Gas turbine rotors are complex dynamic systems with high-dimensional,discrete,and multi-source nonlinear coupling characteristics.Significant amounts of resources and time are spent during the process of solving dynam...Gas turbine rotors are complex dynamic systems with high-dimensional,discrete,and multi-source nonlinear coupling characteristics.Significant amounts of resources and time are spent during the process of solving dynamic characteristics.Therefore,it is necessary to design a lowdimensional model that can well reflect the dynamic characteristics of high-dimensional system.To build such a low-dimensional model,this study developed a dimensionality reduction method considering global order energy distribution by modifying the proper orthogonal decomposition theory.First,sensitivity analysis of key dimensionality reduction parameters to the energy distribution was conducted.Then a high-dimensional rotor-bearing system considering the nonlinear stiffness and oil film force was reduced,and the accuracy and the reusability of the low-dimensional model under different operating conditions were examined.Finally,the response results of a multi-disk rotor-bearing test bench were reduced using the proposed method,and spectrum results were then compared experimentally.Numerical and experimental results demonstrate that,during the dimensionality reduction process,the solution period of dynamic response results has the most significant influence on the accuracy of energy preservation.The transient signal in the transformation matrix mainly affects the high-order energy distribution of the rotor system.The larger the proportion of steady-state signals is,the closer the energy tends to accumulate towards lower orders.The low-dimensional rotor model accurately reflects the frequency response characteristics of the original high-dimensional system with an accuracy of up to 98%.The proposed dimensionality reduction method exhibits significant application potential in the dynamic analysis of highdimensional systems coupled with strong nonlinearities under variable operating conditions.展开更多
We propose a finite dimensional method to compute the solution of nonlinear ill-posed problems approximately and show that under certain conditions, the convergence can be guaranteed. Moreover, we obtain the rate of c...We propose a finite dimensional method to compute the solution of nonlinear ill-posed problems approximately and show that under certain conditions, the convergence can be guaranteed. Moreover, we obtain the rate of convergence of our method provided that the true solution satisfies suitable smoothness condition. Finally, we present two examples from the parameter estimation problems of differential equations and illustrate the applicability of our method.展开更多
This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-d...This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.展开更多
By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is propose...By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.展开更多
Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Co...Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Compressive re- sidual stress and dent profile are important factors to eval- uate the effectiveness of shot peening process. In this pa- per, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of pro- cessing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were de- duced by dimensional analysis method. Secondly, the in- fluence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Fur- thermore, related empirical formulas were given for each di- mensionless parameter based on the simulation results. Fi- nally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this pa- per for analyzing the influence of each individual parameter.展开更多
The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forgin...The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forging load and deformed buIge profile during upset forging of blocks. Simulation of upsetforging of rectangular blocks under various friction condjtions was performed. Comparison of the computed results with experiments and FEM shows good agreement. It is shown that this techniquecan be used for 3D simulation of metal forming process.展开更多
In this paper,a fast element-free Galerkin(FEFG)method for three-dimensional(3D)elasticity problems is established.The FEFG method is a combination of the improved element-free Galerkin(IEFG)method and the dimension s...In this paper,a fast element-free Galerkin(FEFG)method for three-dimensional(3D)elasticity problems is established.The FEFG method is a combination of the improved element-free Galerkin(IEFG)method and the dimension splitting method(DSM).By using the DSM,a 3D problem is converted to a series of 2D ones,and the IEFG method with a weighted orthogonal function as the basis function and the cubic spline function as the weight function is applied to simulate these 2D problems.The essential boundary conditions are treated by the penalty method.The splitting direction uses the finite difference method(FDM),which can combine these 2D problems into a discrete system.Finally,the system equation of the 3D elasticity problem is obtained.Some specific numerical problems are provided to illustrate the effectiveness and advantages of the FEFG method for 3D elasticity by comparing the results of the FEFG method with those of the IEFG method.The convergence and relative error norm of the FEFG method for elasticity are also studied.展开更多
Cloud computing(CC)is an advanced technology that provides access to predictive resources and data sharing.The cloud environment represents the right type regarding cloud usage model ownership,size,and rights to acces...Cloud computing(CC)is an advanced technology that provides access to predictive resources and data sharing.The cloud environment represents the right type regarding cloud usage model ownership,size,and rights to access.It introduces the scope and nature of cloud computing.In recent times,all processes are fed into the system for which consumer data and cache size are required.One of the most security issues in the cloud environment is Distributed Denial of Ser-vice(DDoS)attacks,responsible for cloud server overloading.This proposed sys-tem ID3(Iterative Dichotomiser 3)Maximum Multifactor Dimensionality Posteriori Method(ID3-MMDP)is used to overcome the drawback and a rela-tively simple way to execute and for the detection of(DDoS)attack.First,the pro-posed ID3-MMDP method calls for the resources of the cloud platform and then implements the attack detection technology based on information entropy to detect DDoS attacks.Since because the entropy value can show the discrete or aggregated characteristics of the current data set,it can be used for the detection of abnormal dataflow,User-uploaded data,ID3-MMDP system checks and read risk measurement and processing,bug ratingfile size changes,orfile name changes and changes in the format design of the data size entropy value.Unique properties can be used whenever the program approaches any data error to detect abnormal data services.Finally,the experiment also verifies the DDoS attack detection capability algorithm.展开更多
Three-dimensional(3D)conformal electronic skins(E-skins)have been developed for matching the irregularly surfaces.The 3D conformal E-skins manufactured by direct-curved-surface or dimensional converting methods both n...Three-dimensional(3D)conformal electronic skins(E-skins)have been developed for matching the irregularly surfaces.The 3D conformal E-skins manufactured by direct-curved-surface or dimensional converting methods both need curved-surface calibration.With increase of units’number and complication of mounting-surface morphology,curved-surface calibration becomes intricate.We report a universal cutting and distributing strategy for E-skins.The E-skin incorporates hierarchical and modular tactile sensors to match curvatures and sizes,thereby reducing mounting strain.This strategy enables curved-surface performance of 3D conformal E-skins to be characterized by flatsurface calibration results.An example is provided:Three-level sensors are utilized and calibrated on flat and curved surfaces.Performance variations reduce as sensor size decreases,and performance changes of level II and III sensing units are small after mounting.Their calibration results on curved surface are replaced by those on flat surface,proving low mounting strain facilitates 3D conformal E-skins to avoid complicated curved-surface calibration.展开更多
With a three-dimensional semiclassical ensemble method, we theoretically investigated the nonsequential double ionization of Ar driven by the spatially inhomogeneous few-cycle negatively chirped laser pulses. Our resu...With a three-dimensional semiclassical ensemble method, we theoretically investigated the nonsequential double ionization of Ar driven by the spatially inhomogeneous few-cycle negatively chirped laser pulses. Our results show that the recollision time window can be precisely controlled within an isolated time interval of several hundred attoseconds, which is useful for understanding the subcycle correlated electron dynamics. More interestingly, the correlated electron momentum distribution (CEMD) exhibits a strong dependence on laser intensity. That is, at lower laser intensity, CEMD is located in the first quadrant. As the laser intensity increases,CEMD shifts almost completely to the second and fourth quadrants, and then gradually to the third quadrant.The underlying physics governing the CEMD's dependence on laser intensity is explained.展开更多
The element-free Galerkin(EFG)method,which constructs shape functions via moving least squares(MLS)approximation,represents a fundamental and widely studied meshless method in numerical computation.Although it achieve...The element-free Galerkin(EFG)method,which constructs shape functions via moving least squares(MLS)approximation,represents a fundamental and widely studied meshless method in numerical computation.Although it achieves high computational accuracy,the shape functions are more complex than those in the conventional finite element method(FEM),resulting in great computational requirements.Therefore,improving the computational efficiency of the EFG method represents an important research direction.This paper systematically reviews significant contributions fromdomestic and international scholars in advancing the EFGmethod.Including the improved element-free Galerkin(IEFG)method,various interpolating EFG methods,four distinct complex variable EFG methods,and a series of dimension splitting meshless methods.In the numerical examples,the effectiveness and efficiency of the three methods are validated by analyzing the solutions of the IEFG method for 3D steadystate anisotropic heat conduction,3D elastoplasticity,and large deformation problems,as well as the performance of two-dimensional splitting meshless methods in solving the 3D Helmholtz equation.展开更多
In this paper, we propose a dimensional splitting method for the three dimensional （3D） rotating Navier-Stokes equations. Assume that the domain is a channel bounded by two surfaces and is decomposed by a series of...In this paper, we propose a dimensional splitting method for the three dimensional （3D） rotating Navier-Stokes equations. Assume that the domain is a channel bounded by two surfaces and is decomposed by a series of surfaces i into several sub-domains, which are called the layers of the flow. Every interface i between two sub-domains shares the same geometry. After establishing a semi-geodesic coordinate （S-coordinate） system based on i, Navier-Stoke equations in this coordinate can be expressed as the sum of two operators, of which one is called the membrane operator defined on the tangent space on i, another one is called the bending operator taking value in the normal space on i. Then the derivatives of velocity with respect to the normal direction of the surface are approximated by the Euler central difference, and an approximate form of Navier-Stokes equations on the surface i is obtained, which is called the two-dimensional three-component （2D-3C） Navier-Stokes equations on a two dimensional manifold. Solving these equations by alternate iteration, an approximate solution to the original 3D Navier-Stokes equations is obtained. In addition, the proof of the existence of solutions to 2D-3C Navier-Stokes equations is provided, and some approximate methods for solving 2D-3C Navier-Stot4es equations are presented.展开更多
An empirical expression of cohesion （C） and friction angle （Ф） for layered rock was suggested. This expression was compared with a test result made by the former researchers. The constitutive relationship of a tr...An empirical expression of cohesion （C） and friction angle （Ф） for layered rock was suggested. This expression was compared with a test result made by the former researchers. The constitutive relationship of a transversely isotropic medium and Mohr-Coulomb criterion in which C and Ф vary with directions were employed, and a relative 3D elasto-plastic FEM code was developed, in which the important thing was to adopt a search-trial method to find the orientation angle （p） of shear failure plane （or weakest shear plane） with respect to the major principal stress as well as the corresponding C and Ф Taking an underground opening as the calculation object, the numerical analyses were carried out by using the FEM code for two cases of transversely isotropic rock and isotropic rock, respectively, and the computation results were compared. The results show that when the rock is a transversely isotropic one, the distributions of displacements, plastic zones and stress contours in the surrounding rock will be non-axisymmetric along the tunnel＇s vertical axis, which is very different from that of isotropic rock. The stability of the tunnel in transversely isotropic rock is relatively low.展开更多
In the paper. a visco-elasto plastic constitutive model and a method for determining model parameters for soft clay are presented. In this model total strain of soft clay is assumed to be divided into three parts: ins...In the paper. a visco-elasto plastic constitutive model and a method for determining model parameters for soft clay are presented. In this model total strain of soft clay is assumed to be divided into three parts: instantaneous elastic, visco-elastic and visco-plastic. The characteristics of instantaneous and visco-elastic deformation of soft clay are simulated by Merchant's model, the plastic is by a model with two yield surfaces. And related constitutive equation is conducted. A number of stress-controlled triaxial tests are performed to calculated the model parameters. The visco-elasto-plastic model is used for analysis of the displacement of an embankment on soft ground by use of three-dimensional finite element method. The predicted settlements agree well with the measured data. It is indicated that the viscous characteristics should be taken into account in deformation analysis for soft clay.展开更多
Exact solutions of three-dimensional(3D)crack problems are much less in number than those of two-dimensional ones,especially for multi-field coupling media exhibiting a certain kind of material anisotropy.An exact3Dth...Exact solutions of three-dimensional(3D)crack problems are much less in number than those of two-dimensional ones,especially for multi-field coupling media exhibiting a certain kind of material anisotropy.An exact3Dthermoelastic solution has been reported for a uniformly heated penny-shaped crack in an infinite magnetoelectric space,with impermeable electromagnetic conditions assumed on the crack faces.Exact 3Dsolutions for the penny-shaped crack subjected to uniform or point temperature load are further presented here when the crack faces are electrically and magnetically permeable.The solutions,obtained by the potential theory method,are exact in the sense that all field variables are explicitly derived and expressed in terms of elementary functions.Along with the previously reported solution,the limits or bounds of the stress intensity factor at the crack-tip for a practical crack can be identified.展开更多
In this paper,we study the following perturbation problem with Sobolev critical exponen t:{-Δu=(1+εK(x))u^2*-1+α/2*u^a-1v^3+εh(x)u^pP,x∈R^N,-Δu=(1+εQ(x))v^2*-1+β/2*u^B-1+εl(x)u^q,x∈R^N,u>0,v>0,x∈R^N w...In this paper,we study the following perturbation problem with Sobolev critical exponen t:{-Δu=(1+εK(x))u^2*-1+α/2*u^a-1v^3+εh(x)u^pP,x∈R^N,-Δu=(1+εQ(x))v^2*-1+β/2*u^B-1+εl(x)u^q,x∈R^N,u>0,v>0,x∈R^N where 0<p,q<1,α+β=2*:=2N/N-2,α,β≥3,4.Using a perturbation argument and a finite dimensional reduc tion met hod,we get the exis tence of positive solutions to problem(0.1)and the asymptotic property of the solutions.展开更多
In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner la...In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner layer.Next, three key parameters of the difference scheme are determined respectively by several simple flow models with known analytical solutions.Finally a special five points difference system is given and its application value is showed by a numerical example for the vertical velocity distribution in an Ekman's layer.展开更多
This paper detailedly discusses the locally one-dimensional numerical methods for ef- ficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equatio...This paper detailedly discusses the locally one-dimensional numerical methods for ef- ficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional diffusion equation. The second order finite difference scheme is used to discretize the space fractional derivative and the Crank-Nicolson procedure to the time derivative. We theoretically prove and numerically verify that the presented numerical methods are unconditionally stable and second order convergent in both space and time directions. In particular, for the Riesz fractional dif- fusion equation, the idea of reducing the splitting error is used to further improve the algorithm, and the unconditional stability and convergency are also strictly proved and numerically verified for the improved scheme.展开更多
A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the proba...A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the probability distribution of structural per- formance. From the relationship between the weighting function of orthogonal polynomial and probability density function （PDF） of random variable, the numerical integration formulas are derived for moment computation. Then, distribution of structural uncertainty response can be approximated by the CGC series with the calculated moments. Three engineering appli- cations for the distribution of, the maximum displacement of a ten-bar planer truss, natural frequency of an auto frame, and Von-Mises stress of a bending pipe, are employed to illustrate the computational efficiency and accuracy of the proposed methodology. As compared with plain Monte Carlo simulation （MCS）, the method can obtain the accurate distribution of structural performance. Especially at the tail region of cumulative distribution function （CDF）, results have shown the satisfy- ing estimators for small probabilities, say, Pc [104, 10-3]. That implies the method could be trusted for structural failure prob- ability prediction. As the computational efficiency is concerned, the procedure could save more than two orders of computational resources as compared with the direct numerical integration （NI） and MCS. Furthermore, realization of the procedure does not require computing the performance gradient or Hessian matrix with respect to random variables, or reshaping the finite element matrix as other stochastic finite element （SFE） codes. Therefore, it should be an efficient and reliable routine for uncertainty structural analysis.展开更多
Properties of fractional Brownian motions （fBms） have been investigated by researchers in different fields, e.g. statistics, hydrology, biology, finance, and public transportation, which has helped us better underst...Properties of fractional Brownian motions （fBms） have been investigated by researchers in different fields, e.g. statistics, hydrology, biology, finance, and public transportation, which has helped us better understand many complex time series observed in nature [1-4]. The Hurst exponent H （0 〈 H 〈 1） is the most important parameter characterizing any given time series F（t）, where t represents the time steps, and the fractal dimension D is determined via the relation D = 2 - H.展开更多
基金supported by the China Postdoctoral Science Foundation(No.2024M764171)the Postdoctoral Research Start-up Funds,China(No.AUGA5710027424)+1 种基金the National Natural Science Foundation of China(No.U2341237)the Development and construction funds for the School of Mechatronics Engineering of HIT,China(No.CBQQ8880103624)。
文摘Gas turbine rotors are complex dynamic systems with high-dimensional,discrete,and multi-source nonlinear coupling characteristics.Significant amounts of resources and time are spent during the process of solving dynamic characteristics.Therefore,it is necessary to design a lowdimensional model that can well reflect the dynamic characteristics of high-dimensional system.To build such a low-dimensional model,this study developed a dimensionality reduction method considering global order energy distribution by modifying the proper orthogonal decomposition theory.First,sensitivity analysis of key dimensionality reduction parameters to the energy distribution was conducted.Then a high-dimensional rotor-bearing system considering the nonlinear stiffness and oil film force was reduced,and the accuracy and the reusability of the low-dimensional model under different operating conditions were examined.Finally,the response results of a multi-disk rotor-bearing test bench were reduced using the proposed method,and spectrum results were then compared experimentally.Numerical and experimental results demonstrate that,during the dimensionality reduction process,the solution period of dynamic response results has the most significant influence on the accuracy of energy preservation.The transient signal in the transformation matrix mainly affects the high-order energy distribution of the rotor system.The larger the proportion of steady-state signals is,the closer the energy tends to accumulate towards lower orders.The low-dimensional rotor model accurately reflects the frequency response characteristics of the original high-dimensional system with an accuracy of up to 98%.The proposed dimensionality reduction method exhibits significant application potential in the dynamic analysis of highdimensional systems coupled with strong nonlinearities under variable operating conditions.
文摘We propose a finite dimensional method to compute the solution of nonlinear ill-posed problems approximately and show that under certain conditions, the convergence can be guaranteed. Moreover, we obtain the rate of convergence of our method provided that the true solution satisfies suitable smoothness condition. Finally, we present two examples from the parameter estimation problems of differential equations and illustrate the applicability of our method.
基金supported by the National Natural Science Foundation of China (Grants 11571223, 51404160)Shanxi Province Science Foundation for Youths (Grant 2014021025-1)
文摘This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.
基金supported by the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LY20A010021,LY19A010002,LY20G030025)the Natural Science Founda-tion of Ningbo City,China(Grant Nos.2021J147,2021J235).
文摘By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.
基金supported by the National Natural Science Foun-dation of China (10972228,11002150,and 91016025)the Basic Research Equipment Project of Chinese Academy of Sciences(YZ200930)
文摘Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Compressive re- sidual stress and dent profile are important factors to eval- uate the effectiveness of shot peening process. In this pa- per, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of pro- cessing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were de- duced by dimensional analysis method. Secondly, the in- fluence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Fur- thermore, related empirical formulas were given for each di- mensionless parameter based on the simulation results. Fi- nally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this pa- per for analyzing the influence of each individual parameter.
文摘The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forging load and deformed buIge profile during upset forging of blocks. Simulation of upsetforging of rectangular blocks under various friction condjtions was performed. Comparison of the computed results with experiments and FEM shows good agreement. It is shown that this techniquecan be used for 3D simulation of metal forming process.
基金supported by the National Natural Science Foundation of China(Grant Nos.52004169 and 11571223).
文摘In this paper,a fast element-free Galerkin(FEFG)method for three-dimensional(3D)elasticity problems is established.The FEFG method is a combination of the improved element-free Galerkin(IEFG)method and the dimension splitting method(DSM).By using the DSM,a 3D problem is converted to a series of 2D ones,and the IEFG method with a weighted orthogonal function as the basis function and the cubic spline function as the weight function is applied to simulate these 2D problems.The essential boundary conditions are treated by the penalty method.The splitting direction uses the finite difference method(FDM),which can combine these 2D problems into a discrete system.Finally,the system equation of the 3D elasticity problem is obtained.Some specific numerical problems are provided to illustrate the effectiveness and advantages of the FEFG method for 3D elasticity by comparing the results of the FEFG method with those of the IEFG method.The convergence and relative error norm of the FEFG method for elasticity are also studied.
文摘Cloud computing(CC)is an advanced technology that provides access to predictive resources and data sharing.The cloud environment represents the right type regarding cloud usage model ownership,size,and rights to access.It introduces the scope and nature of cloud computing.In recent times,all processes are fed into the system for which consumer data and cache size are required.One of the most security issues in the cloud environment is Distributed Denial of Ser-vice(DDoS)attacks,responsible for cloud server overloading.This proposed sys-tem ID3(Iterative Dichotomiser 3)Maximum Multifactor Dimensionality Posteriori Method(ID3-MMDP)is used to overcome the drawback and a rela-tively simple way to execute and for the detection of(DDoS)attack.First,the pro-posed ID3-MMDP method calls for the resources of the cloud platform and then implements the attack detection technology based on information entropy to detect DDoS attacks.Since because the entropy value can show the discrete or aggregated characteristics of the current data set,it can be used for the detection of abnormal dataflow,User-uploaded data,ID3-MMDP system checks and read risk measurement and processing,bug ratingfile size changes,orfile name changes and changes in the format design of the data size entropy value.Unique properties can be used whenever the program approaches any data error to detect abnormal data services.Finally,the experiment also verifies the DDoS attack detection capability algorithm.
基金supported in part by National Natural Science Foundation of China(Nos.52475572 and 52175522)Zhejiang Provincial Natural Science Foundation of China(No.LZ24E050003)。
文摘Three-dimensional(3D)conformal electronic skins(E-skins)have been developed for matching the irregularly surfaces.The 3D conformal E-skins manufactured by direct-curved-surface or dimensional converting methods both need curved-surface calibration.With increase of units’number and complication of mounting-surface morphology,curved-surface calibration becomes intricate.We report a universal cutting and distributing strategy for E-skins.The E-skin incorporates hierarchical and modular tactile sensors to match curvatures and sizes,thereby reducing mounting strain.This strategy enables curved-surface performance of 3D conformal E-skins to be characterized by flatsurface calibration results.An example is provided:Three-level sensors are utilized and calibrated on flat and curved surfaces.Performance variations reduce as sensor size decreases,and performance changes of level II and III sensing units are small after mounting.Their calibration results on curved surface are replaced by those on flat surface,proving low mounting strain facilitates 3D conformal E-skins to avoid complicated curved-surface calibration.
基金supported by the National Natural Science Foundation of China (Grant No. 12074329)Nanhu Scholars Program for Young Scholars of Xinyang Normal University。
文摘With a three-dimensional semiclassical ensemble method, we theoretically investigated the nonsequential double ionization of Ar driven by the spatially inhomogeneous few-cycle negatively chirped laser pulses. Our results show that the recollision time window can be precisely controlled within an isolated time interval of several hundred attoseconds, which is useful for understanding the subcycle correlated electron dynamics. More interestingly, the correlated electron momentum distribution (CEMD) exhibits a strong dependence on laser intensity. That is, at lower laser intensity, CEMD is located in the first quadrant. As the laser intensity increases,CEMD shifts almost completely to the second and fourth quadrants, and then gradually to the third quadrant.The underlying physics governing the CEMD's dependence on laser intensity is explained.
基金supported by the National Natural Science Foundation of China(Grant No.12271341).
文摘The element-free Galerkin(EFG)method,which constructs shape functions via moving least squares(MLS)approximation,represents a fundamental and widely studied meshless method in numerical computation.Although it achieves high computational accuracy,the shape functions are more complex than those in the conventional finite element method(FEM),resulting in great computational requirements.Therefore,improving the computational efficiency of the EFG method represents an important research direction.This paper systematically reviews significant contributions fromdomestic and international scholars in advancing the EFGmethod.Including the improved element-free Galerkin(IEFG)method,various interpolating EFG methods,four distinct complex variable EFG methods,and a series of dimension splitting meshless methods.In the numerical examples,the effectiveness and efficiency of the three methods are validated by analyzing the solutions of the IEFG method for 3D steadystate anisotropic heat conduction,3D elastoplasticity,and large deformation problems,as well as the performance of two-dimensional splitting meshless methods in solving the 3D Helmholtz equation.
基金Supported by the National High-Tech Research and Development Program of China (No. 2009AA01A135)the National Natural Science Foundation of China (Nos. 10971165, 11001216, 11071193, 10871156)the Foundation of AVIC Chengdu Aircraft Design and Research Institute
文摘In this paper, we propose a dimensional splitting method for the three dimensional （3D） rotating Navier-Stokes equations. Assume that the domain is a channel bounded by two surfaces and is decomposed by a series of surfaces i into several sub-domains, which are called the layers of the flow. Every interface i between two sub-domains shares the same geometry. After establishing a semi-geodesic coordinate （S-coordinate） system based on i, Navier-Stoke equations in this coordinate can be expressed as the sum of two operators, of which one is called the membrane operator defined on the tangent space on i, another one is called the bending operator taking value in the normal space on i. Then the derivatives of velocity with respect to the normal direction of the surface are approximated by the Euler central difference, and an approximate form of Navier-Stokes equations on the surface i is obtained, which is called the two-dimensional three-component （2D-3C） Navier-Stokes equations on a two dimensional manifold. Solving these equations by alternate iteration, an approximate solution to the original 3D Navier-Stokes equations is obtained. In addition, the proof of the existence of solutions to 2D-3C Navier-Stokes equations is provided, and some approximate methods for solving 2D-3C Navier-Stot4es equations are presented.
基金Project(2010CB732101) supported by the National Basic Research Program of China Project(51079145) supported by the National Natural Science Foundation of China
文摘An empirical expression of cohesion （C） and friction angle （Ф） for layered rock was suggested. This expression was compared with a test result made by the former researchers. The constitutive relationship of a transversely isotropic medium and Mohr-Coulomb criterion in which C and Ф vary with directions were employed, and a relative 3D elasto-plastic FEM code was developed, in which the important thing was to adopt a search-trial method to find the orientation angle （p） of shear failure plane （or weakest shear plane） with respect to the major principal stress as well as the corresponding C and Ф Taking an underground opening as the calculation object, the numerical analyses were carried out by using the FEM code for two cases of transversely isotropic rock and isotropic rock, respectively, and the computation results were compared. The results show that when the rock is a transversely isotropic one, the distributions of displacements, plastic zones and stress contours in the surrounding rock will be non-axisymmetric along the tunnel＇s vertical axis, which is very different from that of isotropic rock. The stability of the tunnel in transversely isotropic rock is relatively low.
基金This work was financially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of Ministry of Education.P.R.China
文摘In the paper. a visco-elasto plastic constitutive model and a method for determining model parameters for soft clay are presented. In this model total strain of soft clay is assumed to be divided into three parts: instantaneous elastic, visco-elastic and visco-plastic. The characteristics of instantaneous and visco-elastic deformation of soft clay are simulated by Merchant's model, the plastic is by a model with two yield surfaces. And related constitutive equation is conducted. A number of stress-controlled triaxial tests are performed to calculated the model parameters. The visco-elasto-plastic model is used for analysis of the displacement of an embankment on soft ground by use of three-dimensional finite element method. The predicted settlements agree well with the measured data. It is indicated that the viscous characteristics should be taken into account in deformation analysis for soft clay.
基金This work was supported by the National Natural Sci- ence Foundation of China （11321202） and the Specialized Research Fund for the Doctoral Program of Higher Educa- tion （2013010 1110120）.
文摘Exact solutions of three-dimensional(3D)crack problems are much less in number than those of two-dimensional ones,especially for multi-field coupling media exhibiting a certain kind of material anisotropy.An exact3Dthermoelastic solution has been reported for a uniformly heated penny-shaped crack in an infinite magnetoelectric space,with impermeable electromagnetic conditions assumed on the crack faces.Exact 3Dsolutions for the penny-shaped crack subjected to uniform or point temperature load are further presented here when the crack faces are electrically and magnetically permeable.The solutions,obtained by the potential theory method,are exact in the sense that all field variables are explicitly derived and expressed in terms of elementary functions.Along with the previously reported solution,the limits or bounds of the stress intensity factor at the crack-tip for a practical crack can be identified.
基金supported by the excellent doctorial dissertation cultivation grant(2018YBZZ067 and 2019YBZZ057)from Central China Normal University.
文摘In this paper,we study the following perturbation problem with Sobolev critical exponen t:{-Δu=(1+εK(x))u^2*-1+α/2*u^a-1v^3+εh(x)u^pP,x∈R^N,-Δu=(1+εQ(x))v^2*-1+β/2*u^B-1+εl(x)u^q,x∈R^N,u>0,v>0,x∈R^N where 0<p,q<1,α+β=2*:=2N/N-2,α,β≥3,4.Using a perturbation argument and a finite dimensional reduc tion met hod,we get the exis tence of positive solutions to problem(0.1)and the asymptotic property of the solutions.
文摘In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner layer.Next, three key parameters of the difference scheme are determined respectively by several simple flow models with known analytical solutions.Finally a special five points difference system is given and its application value is showed by a numerical example for the vertical velocity distribution in an Ekman's layer.
文摘This paper detailedly discusses the locally one-dimensional numerical methods for ef- ficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional diffusion equation. The second order finite difference scheme is used to discretize the space fractional derivative and the Crank-Nicolson procedure to the time derivative. We theoretically prove and numerically verify that the presented numerical methods are unconditionally stable and second order convergent in both space and time directions. In particular, for the Riesz fractional dif- fusion equation, the idea of reducing the splitting error is used to further improve the algorithm, and the unconditional stability and convergency are also strictly proved and numerically verified for the improved scheme.
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the University Network of Excellence in Nuclear Engineering (UNENE) through an Industrial Research Chair program,"Risk-Based Life Cycle Management of Engineering Systems",at the University of Waterloo
文摘A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the probability distribution of structural per- formance. From the relationship between the weighting function of orthogonal polynomial and probability density function （PDF） of random variable, the numerical integration formulas are derived for moment computation. Then, distribution of structural uncertainty response can be approximated by the CGC series with the calculated moments. Three engineering appli- cations for the distribution of, the maximum displacement of a ten-bar planer truss, natural frequency of an auto frame, and Von-Mises stress of a bending pipe, are employed to illustrate the computational efficiency and accuracy of the proposed methodology. As compared with plain Monte Carlo simulation （MCS）, the method can obtain the accurate distribution of structural performance. Especially at the tail region of cumulative distribution function （CDF）, results have shown the satisfy- ing estimators for small probabilities, say, Pc [104, 10-3]. That implies the method could be trusted for structural failure prob- ability prediction. As the computational efficiency is concerned, the procedure could save more than two orders of computational resources as compared with the direct numerical integration （NI） and MCS. Furthermore, realization of the procedure does not require computing the performance gradient or Hessian matrix with respect to random variables, or reshaping the finite element matrix as other stochastic finite element （SFE） codes. Therefore, it should be an efficient and reliable routine for uncertainty structural analysis.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.11173064,11233001,11233008,and U1531131)the Strategic Priority Research Program,the Emergence of Cosmological Structures of the Chinese Academy of Sciences(Grant No.XDB09000000)
文摘Properties of fractional Brownian motions （fBms） have been investigated by researchers in different fields, e.g. statistics, hydrology, biology, finance, and public transportation, which has helped us better understand many complex time series observed in nature [1-4]. The Hurst exponent H （0 〈 H 〈 1） is the most important parameter characterizing any given time series F（t）, where t represents the time steps, and the fractal dimension D is determined via the relation D = 2 - H.
