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.

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).

COMPUTER PROGRAM FOR DIRECTED STRUCTURE TOPOLOGY OPTIMIZATION

To compensate for the imperfection of traditional bi-directional evolutionary structural optimization, material interpolation scheme and sensitivity filter functions are introduced. A suitable filter can overcome the checkerboard and mesh-dependency. And the historical information on accurate elemental sensitivity numbers are used to keep the objective function converging steadily. Apart from rational intervals of the relevant important parameters, the concept of distinguishing between active and non-active elements design is proposed, which can be widely used for improving the function and artistry of structures directly, especially for a one whose accurate size is not given. Furthermore, user-friendly software packages are developed to enhance its accessibility for practicing engineers and architects. And to reduce the time cost for large timeconsuming complex structure optimization, parallel computing is built-in in the MATLAB codes. The program is easy to use for engineers who may not be familiar with either FEA or structure optimization. And developers can make a deep research on the algorithm by changing the MATLAB codes. Several classical examples are given to show that the improved BESO method is superior for its handy and utility computer program software.

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.

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.

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.

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(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.

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.

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.

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.

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.

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.

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.