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New Lower Bounds to Wrap-around L2-discrepancy for U-type Designs with Three-level

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 513-520页

作者： zheng-hong WANG hong QIN School of Mathematics and Statistics South-Central University for NationalitiesWuhan 430074China Faculty of Mathematics and Statistics Central China Normal UniversityWuhan 430079China

The objective of this paper is to study the issue of uniformity on three-level U-type designs in terms of the wrap-around *** on the known formula,we present a new lower bound of wrap-around L2-discrepancy for three-level U-type designs and compare it with those existing ones through figures,numerical simulation and illustrative examples.

关键词： U-type designs wrap-around L2-discrepancy lower bound

Condensed form of complementarity formulation for discontinuous deformation analysis

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Science China(Technological Sciences) 2015年第9期58卷 1509-1519页

作者： LI XiaoKai zheng hong State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil MechanicsChinese Academy of Sciences Key Laboratory of Urban Security and Disaster Engineering Ministry of Education Beijing University of Technology

While the classical discontinuous deformation analysis(DDA) is applied to the analysis of a given block system, one must preset stiffness parameters for artificial springs to be fixed during the open-close iteration. To a great degree, success or failure in applying DDA to a practical problem is dependent on the spring stiffness parameters, which is believed to be the biggest obstacle to more extensive applications of DDA. In order to evade the introduction of the artificial springs, this study reformulates DDA as a mixed linear complementarity problem(MLCP) in the primal form. Then, from the fact that the block displacement vector of each block can be expressed in terms of the contact forces acting on the block, the condensed form of MLCP is derived, which is more efficient than the primal form. Some typical examples including those designed by the DDA inventor are reanalyzed, proving that the procedure is feasible.

关键词： discontinuous deformation analysis contact and impact complementarity theory non-smooth analysis open-close iteration

Two-dimensional numerical manifold method with multilayer covers

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Science China(Technological Sciences) 2016年第4期59卷 515-530页

作者： LIU ZhiJun zheng hong State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil Mechanics Chinese Academy of Sciences Key Laboratory of Urban Security and Disaster Engineering Ministry of Education Beijing University of Technology

In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are *** the presence of steep gradients or strong singularities,in principle,the locally-defined special functions can be added into the NMM space by means of the partition of unity,but they are not available to those complex problems with heterogeneity or nonlinearity,necessitating local refinement on uniform *** is believed to be one of the most important open issues in *** this study multilayer covers are proposed to solve this *** addition to the first layer cover which is the global cover and covers the whole problem domain,the second and higher layer covers with smaller elements,called local covers,are used to cover those local regions with steep gradients or strong *** global cover and the local covers have their own partition of unity,and they all participate in the approximation to the *** advantageous over the existing procedures,the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big *** no limitation to cover layers,meanwhile,the creation of an even error distribution over the whole problem domain is significantly *** typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.

关键词： numerical manifold method finite element method covers hanging nodes structured local refinement short cracks

Coupled thermoelastic theory and associated variational principles based on decomposition of internal energy

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Acta Mechanica Sinica 2020年第1期36卷 107-115页

作者： Jia-hong zheng zheng Zhong Cong-Ying Jiang School of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai200092China School of Science Harbin Institute of Technology(Shenzhen)Shenzhen518055GuangdongChina

A new framework of coupled thermoelasticity is constructed in this paper based on a decomposition of internal energy into free internal energy and dissipative *** equations(*** and gradient equations,constitutive equations including evolving laws)along with proper boundary conditions are all included in this framework,from which two novel dual-complementary variational principles with explicit functionals are *** the conventional thermoelastic theory,the proposed variational principles for thermoelasticity are established without the approximate assumption of small temperature *** verify the usefulness of the proposed variational principles in simulating coupled thermoelastic problems,a coupled thermoelastic example is numerically implemented.

关键词： Coupled thermoelasticity Thermodynamics Dissipation Variational principle

MRT-LBM-based numerical simulation of seepage flow through fractal fracture networks

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Science China(Technological Sciences) 2013年第12期56卷 3115-3122页

作者： FAN Huo zheng hong State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock & Soil Mechanics Chinese Academy of Sciences Institute of Mountain Hazards and Environment Chinese Academy of Sciences University of Chinese Academy of Sciences

The study on seepage flow passing through single fractures is essential and critical for understanding of the law of seepage flow passing through fracture networks and the coupling mechanisms of seepage field and stress field in rock *** using the fractal interpolation to reconstruct a natural coarse fracture,as well as taking into account the microstructure of the fracture,the numerical simulation of seepage flow passing through the coarse fractures with two distinct vertical scaling factors is conducted based on the MRT-LBM model of the lattice Boltzmann ***,after obtaining the length of the preferential flow pathway,the permeability of the two kinds of fractures is estimated *** view of difficulties in locating the preferential flow pathway of natural fracture networks,by numerical tests a transect permeability weighted algorithm for estimating the fracture network permeability is *** algorithm is not specific to one or more particular preferential flow pathways,but considers the contribution of each section to hinder the fluid passing through the *** order to apply the new algorithm,by capturing the structure of fracture networks based on the image-processing technique,the numerical simulations of seepage flow passing through two groups of natural fracture networks is carried out,the permeability is forecasted and the partial flows are reproduced for both *** is found that the preferential flow pathway emerges at the beginning of evolution,then is strengthened subsequently,and finally reaches a steady ***,by using the proposed method some details on local flow can be clearly observed such as backflows and vortices at local branches can exist simultaneously and so forth,suggesting the validness of the proposed method for multiscale simulations of seepage flow.

关键词： MRT-LBM fractal interpolation fracture networks seepage flow simulation microcosmic mechanism

Effects of information transmission delay and channel blocking on synchronization in scale-free Hodgkin-Huxley neuronal networks

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Acta Mechanica Sinica 2011年第6期27卷 1052-1058页

作者： Qing-Yun Wang Yan-hong zheng Department of Dynamics and Control Beihang University 100191 Beijing China School of Mathematics and Computer Science Fujian Normal University 350007 Fuzhou China

In this paper,we investigate the evolution of spatiotemporal patterns and synchronization transitions in dependence on the information transmission delay and ion channel blocking in scale-free neuronal *** the underlying model of neuronal dynamics,we use the Hodgkin-Huxley equations incorporating channel blocking and intrinsic *** is shown that delays play a significant yet subtle role in shaping the dynamics of neuronal *** particular,regions of irregular and regular propagating excitatory fronts related to the synchronization transitions appear intermittently as the delay ***,the fraction of working sodium and potassium ion channels can also have a significant impact on the spatiotemporal dynamics of neuronal *** the fraction of blocked sodium channels increases,the frequency of excitatory events decreases,which in turn manifests as an increase in the neuronal synchrony that,however,is dysfunctional due to the virtual absence of large-amplitude ***,we also show that larger coupling strengths improve synchronization irrespective of the information transmission delay and channel *** presented results are also robust against the variation of the network size,thus providing insights that could facilitate understanding of the joint impact of ion channel blocking and information transmission delay on the spatiotemporal dynamics of neuronal networks.

关键词： Scale-free neuronal networks - Information transmission delay Ion channel blocking Synchronization

A partition-of-unity based three-node triangular element with continuous nodal stress using radial-polynomial basis functions

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Science China(Technological Sciences) 2017年第10期60卷 1518-1536页

作者： YANG YongTao zheng hong XU DongDong State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil MechanicsChinese Academy of Sciences Key Laboratory of Urban Security and Disaster Engineering Ministry of EducationBeijing University of Technology Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources Yangtze River Scientific Research Institute

A partition-of-unity （PU） based ＂FE-Meshfree＂ three-node triangular element （Trig3-RPIM） was recently developed for linear elastic problems. This Trig3-RPIM element employs hybrid shape functions that combine the shape functions of three-node triangular element （Trig3） and radial-polynomial basis functions for the purpose of synergizing the merits of both finite element method and meshfree method. Although Trig3-RPIM element is capable of obtaining higher accuracy and convergence rate than the Trig3 element and four-node iso-parametric quadrilateral element without adding extra nodes or degrees of freedom （DOFs）, the nodal stress field through Trig3-RP1M element is not continuous and extra stress smooth operations are still needed in the post processing stage. To further improve the property of Trig3-RPIM element, a new PU-based triangular element with continuous nodal stress, called Trig3-RPIMcns, is developed. Numerical examples including several linear, free vibration and forced vibration test problems, have confirmed the correctness and feasibility of the proposed Trig3-RPIMcns element.

关键词： partition of unity FE-Meshfree element Trig3-RPlMcns mesh distortion radial-polynomial basis functions

Numerical study of soil-rock mixture:Generation of random aggregate structure

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Science China(Technological Sciences) 2018年第3期61卷 359-369页

作者： CHEN Li YANG YongTao zheng hong State Key Laboratory of Geotechnical Engineering Institute of Rock and Soil Mechanics Chinese Academy of Sciences Key Laboratory of Urban Security and Disaster Engineering Ministry of Education Beijing University of Technology

The soil-rock mixture(SRM) is highly heterogeneous. Before carrying out numerical analysis,a structure model should be generated. A reliable way to obtain such structure is by generating random aggregate structure based on random sequential addition(RSA). The classical RSA is neither efficient nor robust since valid positions to place new inclusions are formulated by trial, which involves repetitive overlapping tests. In this paper, the algorithm of Entrance block between block A and B(EAB)is synergized with background mesh to redesign RSA so that permissible positions to place new inclusions can be predicted,resulting in dramatic improvement in efficiency and robustness.

关键词： soil-rock mixture(SRM) random aggregate structure(RAS) random sequential addition(RSA) EAB algorithm background mesh

Numerical manifold method for steady-state nonlinear heat conduction using Kirchhoff transformation

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Science China(Technological Sciences) 2024年第4期67卷 992-1006页

作者： ZHANG LiMei KONG Heng zheng hong Key Laboratory of Urban Security and Disaster Engineering Ministry of EducationBeijing University of TechnologyBeijing 100124China Beijing Municipal Construction Co. Ltd.Beijing 100048China

The numerical manifold method(NMM)introduces the mathematical and physical cover to solve both continuum and discontinuum problems in a unified *** this study,the NMM for solving steady-state nonlinear heat conduction problems is presented,and heat conduction problems consider both convection and radiation boundary ***,the nonlinear governing equation of thermal conductivity,which is dependent on temperature,is transformed into the Laplace equation by introducing the Kirchhoff *** transformation reserves linearity of both the Dirichlet and the Neumann boundary conditions,but the Robin and radiation boundary conditions remain ***,the NMM is employed to solve the Laplace equation using a simple iteration procedure because the nonlinearity focuses on parts of the problem domain ***,the temperature field is retrieved through the inverse Kirchhoff *** examples are analyzed,demonstrating the advantages of the Kirchhoff transformation over the direct solution of nonlinear equations using the NewtonRaphson *** study provides a new method for calculating nonlinear heat conduction.

关键词： numerical manifold method nonlinear heat conduction temperature-dependent thermal conductivity Kirchhoff transformation convection and radiation boundary conditions