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.

Study on local topology model of low/high streak structures in wall-bounded turbulence by tomographic time-resolved particle image velocimetry

The relationship between the in the logarithmic law （log-law） region of bursting event and the low/high-speed streak a turbulent boundary layer is investigated. A tomographic time-resolved particle image velocimetry （TRPIV） system is used to measure the instantaneous three-dimensional-three-component （3D-3C） velocity field. The momentum thickness based Reynolds number is about 2 460. The topological information in the log-law region is obtained experimentally. It is found that the existence of the quadrupole topological structure implies a three-pair hairpin-like vortex packet, which is in connection with the low/high-speed streak. An idealized 3D topological model is then proposed to characterize the observed hairpin vortex packet and low/high-speed streak.

Hydrothermal Synthesis,Structure and Photo-luminescence of a 2D Lead（Ⅱ） Coordination Polymer with （4,6^3）Topology Based on Pb and 1,2,3,4-Butanetetracarboxylate Nodes

A lead（II） coordination polymer,{[Pb2（butca）（H2O）2]（H2O）2}n （1）,has been synthe-sized by the hydrothermal reaction of Pb（OH）2 and 1,2,3,4-butanetetracarboxylic acid （H4butca） at 160 °C.Single-crystal X-ray analyses reveal that it crystallizes in monoclinic,space group P21/c with a=7.616（5）,b=7.584（4）,c=12.314（7）,β=105.595（12）o,V=685.0（7）3,Z=4,C8H14O12Pb2,Mr=716.57,Dc=3.474 g/cm3,μ=24.610 mm-1,F（000）=644,the final R=0.0381 and wR=0.1176 for 1465 observed reflections with I 〉 2σ（I）.The complex presents a 2D-layered structure featuring two different types of rings,and has a （4,36）topology based on Pb and butca4-nodes.In solid state,complex 1 shows photoluminescence with the maximum emission intensity at 468 nm under 286 nm excitation.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅰ)- EXPERIMENTAL MODEL AND TOPOLOGICAL FLOW PATTERNS ON BOTH ENDWALLS AND BLADE SURFACES

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in the transverse section, and by appling topology theory, the structures on both endwalls and blade surfaces were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅱ)- TOPOLOGICAL FLOW PATTERN AND VORTEX STRUCTURE IN THE TRANSVERSE SECTION OF A BLADE CASCADE

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in transverse section, and by appling topology theory, the topological structures and vortex structure in the transverse section of a blade cascade were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex, and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

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.

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅰ)

Based on the work discussed on the former study, this article first starts from the mathematical model of a kind of complicated financial system, and analyses all possible things that the model shows in the operation of our country's macro_financial system: balance, stable periodic, fractal, Hopf_bifurcation, the relationship between parameters and Hopf_bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro_economic policies and adjustment of some parameter on the whole financial system behavior have been analyzed. This study will deepen people's understanding of the lever function of all kinds of financial policies.

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.

Different effects of economic and structural performance indexes on model construction of structural topology optimization

The objective and constraint functions related to structural optimization designs are classified into economic and performance indexes in this paper.The influences of their different roles in model construction of structural topology optimization are also discussed.Furthermore,two structural topology optimization models,optimizing a performance index under the limitation of an economic index,represented by the minimum compliance with a volume constraint（MCVC）model,and optimizing an economic index under the limitation of a performance index,represented by the minimum weight with a displacement constraint（MWDC）model,are presented.Based on a comparison of numerical example results,the conclusions can be summarized as follows：（1）under the same external loading and displacement performance conditions,the results of the MWDC model are almost equal to those of the MCVC model;（2）the MWDC model overcomes the difficulties and shortcomings of the MCVC model;this makes the MWDC model more feasible in model construction;（3）constructing a model of minimizing an economic index under the limitations of performance indexes is better at meeting the needs of practical engineering problems and completely satisfies safety and economic requirements in mechanical engineering,which have remained unchanged since the early days of mechanical engineering.

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅱ)

Based on the work discussed on the former study, this article first starts from the mathematical model of a kind of complicated financial system, and analyses all possible things that the model shows in the operation of our country's macro_financial system: balance, stable periodic, fractal, Hopf_bifurcation, the relationship between parameters and Hopf_bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro_economic policies and adjustment of some parameter on the whole financial system behavior have been analyzed. This study will deepen people's understanding of the lever function of all kinds of financial policies.

TOPOLOGICAL STRUCTURE OF RENORM ALIZATION CONSTANTS I N QUANTUM FIELD THEORY AT SHORT DISTANCE KUNMING COLLABRATION OF MULTIHADRON DYNAMIOS

The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowski space time is based upon the point set with σ-length on light cone.

The ICM method with objective function transformed by variable discrete condition for continuum structure

ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.

Concurrent multi-scale design optimization of composite frame structures using the Heaviside penalization of discrete material model

This paper deals with the concurrent multi-scale optimization design of frame structure composed of glass or carbon fiber reinforced polymer laminates. In the composite frame structure, the fiber winding angle at the micro-material scale and the geometrical parameter of components of the frame in the macro-structural scale are introduced as the independent variables on the two geometrical scales. Considering manufacturing requirements, discrete fiber winding angles are specified for the micro design variable. The improved Heaviside penalization discrete material optimization interpolation scheme has been applied to achieve the discrete optimization design of the fiber winding angle. An optimization model based on the minimum structural compliance and the specified fiber material volume constraint has been established. The sensitivity information about the two geometrical scales design variables are also deduced considering the characteristics of discrete fiber winding angles. The optimization results of the fiber winding angle or the macro structural topology on the two single geometrical scales, together with the concurrent two-scale optimization, is separately studied and compared in the paper. Numerical examples in the paper show that the concurrent multi-scale optimization can further explore the coupling effect between the macro-structure and micro-material of the composite to achieve an ultralight design of the composite frame structure. The novel two geometrical scales optimization model provides a new opportunity for the design of composite structure in aerospace and other industries.

Solvent Dependent Assembly,Structural Diversity and Topology Analysis in Two Novel Ni Coordination Polymers

Solvent dependent assembly obtained two novel Ni coordination polymers with H_2 tbtpa and flexible 1,2-bix ligand（H_2tbtpa = tetrabromoterephthalic acid and 1,2-bix = 1,2-bis（imidazol-1-ylmethyl）benzene）,formulated as [Ni_（0.5）（tbtpa）_（0.5）（1,2-bix）·（H_2O）]_n（1） and [Ni（tbtpa）（1,2-bix）（H_2O）_2]_n（2）.They have been structurally characterized by single-crystal and powder X-ray diffraction,elemental analysis,FT-IR spectra and TGA.Compound 1 crystalizes in triclinic,space group P1 with a = 9.0276（4）,b = 10.0012（6）,c = 11.4955（5） A,α = 69.121（5）,β = 76.398（4）,γ = 89.668（4）o,C_（36）H_（32）Br_4 Ni N_8O_6,Mr = 1051.04,V = 939.05（8） A^3,Z = 1,Dc = 1.859 g·cm^-3,μ = 6.222 mm^-1,F（000） = 520,8.502≤2θ≤134.16°,λ（Cu Kα） = 1.54184 A,T = 294（6） K,the final R = 0.0750,w R = 0.1988 and S = 1.033.Compound 2 crystalizes in triclinic,space group P1 with a = 11.1257（7）,b = 11.5062（6）,c = 12.3529（4） A,α = 88.861（3）,β = 84.572（4）,γ = 64.235（6）o,C_（22）H_（18）Br_4 Ni N_4O_6,Mr = 812.75,V = 1417.36（1） A^3,Z = 2,Dc = 1.904 g·cm^-3,μ = 7.968 mm^-1,F（000） = 788,7.2≤2θ≤134.1°,λ（Cu Kα） = 1.54184 A,T = 294（6） K,the final R = 0.0414,w R = 0.0865 and S = 1.025.1 shows a two-dimensional（4,4）-sql topology and 2 manifests a three-dimensional 6~58 Cd SO_4 topology coordination polymer network.

Synthesis and Crystal Structure of a Novel Cobalt(Ⅱ) Coordination Polymer with 1,2,4,5-Benzenetetracarboxylate

A novel cobalt（II） coordination polymer,[Co（BTEC）1/2]n 1,has been synthesized with Co（NO3）2·6H2O and 1,2,4,5-benzenetetracarboxylic acid （H4BTEC） by the hydrothermal method,and characterized by elemental analysis,IR and single-crystal X-ray diffraction. Crystallographic data for 1： C5HO4Co,Mr = 183.99,monoclinic,space group C2/c,a = 16.619（6）,b = 7.416（3）,c = 8.040（3）A,β = 90.612（4）°,V = 990.8（6） A^3,Z = 8,Dc = 2.467 g/cm^3,μ = 3.390 mm^-1,F（000） = 720,R = 0.0307 and wR = 0.0847 for 912 observed reflections （I 〉 2σ（I））. X-ray crystal structural analysis revealed that each Co（II） adopts a tetrahedral coordination mode to link four separate BTEC ligands via uniform monodentate carboxylate groups and each BTEC ligand possesses an 8-connected geometry to connect eight Co（II） ions. Complex 1 exhibits a rare （4,8）-connected net with （45.6）2（410.614.84） topology.

THEORETICAL STUDY ON THE BIFURCATION OF VORTEXES STRUCTURE FOR FLOW IN CURVED TUBE

The number and distribution of the singular points of streamlines in the cross-section of steady flow through a curved tube ate discussed by using the method of topological structure analysis. And a theoretical criterion is obtained for the bifurcation of flow vortexes for the secondary flow turning from two-vortex structure into four-vortex structure. Furthermore, the critical Dean number for bifurcation and the semi-analytical expressions of stream function and axial velocity are given by using Galerkin technique. The result of calculation is consistent with the theoretical criterion.

Topological structure effect on far-infrared spectra in a GaAs/InAs nanoring

On the basis of the growth mechanism of a GaAs/InAs nanoring, we propose a fine model which reflects the confinement details of real nanoring. Through calculations of the two-electron energy and far-infrared （FIR） spectra, we find that the ring topological structure and electron-electron interaction have great influence on the FIR spectra. The two unknown transition peaks in the experiment are determined theoretically. The theoretical results are in good agreement with the experiments.

TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.

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.