The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic...The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.展开更多
The non-ordinary state-based peridynamic(NOSB PD)model has the capability of incorporating existing constitutive relationships in the classical continuum mechanics.In the present work,we first develop an NOSB PD model...The non-ordinary state-based peridynamic(NOSB PD)model has the capability of incorporating existing constitutive relationships in the classical continuum mechanics.In the present work,we first develop an NOSB PD model corresponding to the Johnson–Holmquist II(JH-2)constitutive damage model,which can describe the severe damage of concrete under intense impact compression.Besides,the numerical oscillation problem of the NOSB PD caused by zero-energy mode is analyzed and hence a bond-associated non-ordinary state-based peridynamic(BA-NOSB PD)model is adopted to remove the oscillation.Then,the elastic deformation of a three-dimensional bar is analyzed to verify the capability of BA-NOSB PD in eliminating the numerical oscillation.Furthermore,concrete spalling caused by the interaction of incident compression wave and reflected tension wave is simulated.The dynamic tensile fracture process of concrete multiple spalling is accurately reproduced for several examples according to the spalling number and spalling thickness analysis,illustrating the approach can well simulate and analyze the concrete spalling discontinuities.展开更多
Strain hardening and strain rate play an important role in dynamic deformation and failure problems such as high-velocity impact cases.In this paper,a non-ordinary state-based peridynamic model for failure and damage ...Strain hardening and strain rate play an important role in dynamic deformation and failure problems such as high-velocity impact cases.In this paper,a non-ordinary state-based peridynamic model for failure and damage of concrete materials subjected to impacting condition is proposed,taking the advantages of both damage model and nonlocal peridynamic method.The Holmquist-Johnson-Cook(HJC)model describing the mechanical character and damage of concrete materials under large strain,high strain rate and high hydrostatic pressure was reformulated in the framework of non-ordinary statebased peridynamic theory,and the corresponding numerical approach was developed.The proposed model and numerical approach were validated through simulating typical impacting examples and comparing the results with available experimental observations and results in literature.展开更多
In this study,a new state-based peridynamic formulation is developed for functionally graded Euler-Bernoulli beams.The equation of motion is developed by using Lagrange’s equation and Taylor series.Both axial and tra...In this study,a new state-based peridynamic formulation is developed for functionally graded Euler-Bernoulli beams.The equation of motion is developed by using Lagrange’s equation and Taylor series.Both axial and transverse displacements are taken into account as degrees of freedom.Four different boundary conditions are considered including pinned support-roller support,pinned support-pinned support,clamped-clamped and clamped-free.Peridynamic results are compared against finite element analysis results for transverse and axial deformations and a very good agreement is observed for all different types of boundary conditions.展开更多
In process industries,the characteristics of industrial activities focus on the integrality and continuity of production process,which can contribute to excavating the appropriate features for industrial anomaly detec...In process industries,the characteristics of industrial activities focus on the integrality and continuity of production process,which can contribute to excavating the appropriate features for industrial anomaly detection.From this perspective,this paper proposes a novel state-based control feature extraction approach,which regards the finite control operations as different states.Furthermore,the procedure of state transition can adequately express the change of successive control operations,and the statistical information between different states can be used to calculate the feature values.Additionally,OCSVM(One Class Support Vector Machine)and BPNN(BP Neural Network),which are optimized by PSO(Particle Swarm Optimization)and GA(Genetic Algorithm)respectively,are introduced as alternative detection engines to match with our feature extraction approach.All experimental results clearly show that the proposed feature extraction approach can effectively coordinate with the optimized classification algorithms,and the optimized GA-BPNN classifier is suggested as a more applicable detection engine by comparing its average detection accuracies with the ones of PSO-OCSVM classifier.展开更多
We solve the local uniaxial tension of an infinite rod in the framework of non-ordinary state-based peridynamics.The singular solutions of stress and displacement are acquired.When the influencing range of the window ...We solve the local uniaxial tension of an infinite rod in the framework of non-ordinary state-based peridynamics.The singular solutions of stress and displacement are acquired.When the influencing range of the window function approaches zero,these two solutions will return to the solutions of the classical elasticity.The analysis shows that the singularities of the solutions stem from such a feature of the window function that must be represented by a rapidly decreasing function in physics.Contrary to the classical elasticity,the stress solution of peridynamics is smoother than the displacement solution.In addition,a criterion used to select the window function is proposed in this paper.展开更多
This study demonstrates a homogenization approach via a modified state-based peridynamic(PD)method to predict the effective elastic properties of composite materials with periodic microstructure.The procedure of model...This study demonstrates a homogenization approach via a modified state-based peridynamic(PD)method to predict the effective elastic properties of composite materials with periodic microstructure.The procedure of modeling the PD unit cell(UC)of continuous fiber-reinforced composite is presented.Periodic boundary conditions are derived and implemented through the Lagrange multiplier method.A matrix-dominated approach for modeling the interphase properties between dissimilar materials is proposed.The periodicity and continuity assumptions are employed to determine the stress and strain fields,as well as the effective elastic properties.The PD-UCs of square and hexagonal packs as well as the 0/90 laminate microstructure are modeled and compared with the analytical,numerical and experimental results from the literature.Good agreement of predicted effective properties can be observed.Unlike other PD homogenization approaches,the effective material properties can be directly and individually obtained from simple loading conditions.展开更多
We establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models.We consider state-based peridynamic models where the force at a material point is due to bo...We establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models.We consider state-based peridynamic models where the force at a material point is due to both the strain between two points and the change in volume inside the domain of the nonlocal interaction.The pairwise interactions between points are mediated by a bond potential of multi-well type while multi-point interactions are associated with the volume change mediated by a hydrostatic strain potential.The hydrostatic potential can either be a quadratic function,delivering a linear force–strain relation,or a multi-well type that can be associated with the material degradation and cavitation.We first show the well-posedness of the peridynamic formulation and that peridynamic evolutions exist in the Sobolev space H2.We show that the finite element approximations converge to the H2 solutions uniformly as measured in the mean square norm.For linear continuous fi nite elements,the convergence rate is shown to be Ct Δt+Csh2/ε2,where𝜖is the size of the horizon,his the mesh size,and Δt is the size of the time step.The constants Ct and Cs are independent of Δt and h and may depend on ε through the norm of the exact solution.We demonstrate the stability of the semi-discrete approximation.The stability of the fully discrete approximation is shown for the linearized peridynamic force.We present numerical simulations with the dynamic crack propagation that support the theoretical convergence rate.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
This study summarizes the examination data of registration labels for ordinary cosmetics in Beijing from May 2021 to April 2024.It analyzes and categorizes the issues identified during label evaluations,explores the u...This study summarizes the examination data of registration labels for ordinary cosmetics in Beijing from May 2021 to April 2024.It analyzes and categorizes the issues identified during label evaluations,explores the underlying causes,and proposes regulatory countermeasures and recommendations for registrants,regulatory authorities,and social organizations.The objective is to offer practical insights and regulatory guidance to support the enhancement of cosmetic registration and regulatory standards.展开更多
Petrography and mineral chemistry of 24 ordinary chondrites from the Grove Mountains, Antarctica, have been studied in order to identify their chemical-petrographic types. These samples were selected from a total of 4...Petrography and mineral chemistry of 24 ordinary chondrites from the Grove Mountains, Antarctica, have been studied in order to identify their chemical-petrographic types. These samples were selected from a total of 4448 Grove Mountains (GRV) meteorites collected during the 19th Chinese Antarctic Research Expedition so as to make an estimation of the large GRV meteorite collection. The chemical-petrographic types of these meteorites are presented below: 1 H3,2 H4, 4 H5, 2 H6, 1 L4, 7 L5, 5 L6, 1 LL4 and 1 LL6. The new data weaken the previous report that unequilibrated ordinary chondrites are unusually abundant in the Grove Mountains region. However, this work confirms significant differences in distribution patterns of chemical-petrographic types between the Grove Mountains and other regions in Antarctica. Many of these meteorites show significant terrestrial weathering, probably due to a high abundance ratio of meteorites found in moraines to those on blue ice. Nine meteorites experienced severe shock metamorphism, as evidenced by undulose extinction and intense fracturing of silicates and presence of shock-induced melt veins and pockets. These heavily shocked meteorites provided us with natural samples for the study of high-pressure polymorphs of minerals.展开更多
Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D G...Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.展开更多
Accurate mapping of soil salinity and recognition of its influencing factors are essential for sustainable crop production and soil health. Although the influencing factors have been used to improve the mapping accura...Accurate mapping of soil salinity and recognition of its influencing factors are essential for sustainable crop production and soil health. Although the influencing factors have been used to improve the mapping accuracy of soil salinity, few studies have considered both aspects of spatial variation caused by the influencing factors and spatial autocorrelations for mapping. The objective of this study was to demonstrate that the ordinary kriging combined with back-propagation network(OK_BP), considering the two aspects of spatial variation, which can benefit the improvement of the mapping accuracy of soil salinity. To test the effectiveness of this approach, 70 sites were sampled at two depths(0–30 and 30–50 cm) in Ningxia Hui Autonomous Region, China. Ordinary kriging(OK), back-propagation network(BP) and regression kriging(RK) were used in comparison analysis; the root mean square error(RMSE), relative improvement(RI) and the decrease in estimation imprecision(DIP) were used to judge the mapping quality. Results showed that OK_BP avoided the both underestimation and overestimation of the higher and lower values of interpolation surfaces. OK_BP revealed more details of the spatial variation responding to influencing factors, and provided more flexibility for incorporating various correlated factors in the mapping. Moreover, OK_BP obtained better results with respect to the reference methods(i.e., OK, BP, and RK) in terms of the lowest RMSE, the highest RI and DIP. Thus, it is concluded that OK_BP is an effective method for mapping soil salinity with a high accuracy.展开更多
The refraction of rays in the Savart polariscope is different from the isotropic medium. We have analysed and discussed the refraction of rays in the Savart polariscope on the basis of the Snell law. The refraction fo...The refraction of rays in the Savart polariscope is different from the isotropic medium. We have analysed and discussed the refraction of rays in the Savart polariscope on the basis of the Snell law. The refraction formulae of the extraordinary rays and ordinary rays were derived. Results obtained may provide theoretical and practical guide lines for studying, developing and engineering of polarization interference imaging spectrometer.展开更多
The mining industry often uses shotcrete for ground stabilization. However, cracking within shotcrete is commonly observed, which delays production schedules and increases maintenance costs. A possible crack reduction...The mining industry often uses shotcrete for ground stabilization. However, cracking within shotcrete is commonly observed, which delays production schedules and increases maintenance costs. A possible crack reduction method is using expansive shotcrete mixture consisting of calcium sulfoaluminate cement(CSA), ordinary Portland cement(OPC), and calcium sulfate(CS) to reduce shrinkage. Furthermore, fibers can be added to the mixture to restrain expansion and impede cracking. The objective of this paper is to study the effects of nylon fiber, glass fiber, and steel fiber on an expansive shotcrete mixture that can better resist cracking. In this study, parameters such as density, water absorption, volume of permeable voids, unconfined compressive strength(UCS), splitting tensile strength(STS), and volume change of fiber-added expansive mixtures were determined at different time periods(i.e. the strengths on the 28 th day, and the volume changes on the 1 st, 7 th, 14 th, 21 st, and 28 th days). The results show that addition of fibers can improve mixture durability, in the form of decreased water absorption and reduced permeable pore space content. Moreover, the expansion of the CSA-OPC-CS mixture was restrained up to50% by glass fiber, up to 43% by nylon fiber, and up to 28% by steel fiber. The results show that the STS was improved by 57% with glass fiber addition, 43% with steel fiber addition, and 38% with nylon fiber addition. The UCS was also increased by 31% after steel fiber addition, 26% after nylon fiber addition, and16% after glass fiber addition. These results suggest that fiber additions to the expansive shotcrete mixtures can improve durability and strengths while controlling expansion.展开更多
The nanometer and ordinary anatase titanium dioxide(TiO_2) powders were adopted as the sonocatalysts for the degradation of methyl orange used as a model compound for the first time. It was found that the sonocatalyti...The nanometer and ordinary anatase titanium dioxide(TiO_2) powders were adopted as the sonocatalysts for the degradation of methyl orange used as a model compound for the first time. It was found that the sonocatalytic degradation effect of methyl orange in the presence of TiO_2 powder were much better than that without TiO_2, but the sonocatalytic activity of the nanometer anatase TiO_2 particle was obviously higher than that of ordinary anatase TiO_2 particle. Although there are many factors influencing sonocatalytic degradation of methyl orange, the experimental results showed that the best degradation ratio of methyl orange could be obtained when the experimental conditions were: initial concentration 15 mg/L, nanometer anatase TiO_2 adding amount 750 mg/L, ultrasonic frequency 40 kHz, output power 50 W, pH = 3.0 and temperature 40℃ within 150 min. In addition, the catalytic activity of reused nanometer anatase TiO_2 catalyst was also studied and found to decline gradually comparing with initial nanometer anatase TiO_2 catalyst. All experiments indicated that the method of the sonocatalytic degradation of organic pollutants in the presence of TiO_2 powder was an advisable choice for non- or low-transparent organic wastewaters.展开更多
In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference me...In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.展开更多
China is the largest producer and user of ordinary Portland cement(OPC),and the rapid growth of infrastructure development demands more sustainable building materials for concrete structures.Alkali-activated materials...China is the largest producer and user of ordinary Portland cement(OPC),and the rapid growth of infrastructure development demands more sustainable building materials for concrete structures.Alkali-activated materials(AAMs)are a new type of energy-saving and environmentally friendly building material with a wide range of potential applications.This paper compares the durability of AAMs and 0 PC-based materials un der sulfate attack,acid corrosion,carb on ation,and chloride penetratio n.Different AAMs have shown distinct durability properties due to different compositions being formed when different raw materials are used.According to the calcium(Ca)concentration of the raw materials,this paper interprets the deterioration mechanisms of three categories of AAMs:calcium-free,low-calcium,and calcium-rich.Conflicts found in the most recent research are highlighted,as they raise concerns regarding the consistenee and long-term properties of AAMs.Nevertheless,AAMs show better durability performances than OPC-based materials in general.展开更多
基金supported by the National Key R&D Program of China(2020YFA0710500).
文摘The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.
基金supported by the Fundamental Research Funds for the Central Universities(Grant B200202231)the National Natural Science Foundation of China(Grants 11932006,11672101,U1934206,and 12002118)+1 种基金the National Key Research&Development Plan of China(Grants 2018 YFC0406703 and 2017YFC1502603)the China Postdoctoral Science Foundation(Grant 2019M651667).
文摘The non-ordinary state-based peridynamic(NOSB PD)model has the capability of incorporating existing constitutive relationships in the classical continuum mechanics.In the present work,we first develop an NOSB PD model corresponding to the Johnson–Holmquist II(JH-2)constitutive damage model,which can describe the severe damage of concrete under intense impact compression.Besides,the numerical oscillation problem of the NOSB PD caused by zero-energy mode is analyzed and hence a bond-associated non-ordinary state-based peridynamic(BA-NOSB PD)model is adopted to remove the oscillation.Then,the elastic deformation of a three-dimensional bar is analyzed to verify the capability of BA-NOSB PD in eliminating the numerical oscillation.Furthermore,concrete spalling caused by the interaction of incident compression wave and reflected tension wave is simulated.The dynamic tensile fracture process of concrete multiple spalling is accurately reproduced for several examples according to the spalling number and spalling thickness analysis,illustrating the approach can well simulate and analyze the concrete spalling discontinuities.
基金The authors acknowledge the support from the National Key R&D Program of China(No.2018YFC0406703)National Natural Science Foundation of China(No.51679077)the Fundamental Research Funds for the Central Universities in China(No.2015B18314,2017B13014).
文摘Strain hardening and strain rate play an important role in dynamic deformation and failure problems such as high-velocity impact cases.In this paper,a non-ordinary state-based peridynamic model for failure and damage of concrete materials subjected to impacting condition is proposed,taking the advantages of both damage model and nonlocal peridynamic method.The Holmquist-Johnson-Cook(HJC)model describing the mechanical character and damage of concrete materials under large strain,high strain rate and high hydrostatic pressure was reformulated in the framework of non-ordinary statebased peridynamic theory,and the corresponding numerical approach was developed.The proposed model and numerical approach were validated through simulating typical impacting examples and comparing the results with available experimental observations and results in literature.
文摘In this study,a new state-based peridynamic formulation is developed for functionally graded Euler-Bernoulli beams.The equation of motion is developed by using Lagrange’s equation and Taylor series.Both axial and transverse displacements are taken into account as degrees of freedom.Four different boundary conditions are considered including pinned support-roller support,pinned support-pinned support,clamped-clamped and clamped-free.Peridynamic results are compared against finite element analysis results for transverse and axial deformations and a very good agreement is observed for all different types of boundary conditions.
基金This work is supported by the Program of Hainan Association for Science and Technology Plans to Youth R&D Innovation(Grant No.QCXM201910)the Natural Science Foundation of Liaoning Province(Grant No.2019-MS-149),the Social Science Planning Foundation of Liaoning Province(Grant No.L18AGL007)+1 种基金the National Natural Science Foundation of China(Grant Nos.61802092,51704138 and 61501447)the Scientific Research Setup Fund of Hainan University(Grant No.KYQD(ZR)1837).
文摘In process industries,the characteristics of industrial activities focus on the integrality and continuity of production process,which can contribute to excavating the appropriate features for industrial anomaly detection.From this perspective,this paper proposes a novel state-based control feature extraction approach,which regards the finite control operations as different states.Furthermore,the procedure of state transition can adequately express the change of successive control operations,and the statistical information between different states can be used to calculate the feature values.Additionally,OCSVM(One Class Support Vector Machine)and BPNN(BP Neural Network),which are optimized by PSO(Particle Swarm Optimization)and GA(Genetic Algorithm)respectively,are introduced as alternative detection engines to match with our feature extraction approach.All experimental results clearly show that the proposed feature extraction approach can effectively coordinate with the optimized classification algorithms,and the optimized GA-BPNN classifier is suggested as a more applicable detection engine by comparing its average detection accuracies with the ones of PSO-OCSVM classifier.
基金the National Natural Science Foundation of China (11672129)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics, MCMS-I-0218G01)
文摘We solve the local uniaxial tension of an infinite rod in the framework of non-ordinary state-based peridynamics.The singular solutions of stress and displacement are acquired.When the influencing range of the window function approaches zero,these two solutions will return to the solutions of the classical elasticity.The analysis shows that the singularities of the solutions stem from such a feature of the window function that must be represented by a rapidly decreasing function in physics.Contrary to the classical elasticity,the stress solution of peridynamics is smoother than the displacement solution.In addition,a criterion used to select the window function is proposed in this paper.
基金This work is supported by the National Natural Science Foundation of China under Grant Nos.1190219711972234 and is sponsored by Shanghai Sailing Program under Contract No.19YF1421700.
文摘This study demonstrates a homogenization approach via a modified state-based peridynamic(PD)method to predict the effective elastic properties of composite materials with periodic microstructure.The procedure of modeling the PD unit cell(UC)of continuous fiber-reinforced composite is presented.Periodic boundary conditions are derived and implemented through the Lagrange multiplier method.A matrix-dominated approach for modeling the interphase properties between dissimilar materials is proposed.The periodicity and continuity assumptions are employed to determine the stress and strain fields,as well as the effective elastic properties.The PD-UCs of square and hexagonal packs as well as the 0/90 laminate microstructure are modeled and compared with the analytical,numerical and experimental results from the literature.Good agreement of predicted effective properties can be observed.Unlike other PD homogenization approaches,the effective material properties can be directly and individually obtained from simple loading conditions.
文摘We establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models.We consider state-based peridynamic models where the force at a material point is due to both the strain between two points and the change in volume inside the domain of the nonlocal interaction.The pairwise interactions between points are mediated by a bond potential of multi-well type while multi-point interactions are associated with the volume change mediated by a hydrostatic strain potential.The hydrostatic potential can either be a quadratic function,delivering a linear force–strain relation,or a multi-well type that can be associated with the material degradation and cavitation.We first show the well-posedness of the peridynamic formulation and that peridynamic evolutions exist in the Sobolev space H2.We show that the finite element approximations converge to the H2 solutions uniformly as measured in the mean square norm.For linear continuous fi nite elements,the convergence rate is shown to be Ct Δt+Csh2/ε2,where𝜖is the size of the horizon,his the mesh size,and Δt is the size of the time step.The constants Ct and Cs are independent of Δt and h and may depend on ε through the norm of the exact solution.We demonstrate the stability of the semi-discrete approximation.The stability of the fully discrete approximation is shown for the linearized peridynamic force.We present numerical simulations with the dynamic crack propagation that support the theoretical convergence rate.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
文摘This study summarizes the examination data of registration labels for ordinary cosmetics in Beijing from May 2021 to April 2024.It analyzes and categorizes the issues identified during label evaluations,explores the underlying causes,and proposes regulatory countermeasures and recommendations for registrants,regulatory authorities,and social organizations.The objective is to offer practical insights and regulatory guidance to support the enhancement of cosmetic registration and regulatory standards.
文摘Petrography and mineral chemistry of 24 ordinary chondrites from the Grove Mountains, Antarctica, have been studied in order to identify their chemical-petrographic types. These samples were selected from a total of 4448 Grove Mountains (GRV) meteorites collected during the 19th Chinese Antarctic Research Expedition so as to make an estimation of the large GRV meteorite collection. The chemical-petrographic types of these meteorites are presented below: 1 H3,2 H4, 4 H5, 2 H6, 1 L4, 7 L5, 5 L6, 1 LL4 and 1 LL6. The new data weaken the previous report that unequilibrated ordinary chondrites are unusually abundant in the Grove Mountains region. However, this work confirms significant differences in distribution patterns of chemical-petrographic types between the Grove Mountains and other regions in Antarctica. Many of these meteorites show significant terrestrial weathering, probably due to a high abundance ratio of meteorites found in moraines to those on blue ice. Nine meteorites experienced severe shock metamorphism, as evidenced by undulose extinction and intense fracturing of silicates and presence of shock-induced melt veins and pockets. These heavily shocked meteorites provided us with natural samples for the study of high-pressure polymorphs of minerals.
基金The paper was financially supported by the National Natural Science Foundation of China (No. 19802008)Excellent Doctoral Dissertation Grant of the Ministry of Education of China (No. 199927)
文摘Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.
基金Under the auspices of the National Natural Science Foundation of China(No.41571217)the National Key Research and Development Program of China(No.2016YFD0300801)
文摘Accurate mapping of soil salinity and recognition of its influencing factors are essential for sustainable crop production and soil health. Although the influencing factors have been used to improve the mapping accuracy of soil salinity, few studies have considered both aspects of spatial variation caused by the influencing factors and spatial autocorrelations for mapping. The objective of this study was to demonstrate that the ordinary kriging combined with back-propagation network(OK_BP), considering the two aspects of spatial variation, which can benefit the improvement of the mapping accuracy of soil salinity. To test the effectiveness of this approach, 70 sites were sampled at two depths(0–30 and 30–50 cm) in Ningxia Hui Autonomous Region, China. Ordinary kriging(OK), back-propagation network(BP) and regression kriging(RK) were used in comparison analysis; the root mean square error(RMSE), relative improvement(RI) and the decrease in estimation imprecision(DIP) were used to judge the mapping quality. Results showed that OK_BP avoided the both underestimation and overestimation of the higher and lower values of interpolation surfaces. OK_BP revealed more details of the spatial variation responding to influencing factors, and provided more flexibility for incorporating various correlated factors in the mapping. Moreover, OK_BP obtained better results with respect to the reference methods(i.e., OK, BP, and RK) in terms of the lowest RMSE, the highest RI and DIP. Thus, it is concluded that OK_BP is an effective method for mapping soil salinity with a high accuracy.
基金supported by the State Key Program of National Natural Science of China (Grant No 40537031)the National Natural Science Foundation of China (Grant Nos 40375010 and 60278019)+2 种基金the Science and Technology Plan Foundation of Shaanxi Province of China (Contract No 2005K04-G18)the special research project of Shaanxi Provincial Educational Department of China (Grant Nos 07JK261 and 05JK197)the research project of Xi’an Polytechnic University of China (Grant No 2006XG34)
文摘The refraction of rays in the Savart polariscope is different from the isotropic medium. We have analysed and discussed the refraction of rays in the Savart polariscope on the basis of the Snell law. The refraction formulae of the extraordinary rays and ordinary rays were derived. Results obtained may provide theoretical and practical guide lines for studying, developing and engineering of polarization interference imaging spectrometer.
基金financial support from Natural Sciences and Engineering ResearchCouncil(NSERC)(NSERC EGP 501335-16) along with the donated CSA cement
文摘The mining industry often uses shotcrete for ground stabilization. However, cracking within shotcrete is commonly observed, which delays production schedules and increases maintenance costs. A possible crack reduction method is using expansive shotcrete mixture consisting of calcium sulfoaluminate cement(CSA), ordinary Portland cement(OPC), and calcium sulfate(CS) to reduce shrinkage. Furthermore, fibers can be added to the mixture to restrain expansion and impede cracking. The objective of this paper is to study the effects of nylon fiber, glass fiber, and steel fiber on an expansive shotcrete mixture that can better resist cracking. In this study, parameters such as density, water absorption, volume of permeable voids, unconfined compressive strength(UCS), splitting tensile strength(STS), and volume change of fiber-added expansive mixtures were determined at different time periods(i.e. the strengths on the 28 th day, and the volume changes on the 1 st, 7 th, 14 th, 21 st, and 28 th days). The results show that addition of fibers can improve mixture durability, in the form of decreased water absorption and reduced permeable pore space content. Moreover, the expansion of the CSA-OPC-CS mixture was restrained up to50% by glass fiber, up to 43% by nylon fiber, and up to 28% by steel fiber. The results show that the STS was improved by 57% with glass fiber addition, 43% with steel fiber addition, and 38% with nylon fiber addition. The UCS was also increased by 31% after steel fiber addition, 26% after nylon fiber addition, and16% after glass fiber addition. These results suggest that fiber additions to the expansive shotcrete mixtures can improve durability and strengths while controlling expansion.
基金Foundation item: The National Natural Science Foundation of China(No. 20371023)
文摘The nanometer and ordinary anatase titanium dioxide(TiO_2) powders were adopted as the sonocatalysts for the degradation of methyl orange used as a model compound for the first time. It was found that the sonocatalytic degradation effect of methyl orange in the presence of TiO_2 powder were much better than that without TiO_2, but the sonocatalytic activity of the nanometer anatase TiO_2 particle was obviously higher than that of ordinary anatase TiO_2 particle. Although there are many factors influencing sonocatalytic degradation of methyl orange, the experimental results showed that the best degradation ratio of methyl orange could be obtained when the experimental conditions were: initial concentration 15 mg/L, nanometer anatase TiO_2 adding amount 750 mg/L, ultrasonic frequency 40 kHz, output power 50 W, pH = 3.0 and temperature 40℃ within 150 min. In addition, the catalytic activity of reused nanometer anatase TiO_2 catalyst was also studied and found to decline gradually comparing with initial nanometer anatase TiO_2 catalyst. All experiments indicated that the method of the sonocatalytic degradation of organic pollutants in the presence of TiO_2 powder was an advisable choice for non- or low-transparent organic wastewaters.
基金heprojectissupportedbyNNSFofChina (No .1 9972 0 39) .
文摘In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.
基金Financial support from the National Natural Science Foundation of China(51778003,51878263,and 51608004)Opening Foundation of State Key Laboratory of High Performance Civil Engineering Materials(2018CEM002)+1 种基金Anhui Provincial Education Department(gxfxZD2016134)Anhui Province Higher Education Revitalization Program([2014]No.11).
文摘China is the largest producer and user of ordinary Portland cement(OPC),and the rapid growth of infrastructure development demands more sustainable building materials for concrete structures.Alkali-activated materials(AAMs)are a new type of energy-saving and environmentally friendly building material with a wide range of potential applications.This paper compares the durability of AAMs and 0 PC-based materials un der sulfate attack,acid corrosion,carb on ation,and chloride penetratio n.Different AAMs have shown distinct durability properties due to different compositions being formed when different raw materials are used.According to the calcium(Ca)concentration of the raw materials,this paper interprets the deterioration mechanisms of three categories of AAMs:calcium-free,low-calcium,and calcium-rich.Conflicts found in the most recent research are highlighted,as they raise concerns regarding the consistenee and long-term properties of AAMs.Nevertheless,AAMs show better durability performances than OPC-based materials in general.
