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.

Elimination of cracks in stainless steel casings via 3D printed sand molds with an internal topology structure

The important supporting component in a gas turbine is the casing,which has the characteristics of large size,complex structure,and thin wall.In the context of existing 3DP sand casting processes,casting crack defects are prone to occur.This leads to an increase in the scrap rate of casings,causing significant resource wastage.Additionally,the presence of cracks poses a significant safety hazard after the casings are put into service.The generation of different types of crack defects in stainless steel casings is closely related to casting stress and the high-temperature concession of the sand mold.Therefore,the types and causes of cracks in stainless steel casing products,based on their structural characteristics,were systematically analyzed.Various sand molds with different internal topology designs were printed using the 3DP technology to investigate the impact of sand mold structures on high-temperature concession.The optimal sand mold structure was used to cast casings,and the crack suppression effect was verified by analyzing its eddy current testing results.The experimental results indicate that the skeleton structure has an excellent effect on suppressing cracks in the casing.This research holds important theoretical and engineering significance in improving the quality of casing castings and reducing production costs.

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.

Topology and Vortex Structures of Turbine Cascade with Different Tip Clearances

This paper uses the topology theory to analyze the surface flowspectrums of straight, positively curved and negatively curvedcascades with relative tip clearances of 0.023 and 0.036, findsapparent differences of topology and vortex structures in the bladetip and the suction side wall corner of single type of cascade withthis two clearances, and studies the mechanism of the differenceformation as well as their effects o the energy loss.

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.

Topological Structure-Modulated Collagen Carbon as Two-in-One Energy Storage Configuration toward Ultrahigh Power and Energy Density

Efficient energy storage devices with suitable electrode materials,that integrate high power and high energy,are the crucial requisites of the renewable power source,which have unwrapped new possibilities in the sustainable development of energy and the environment.Herein,a facile collagen microstructure modulation strategy is proposed to construct a nitrogen/oxygen dual-doped hierarchically porous carbon fiber with ultrahigh specific surface area(2788 m^(2)g^(-1))and large pore volume(4.56 cm^(3)g^(-1))via local microfibrous breakage/disassembly of natural structured proteins.Combining operando spectroscopy and density functional theory unveil that the dual-heteroatom doping could effectively regulate the electronic structure of carbon atom framework with enhanced electric conductivity and electronegativity as well as decreased diffusion resistance in favor of rapid pseudocapacitive-dominated Li^(+)-storage(353 mAh g^(-1)at 10 A g^(-1)).Theoretical calculations reveal that the tailored micro-/mesoporous structures favor the rapid charge transfer and ion storage,synergistically realizing high capacity and superior rate performance for NPCF-H cathode(75.0 mAh g^(-1)at 30 A g^(-1)).The assembled device with NPCF-H as both anode and cathode achieves extremely high energy density(200 Wh kg^(-1))with maximum power density(42600 W kg^(-1))and ultralong lifespan(80%capacity retention over 10000 cycles).

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.

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.

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.

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.

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.

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.

TRPIV measurement of turbulent coherent structures in a drag-reducing flow by polymers

Fully developed turbulent flow fields with and without polymer solution at the same Reynolds number were measured by time-resolved particle image velocimetry （TRPIV） in a water channel to investigate the mechanism of drag-reducing solution from the view of coherent structures manipulation. The streamwise mean velocity and Reynolds stress profiles in the solution were compared with those in water. After adding the polymer solution, the Reynolds stress in the near-wall area decreases significantly. The result relates tightly to the decease of the coherent structures＇ bursting. The spatial topology of coherent structures during bursts has been extracted by the new mu-level criterion based on locally averaged velocity structure function. The effect of polymers on turbulent coherent structures mainly reflects in the intensity, not in the shape. In the solution, it is by suppressing the coherent structures that the wall friction is reduced.

Research on Several Prediction Methods of Membrane Protein Structure and Topology

Since present prediction methods of membrane protein structure and topology made use of mixed data sets both from experiments and prediction as training and test sets, the reliability and accuracy of their prediction is still under debate. To benchmark the performance of these methods, this commentary uses a test set of membrane proteins created by European Bioinformatics Institute with either available 3 D structure or experimentally confirmed transmembrane regions. Then the prediction results are compared and the problems existing in these methods and important features for successful prediction are pointed out, which may help users to choose a more reliable prediction from different results. Based upon recent advances in membrane protein, possible means to improve topology prediction accuracy are discussed.

THE TOPOLOGICAL OPTIMIZATION FOR TRUSS STRUCTURES WITH STRESS CONSTRAINTS BASED ON THE EXIST-NULL COMBINED MODEL

A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.

TOPOLOGICAL STRUCTURES OF VORTEX AND HELICITY ANALYSIS

The topological structures of the vortex filaments and vortex tubes with an exact solution of a straight spiral vortex tube are discussed. It is found that there are some confusions about the calculation of the helicity of a knotted vortex filament and some linked vortex filaments by using different methods. How to unify these methods is explained and the right results are given. (Edited author abstract) 5 Refs.

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.

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.