and bipy bridge Cd(II) ions form a 2D double-layer,consisting of a couple of(4,4) grid layers,which can be viewed as a(3,4)-connected network.In both compounds,the 2D structures are stabilized by hydrogen bonding interactions to give 3D supramolecular frameworks.Additionally,FT-IR spectroscopy,UV-Visible spectroscopy,and the fluorescent properties are discussed.

Structural Topology Optimization by Combining BESO with Reinforcement Learning

In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast to conventional approaches which only generate a certain quasi-optimal solution,the goal of the combined method is to provide more quasi-optimal solutions for designers such as the idea of generative design.Two key components were adopted.First,besides sensitivity,value function updated by Monte-Carlo reinforcement learning was utilized to measure the importance of each element,which made the solving process convergent and closer to the optimum.Second,ε-greedy policy added a random perturbation to the main search direction so as to extend the search ability.Finally,the quality and diversity of solutions could be guaranteed by controlling the value of compliance as well as Intersection-over-Union(IoU).Results of several 2D and 3D compliance minimization problems,including a geometrically nonlinear case,show that the combined method is capable of generating a group of good and different solutions that satisfy various possible requirements in engineering design within acceptable computation cost.

A Spatio-Temporal Heterogeneity Data Accuracy Detection Method Fused by GCN and TCN

Spatio-temporal heterogeneous data is the database for decisionmaking in many fields,and checking its accuracy can provide data support for making decisions.Due to the randomness,complexity,global and local correlation of spatiotemporal heterogeneous data in the temporal and spatial dimensions,traditional detection methods can not guarantee both detection speed and accuracy.Therefore,this article proposes a method for detecting the accuracy of spatiotemporal heterogeneous data by fusing graph convolution and temporal convolution networks.Firstly,the geographic weighting function is introduced and improved to quantify the degree of association between nodes and calculate the weighted adjacency value to simplify the complex topology.Secondly,design spatiotemporal convolutional units based on graph convolutional neural networks and temporal convolutional networks to improve detection speed and accuracy.Finally,the proposed method is compared with three methods,ARIMA,T-GCN,and STGCN,in real scenarios to verify its effectiveness in terms of detection speed,detection accuracy and stability.The experimental results show that the RMSE,MAE,and MAPE of this method are the smallest in the cases of simple connectivity and complex connectivity degree,which are 13.82/12.08,2.77/2.41,and 16.70/14.73,respectively.Also,it detects the shortest time of 672.31/887.36,respectively.In addition,the evaluation results are the same under different time periods of processing and complex topology environment,which indicates that the detection accuracy of this method is the highest and has good research value and application prospects.

Effects of water and salt for groundwater-soil systems on root growth and architecture of Tamarix chinensis in the Yellow River Delta,China

To test the patterns of the root morphology and architecture indexes of Tamarix chinensis in response to water and salt changes in the two media of the groundwater and soil,three-year-old T.chinensis seedlings were chosen as the research object.Groundwater with four salinity levels was created,and three groundwater level(GL)were applied for each salinity treatment to measure the root growth and architecture indexes.In the fresh water and brackish water treatments,the topological index(TI)of the T.chinensis roots was close to 0.5,and the root architecture was close to a dichotomous branching pattern.In the saline water and saltwater treatments,the TI of the T.chinensis roots was large and close to 1.0,and the root architecture was close to a herringbone-like branching pattern.Under different GLs and salinities,the total root length was significantly greater than the internal link length,the external link length was greater than the internal link length,and the root system showed an outward expansion strategy.The treatment with fresh water and a GL of 1.5 m was the most suitable for T.chinensis root growth,while the root growth of T.chinensis was the worst in the treatment with saline water and a GL of 0.3 m.T.chinensis can adapt to the changes in soil water and salt by regulating the growth and morphological characteristics of the root system.T.chinensis can adapt to high-salt environments by reducing its root branching and to water deficiencies by expanding the distribution and absorption area of the root system.

Experimental observation of multiple topological nodal structure in LaSb_(2)

Unconventional fermions in the immensely studied topological semimetals are the source for rich exotic topological properties.Here,using symmetry analysis and first-principles calculations,we propose the coexistence of multiple topological nodal structure in LaSb_(2),including topological nodal surfaces,nodal lines and in particular eightfold degenerate nodal points,which have been scarcely observed in a single material.Further,utilizing angle-resolved photoemission spectroscopy,we confirm the existence of nodal surfaces and eightfold degenerate nodal points in LaSb_(2).The intriguing multiple topological nodal structure might play a crucial role in giving rise to the large linear magnetoresistance.Our work renews the insights into the exotic topological phenomena in LaSb_(2).

Optimization Design and Performance Analysis of Vehicle Powertrain Mounting System

The design strategies for powertrain mounting systems play an important role in the reduction of vehicular vibration and noise. As stiffness and damping elements connecting the transmission system and vehicle body, the rubber mount exhibits better vibration isolation performance than the rigid connection. This paper presents a complete design process of the mounting system, including the vibration decoupling, vibration simulation analysis, topology optimization, and experimental verification. Based on the 6?degrees?of?freedom vibration coupling model of the powertrain mounting system, an optimization algorithm is used to extract the best design parameters of each mount, thus rendering the mounting system fully decoupled and the natural frequency well configured, and the optimal parameters are used to design the mounting system. Subsequently, vibration simulation analysis is applied to the mounting system, considering both transmission and road excitations. According to the results of finite element analysis, the topological structure of the metal frame of the front mount is optimized to improve the strength and dynamic characteristics of the mounting system. Finally, the vibration bench test is used to verify the availability of the optimization design with the analysis of acceleration response and vibration transmissibility of the mounting system. The results show that the vibration isolation performance of the mounting system can be improved effectively using the vibration optimal decoupling method, and the structural modification of the metal frame can well promote the dynamic characteristics of the mounting system.

Brain networks modeling for studying the mechanism underlying the development of Alzheimer’s disease

Alzheimer’s disease is a primary age-related neurodegenerative disorder that can result in impaired cognitive and memory functions.Although connections between changes in brain networks of Alzheimer’s disease patients have been established,the mechanisms that drive these alterations remain incompletely understood.This study,which was conducted in 2018 at Northeastern University in China,included data from 97 participants of the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset covering genetics,imaging,and clinical data.All participants were divided into two groups:normal control(n=52;20 males and 32 females;mean age 73.90±4.72 years)and Alzheimer’s disease(n=45,23 males and 22 females;mean age 74.85±5.66).To uncover the wiring mechanisms that shaped changes in the topology of human brain networks of Alzheimer’s disease patients,we proposed a local naive Bayes brain network model based on graph theory.Our results showed that the proposed model provided an excellent fit to observe networks in all properties examined,including clustering coefficient,modularity,characteristic path length,network efficiency,betweenness,and degree distribution compared with empirical methods.This proposed model simulated the wiring changes in human brain networks between controls and Alzheimer’s disease patients.Our results demonstrate its utility in understanding relationships between brain tissue structure and cognitive or behavioral functions.The ADNI was performed in accordance with the Good Clinical Practice guidelines,US 21 CFR Part 50-Protection of Human Subjects,and Part 56-Institutional Review Boards(IRBs)/Research Good Clinical Practice guidelines Institutional Review Boards(IRBs)/Research Ethics Boards(REBs).

Monodomain Liquid Crystals of Two-Dimensional Sheets by Boundary-Free Sheargraphy

Eliminating topological defects to achieve monodomain liquid crystals is highly significant for the fundamental studies of soft matter and building long-range ordered materials.However,liquid crystals are metastable and sensitive to external stimuli,such as flow,confinement,and electromagnetic fields,which cause their intrinsic polycrystallinity and topological defects.Here,we achieve the monodomain liquid crystals of graphene oxide over 30 cm through boundary-free sheargraphy.The obtained monodomain liquid crystals exhibit large-area uniform alignment of sheets,which has the same optical polarized angle and intensity.The monodomain liquid crystals provide bidirectionally ordered skeletons,which can be applied as lightweight thermal management materials with bidirectionally high thermal and electrical conductivity.Furthermore,we extend the controllable topology of two-dimensional colloids by introducing singularities and disclinations in monodomain liquid crystals.Topological structures with defect strength from−2 to+2 were realized.This work provides a facile methodology to study the structural order of soft matter at a macroscopic level,facilitating the fabrication of metamaterials with tunable and highly anisotropic architectures.

Reversible lithium storage in sp^(2) hydrocarbon frameworks

Polymer materials offer controllable structure-dependent performances in separation,catalysis and drug release.Their molecular structures can be precisely tailored to accept Li^(+)for energy storage applications.Here the design of sp^(2)carbon-based polyphenylene(PPH)with high lithium-ion uptakes and long-term stability is reported.Linear-PPH(L-PPH)exceeds the performance of crosslink-PPH(C-PPH),due to the fact that it has an ordered lamellar structure,promoting the Li^(+)intercalation/deintercalation channel.The L-PPH cell shows a clear charge and discharge plateau at 0.35 and 0.15 V vs.Li^(+)/Li,respectively,which is absent in the C-PPH cell.The Li^(+)storage capacity of L-PPH is five times that of the C-PPH.The reversible storage capacity is further improved to 261 m Ah g;by functionalizing the L-PPH with the–SO_(3)H groups.In addition,the Li-intercalated structures of C-PPH and L-PPH are investigated via near-edge X-ray absorption fine structure(NEXAFS),suggesting the high reversible Li^(+)–C=C bond interaction at L-PPH.This strategy,based on new insight into sp^(2)functional groups,is the first step toward a molecular understanding of the structure storage-capacity relationship in sp^(2)carbon-based polymer.

Endpoints of Multi-Valued Weak Contractions on the Metric Space of Partially Ordered Groups

The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).

Theoretical and experimental study on white light interferometric sensing network with double-ring topology

A white-light interferometric fiber-optic sensing network based on the double-ring topology is demonstrated,which can be applied to the measurements of quasi-distributed strain and temperature in a smart structure.In order to increase the multiplexing capacity,decrease the measurement cost of each sensor,and improve the ability of reliability of the sensor network,a double-port interrogating technology was used.The double-ring fiber optical sensing network based on the space division multiplexing(SDM)is further developed.The low coherent multiplexing principle in the double-ring network structure is analyzed.Based on the optical path matching condition of SDM,the intensity characteristic of the interference signal in the sensor is deduced.The characteristics of the double-ring sensing network connecting 9 sensors and its property of robust resisting destruction are verified by experiments,and the results are analyzed and discussed.

New method for controlling minimum length scales of real and void phase materials in topology optimization

Minimum length scale control on real and void material phases in topology optimization is an important topic of research with direct implications on numerical stability and solution manufacturability.And it also is a challenge area of research due to serious conflicts of both the solid and the void phase element densities in phase mixing domains of the topologies obtained by existing methods.Moreover,there is few work dealing with controlling distinct minimum feature length scales of real and void phase materials used in topology designs.A new method for solving the minimum length scale controlling problem of real and void material phases,is proposed.Firstly,we introduce two sets of coordinating design variable filters for these two material phases,and two distinct smooth Heaviside projection functions to destroy the serious conflicts in the existing methods(e.g.Guest Comput Methods Appl Mech Eng 199(14):123-135,2009).Then,by introducing an adaptive weighted 2-norm aggregation constraint function,we construct a coordinating topology optimization model to ensure distinct minimum length scale controls of real and void phase materials for the minimum compliance problem.By adopting a varied volume constraint limit scheme,this coordinating topology optimization model is transferred into a series of coordinating topology optimization sub-models so that the structural topology configuration can stably and smoothly changes during an optimization process.The structural topology optimization sub-models are solved by the method of moving asymptotes(MMA).Then,the proposed method is extended to the compliant mechanism design problem.Numerical examples are given to demonstrate that the proposed method is effective and can obtain a good 0/1 distribution final topology.

Network structure of thermonuclear reactions in nuclear landscape

Nucleosynthesis is a complex process in astro-nuclear evolution.In this work,we constructed a directed,multi-layer,nuclear reaction network,using the substrate-product method from a thermonuclear reaction database,JINA REACLIB.The network contained four layers,namely n-,p-,h-and r-,which correspond to the types of reactions involved in neutrons,protons,~4He and the remaining atomic particles,respectively.The degree values(i.e.numbers of reactions),for three layers of n-,p-,and h-,have a significant correlation with one another,and their topological structures exhibit a similar regularity.However,the r-layer has a more complex topological structure compared to the other layers;thus,its correlation of degree values with the other three layers is not as strong as that seen in the other layers.To analyze the motif structure of the nuclear reaction network,we used the software package"mfinder".We identified the most frequent reaction patterns of the interconnections that occurred amongst the different nuclides.This work provides a novel approach to investigating the nuclear reaction network that prevails in the astrophysical context.

Development of lunar regolith composite and structure via laser-assisted sintering

Aiming at the exploration and resource utilization activities on the Moon,in situ resource utilization and in situ manufacturing are proposed to minimize the dependence on the ground transportation supplies.In this paper,a laser-assisted additive manufacturing process is developed to fabricate lunar regolith composites with PA12/SiO2 mixing powders.The process parameters and composite material compositions are optimized in an appropriate range through orthogonal experiments to establish the relationship of process–structure–property for lunar regolith composites.The optimal combination of composite material compositions and process parameters are mixing ratio of 50/50 in volume,laser power of 30 W,scanning speed of 3500 mm/s,and scanning hatch space of 0.2 mm.The maximum tensile strength of lunar regolith composites reaches 9.248 MPa,and the maximum depth of surface variation is 120.79μm,which indicates poor powder fusion and sintering quality.Thereafter,the mechanical properties of laser-sintered lunar regolith composites are implemented to the topology optimization design of complex structures.The effectiveness and the feasibility of this laser-assisted process are potentially developed for future lightweight design and manufacturing of the solar panel installed on the lunar rover.