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.

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 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.

Structural Topology and Dynamic Response Analysis of an Electric Torque Vectoring Drive-Axle for Electric Vehicles

In-wheel motor-drive electric vehicles have the advantage of independently controllable wheel torque and the disadvantages of unsprung mass rise and power restriction.To address the disadvantages,a centralized layout electric torque vectoring drive-axle system(E-TVDS)with dual motors is proposed,which can realize arbitrary distribution of driving torque between the left and right wheels.First,the speed and torque distribution principle of E-TVDS based on velocity diagram are analyzed,and a virtual prototype of the whole vehicle with basic gear ratio relation model of the E-TVDS is built for simulation to verify the theoretical results and the basic effect of E-TVDS on the steering performance of the vehicle.Second,the charac-teristics of 36 types of the novel E-TVDS topology structure are compared and analyzed,and the optimal structure scheme is selected.Third,the accurate multiple degrees of freedom dynamic model for the optimal structure is established by using the bond graph method,and its dynamic response characteristics are analyzed.The results show that the vehicle equipped with the proposed E-TVDS can distribute the driving torque with the almost identical amount but opposite sign between the left and right wheels in any direction,and varying amount according to different chassis dynamics control requirements,and the torque response performance is great with little delay and overshoot.The function and dynamic response of the proposed E-TVDS show that it has potential application value for various performance improvements of electric vehicles.

Parameterized level set method for structural topology optimization based on the Cosserat elasticity

When describing the mechanical behavior of some engineering materials,such as composites,grains,biological materials and cellular solids,the Cosserat continuum theory has more powerful capabilities compared with the classical Cauchy elasticity since an additional local rotation of point and its counterpart(couple stress)are considered in the Cosserat elasticity to represent the material microscale effects.In this paper,a parameterized level set topology optimization method is developed based on the Cosserat elasticity for the minimum compliance problem of the Cosserat solids.The influence of material characteristic length and Cosserat shear modulus on the optimized structure is investigated in detail.It can be found that the microstructural constants in the Cosserat elasticity have a significant impact on the optimized topology configurations.In addition,the minimum feature size and the geometric complexity of the optimized structure can be controlled implicitly by adjusting the parameters of the characteristic length and Cosserat shear modulus easily.Furthermore,the optimized structure obtained by the developed Cosserat elasticity based parameterized level set method will degenerate to the result by using the classical Cauchy elasticity based parameterized level set method when the Cosserat shear modulus approaches zero.

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.

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.

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.

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.

A NEW METHOD FOR STRUCTURAL TOPOLOGICAL OPTIMIZATION BASED ON THE CONCEPT OF INDEPENDENT CONTINUOUS VARIABLES AND SMOOTH MODEL

A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in conventional models and algorithms for the optimization of the structural topology. Its application to truss topological optimization with stress and displacement constraints is satisfactory, with convergence faster than that of sectional optimizations.

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.

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.

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.

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).

Structure-controlled slow dynamics in Al−Mg melts

Molecular dynamics simulation was employed to investigate the dynamical and structural properties of Al−Mg melts with the Al concentration systematically changed.The results show that the viscosity of Al67Mg33 abnormally surpasses that of Al85Mg15 below 550 K,inconsistent with the tendency at high temperatures.The evolution of the icosahedral order population is found to account for this dynamic behavior.Structural analysis shows a preferred bonding between Al and Mg atoms in the nearest neighbor shells,while a repelling tendency between them in the second shells,leading to the prepeak emergence in the partial static structure factors.The formation of icosahedral clusters is constrained in the Al-rich compositions because of the lack of sufficient Mg atoms to stabilize the clusters geometrically.These results demonstrate the structural consequence through the interplay between geometric packing and chemical interaction.These findings are crucial to understanding the structure−dynamic properties in Al−Mg melts.

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.

An efficient reliability evaluation method for industrial wireless sensor networks

Aimed at the difficulties in accurately, comprehensively and systematically evaluating the reliability of industrial wireless sensor networks （WSNs）, a time-evolving state transition-Monte Carlo （TEST-MC） evaluation method and a novel network function value representation method are proposed to evaluate the reliability of the IWSNs. First, the adjacency matrix method is used to characterize three typical topologies of WSNs including the mesh network, tree network and ribbon network. Secondly, the network function value method is used to evaluate the network connectivity, and the TEST-MC evaluation method is used to evaluate network reliability and availability. Finally, the variations in the reliability, connectivity and availability of these three topologies are presented. Simulation results show that the proposed method can quickly analyze the reliability of the networks containing typical WSN topologies, which provides an effective method for the comprehensive and accurate evaluation of the reliability of WSNs.

Calculation connectivity reliability of road networks based on recursive decomposition arithmetic

In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic is reviewed. Then the characteristics of road networks, which are different from general networks, are analyzed. Under this condition, an improved recursive decomposition arithmetic is put forward which fits road networks better. Furthermore, detailed calculation steps are presented which are convenient for the computer, and the advantage of the approximate arithmetic is analyzed based on this improved arithmetic. This improved recursive decomposition arithmetic directly produces disjoint minipaths and avoids the non-polynomial increasing problems. And because the characteristics of road networks are considered, this arithmetic is greatly simplified. Finally, an example is given to prove its validity.