Based on the discrete element method and hydrostatics theory,an improved Archimedes principle is proposed to study the rules pertaining to resistance changes during the penetration process of an intruder into the part...Based on the discrete element method and hydrostatics theory,an improved Archimedes principle is proposed to study the rules pertaining to resistance changes during the penetration process of an intruder into the particulate materials.The results illustrate the fact that the lateral contribution to the resistance is very small,while the tangential force of the lateral resistance originates from friction effects.Conversely,the resistance of particulate materials on the intruder mainly occurs at the bottom part of the intruding object.Correspondingly,the factors that determine the resistance of the bottom part of the intruding object and the rules pertaining to resistance changes are analyzed.It is found that when the volume density and friction coefficient of the particles and the radius of the bottom surface of the cylindrical intruder are varied,the resistance–depth curve consists of a nonlinear segment and a linear region.The intersection of the two stages occurs at the same location h/˜R=0.15±0.055.The slope of the linear stage is determined by the friction coefficient of the particles.Accordingly,the relationship between the slope and the friction coefficient is quantified.Finally,it is shown that the slope is independent of the geometry of the intruder.展开更多
Quasistatic magnetic fields generated by nonrelativistic intense linearly polarized (LP) and circularly polarized (CP) laser pulses in an initially uniform underdense plasma in the collision-dominated limit are in...Quasistatic magnetic fields generated by nonrelativistic intense linearly polarized (LP) and circularly polarized (CP) laser pulses in an initially uniform underdense plasma in the collision-dominated limit are investigated analytically. Using a selfconsistent analytical model, we perform a detailed derivation of quasistatic magnetic fields in the laser pulse envelope in the collision-dominated limit to obtain exact analytical expressions for magnetic fields and discuss the dependence of magnetic fields on laser and plasma parameters. Equations for quasistatic magnetic fields including both axial componentBz and the azimuthal one Be are derived simultaneously from such a selfconsistent model. The dependence of quasistatic magnetic field on incident laser intensity, transverse focused radius of laser pulse, electron density and electron temperature is discussed.展开更多
This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for t...This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for the stress approximation,degree k+1 for the velocity approximation,and degree k for the numerical trace of velocity on the inter-element boundaries.The temporal discretization in the fully discrete method adopts a backward Euler difference scheme.We show the existence and uniqueness of the semi-discrete and fully discrete solutions,and derive optimal a priori error estimates.Numerical examples are provided to support the theoretical analysis.展开更多
Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments.The paper considers a linear elasticity system with strongly heterogeneous...Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments.The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca friction law,and studies the homogenization theories under the frameworks of H-convergence and small ε-periodicity.The qualitative result is based on H-convergence,which shows the original oscillating solutions will converge weakly to the homogenized solution,while the author’s quantitative result provides an estimate of asymptotic errors in H^(1)-norm for the periodic homogenization.This paper also designs several numerical experiments to validate the convergence rates in the quantitative analysis.展开更多
In creeping solids,plane stress and plane strain solutions for asymptotic singular crack-tip fields have been first put forward by Riedel and Rice with C^(*)as the dominating parameter and developed by Xiang and Guo i...In creeping solids,plane stress and plane strain solutions for asymptotic singular crack-tip fields have been first put forward by Riedel and Rice with C^(*)as the dominating parameter and developed by Xiang and Guo into three-dimensional solution(3D)for stationary cracks under the domination of C^(*)with the constraint factor Tz.However,how to characterize the 3D crack-tip fields under creep damage-induced quasistatic growing conditions remains challenging.In this study,we reveal that,for 3D quasistatic growing cracks,the leading singular solution can effectively characterize the crack-tip stress distributions with relative errors less than 10.8%for relative creep time up to 0.8 in various specimens with finite thickness.For a given relative time,Tz distributions can be unified by the equivalent thickness concept,Beq.The results show that C^(*)-T_(z) can effectively quantify both the load and constraint effects on the crack-tip fields.Such geometry independent dominance can considerably simplify the treatments of load and constraint effects,thereby promoting the application of fracture mechanics in high-temperature damage tolerance designs.展开更多
Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of visco...Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.展开更多
Downburst event is identified as a major cause to failure of transmission lines in non-coastal regions.In this paper,a novel nonlinear analytical frame for quasi-static buffeting responses of hinged and multi-span ins...Downburst event is identified as a major cause to failure of transmission lines in non-coastal regions.In this paper,a novel nonlinear analytical frame for quasi-static buffeting responses of hinged and multi-span insulator-line systems are derived based on the theory of cable structure.The closed-form solutions are presented and applied to predict nonlinear response including displacements and other reactions of the system subjected to a moving downburst wind in a case study.Accuracy and efficiency of the derived analytical frame are validated via comparisons with results from finite element method.展开更多
Presents a practical way of calculation for stiffness of cylindrical roller bearing based on traditional quasistatic analytical methods subject to radial force and bending moment,which take into consideration the effe...Presents a practical way of calculation for stiffness of cylindrical roller bearing based on traditional quasistatic analytical methods subject to radial force and bending moment,which take into consideration the effect of such factors as thickness of oil elastohydrodynamic film,pressure,shear force,friction force of cage,centrifugal force and slides,taken into consideration and presents the results of stiffness calculation with a typical example with an aeroengine cylindrical roller bearing were given in the paper.And,discusses the effect of major parameters’influence on stiffness.展开更多
Nonlinear bending of cantilever incompressible poroelastic beams subjected to a uniform load is investigated with the constraint that fluid flow is only in the axial direction. The governing equations for large deflec...Nonlinear bending of cantilever incompressible poroelastic beams subjected to a uniform load is investigated with the constraint that fluid flow is only in the axial direction. The governing equations for large deflection of the poroelastic beam are derived from theory of incompressible saturated porous media. Then, nonlinear responses of a cantilever beam with impermeable fixed end and permeable free end are examined with the Galerkin truncation method. The deflections and bending moments of the poroelastic beam and the equivalent couples of the pore fluid pressures are shown in figures. The differences of the results between the large deflection and the small deflection theories are analyzed. It is shown that the results of the large deflection theory are smaller than those of the small deflection theory, and the time needed to approach their stationary states for the large deflection theory is shorter than that for the small deflection theory.展开更多
The near crack line field analysis method has been used to investigate into Mode III quasistatically propagating crack in an elastic-perfectly plastic material. The significance of this paper is that the usual small s...The near crack line field analysis method has been used to investigate into Mode III quasistatically propagating crack in an elastic-perfectly plastic material. The significance of this paper is that the usual small scale yielding theory has been broken through. By obtaining the general solutions of the stresses and the displacement rate of the near crack line plastic region, and by matching the general solutions with the precise elastic fields (not the usual elastic K-dominant fields) at the elastic-plastic boundary, the precise and new solutions of the stress and deformation fields, the size of the plastic region and the unit normal vector of the elastic-plastic boundary have been obtained near the crack line. The solutions of this paper are sufficiently precise near the crack line region because the roughly qualitative assumptions of the small scale yielding theory have not been used and no other roughly qualitative assumptions have been taken, either. The analysis of this paper shows that the assumingly 'steady-state case' for stable crack growth, which has been discussed attentively in previous works, do not exist, and the plastic strains near the crack line do not have singularities, Two most important cases for stable crack growth have been discussed.展开更多
The quasistatic axial magnetic fields in plasmas produced by ultrashort laser pulses were measured by measuring the Faraday rotation angle of the backscattered emission. The spatial distribution of the axial magnetic ...The quasistatic axial magnetic fields in plasmas produced by ultrashort laser pulses were measured by measuring the Faraday rotation angle of the backscattered emission. The spatial distribution of the axial magnetic field was obtained with a peak value as high as 170 Tesla. Theory suggests that the axial magnetic field is generated by dynamo effect in laser-plasma interaction.展开更多
基金This study was financially supported by the National Key Research and Development Program of China(Grant No.2018YFA0605902)the National Natural Science Foundation of China(Grant Nos.11572067 and 11772085).
文摘Based on the discrete element method and hydrostatics theory,an improved Archimedes principle is proposed to study the rules pertaining to resistance changes during the penetration process of an intruder into the particulate materials.The results illustrate the fact that the lateral contribution to the resistance is very small,while the tangential force of the lateral resistance originates from friction effects.Conversely,the resistance of particulate materials on the intruder mainly occurs at the bottom part of the intruding object.Correspondingly,the factors that determine the resistance of the bottom part of the intruding object and the rules pertaining to resistance changes are analyzed.It is found that when the volume density and friction coefficient of the particles and the radius of the bottom surface of the cylindrical intruder are varied,the resistance–depth curve consists of a nonlinear segment and a linear region.The intersection of the two stages occurs at the same location h/˜R=0.15±0.055.The slope of the linear stage is determined by the friction coefficient of the particles.Accordingly,the relationship between the slope and the friction coefficient is quantified.Finally,it is shown that the slope is independent of the geometry of the intruder.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60621063,60678007,and 10774184)the Chinese Academy of Sciences (Grant No. KJCX2-YW-T01)the National Basic Research Program of China (Grant No. 2007CB815101)
文摘Quasistatic magnetic fields generated by nonrelativistic intense linearly polarized (LP) and circularly polarized (CP) laser pulses in an initially uniform underdense plasma in the collision-dominated limit are investigated analytically. Using a selfconsistent analytical model, we perform a detailed derivation of quasistatic magnetic fields in the laser pulse envelope in the collision-dominated limit to obtain exact analytical expressions for magnetic fields and discuss the dependence of magnetic fields on laser and plasma parameters. Equations for quasistatic magnetic fields including both axial componentBz and the azimuthal one Be are derived simultaneously from such a selfconsistent model. The dependence of quasistatic magnetic field on incident laser intensity, transverse focused radius of laser pulse, electron density and electron temperature is discussed.
基金This work was supported by the National Natural Science Foundation of China(Grant No.12171340).
文摘This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for the stress approximation,degree k+1 for the velocity approximation,and degree k for the numerical trace of velocity on the inter-element boundaries.The temporal discretization in the fully discrete method adopts a backward Euler difference scheme.We show the existence and uniqueness of the semi-discrete and fully discrete solutions,and derive optimal a priori error estimates.Numerical examples are provided to support the theoretical analysis.
基金supported by the National Natural Science Foundation of China(No.51739007)the Hong Kong RGC General Research Fund(Nos.14305222,14304021)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDC06030101)。
文摘Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments.The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca friction law,and studies the homogenization theories under the frameworks of H-convergence and small ε-periodicity.The qualitative result is based on H-convergence,which shows the original oscillating solutions will converge weakly to the homogenized solution,while the author’s quantitative result provides an estimate of asymptotic errors in H^(1)-norm for the periodic homogenization.This paper also designs several numerical experiments to validate the convergence rates in the quantitative analysis.
基金supported by the National Key Research and Development Program of China(Grant No.2019YFA0705400)the Natural Science Foundation of Jiangsu Province(Grant No.BK20212008)+2 种基金the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(Grant No.MCMS-I-0421K01)the Fundamental Research Funds for the Central Universities(Grant Nos.NJ2020003,and NZ2020001)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In creeping solids,plane stress and plane strain solutions for asymptotic singular crack-tip fields have been first put forward by Riedel and Rice with C^(*)as the dominating parameter and developed by Xiang and Guo into three-dimensional solution(3D)for stationary cracks under the domination of C^(*)with the constraint factor Tz.However,how to characterize the 3D crack-tip fields under creep damage-induced quasistatic growing conditions remains challenging.In this study,we reveal that,for 3D quasistatic growing cracks,the leading singular solution can effectively characterize the crack-tip stress distributions with relative errors less than 10.8%for relative creep time up to 0.8 in various specimens with finite thickness.For a given relative time,Tz distributions can be unified by the equivalent thickness concept,Beq.The results show that C^(*)-T_(z) can effectively quantify both the load and constraint effects on the crack-tip fields.Such geometry independent dominance can considerably simplify the treatments of load and constraint effects,thereby promoting the application of fracture mechanics in high-temperature damage tolerance designs.
文摘Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.
基金supported in part by Science and Technology Foundation of State Grid Shandong Electric Power Company(Grant No.52062518000U)National Natural Science Foundation of China(Grant Nos.51720105005 and 51478373)+1 种基金by Science and Technology Foundation of State Grid Shandong Electric Power Company(Grant No.52062518000U)National Natural Science Foundation of China(Grant Nos.51720105005 and 51478373)are greatly acknowledged.
文摘Downburst event is identified as a major cause to failure of transmission lines in non-coastal regions.In this paper,a novel nonlinear analytical frame for quasi-static buffeting responses of hinged and multi-span insulator-line systems are derived based on the theory of cable structure.The closed-form solutions are presented and applied to predict nonlinear response including displacements and other reactions of the system subjected to a moving downburst wind in a case study.Accuracy and efficiency of the derived analytical frame are validated via comparisons with results from finite element method.
文摘Presents a practical way of calculation for stiffness of cylindrical roller bearing based on traditional quasistatic analytical methods subject to radial force and bending moment,which take into consideration the effect of such factors as thickness of oil elastohydrodynamic film,pressure,shear force,friction force of cage,centrifugal force and slides,taken into consideration and presents the results of stiffness calculation with a typical example with an aeroengine cylindrical roller bearing were given in the paper.And,discusses the effect of major parameters’influence on stiffness.
基金Project supported by the Science Foundation of Shanghai Municipal Commission of Science and Technology (Grant No.06ZR14037), and the Shanghai Leading Acadeemic Discipline Project (Grant No.Y0103)
文摘Nonlinear bending of cantilever incompressible poroelastic beams subjected to a uniform load is investigated with the constraint that fluid flow is only in the axial direction. The governing equations for large deflection of the poroelastic beam are derived from theory of incompressible saturated porous media. Then, nonlinear responses of a cantilever beam with impermeable fixed end and permeable free end are examined with the Galerkin truncation method. The deflections and bending moments of the poroelastic beam and the equivalent couples of the pore fluid pressures are shown in figures. The differences of the results between the large deflection and the small deflection theories are analyzed. It is shown that the results of the large deflection theory are smaller than those of the small deflection theory, and the time needed to approach their stationary states for the large deflection theory is shorter than that for the small deflection theory.
文摘The near crack line field analysis method has been used to investigate into Mode III quasistatically propagating crack in an elastic-perfectly plastic material. The significance of this paper is that the usual small scale yielding theory has been broken through. By obtaining the general solutions of the stresses and the displacement rate of the near crack line plastic region, and by matching the general solutions with the precise elastic fields (not the usual elastic K-dominant fields) at the elastic-plastic boundary, the precise and new solutions of the stress and deformation fields, the size of the plastic region and the unit normal vector of the elastic-plastic boundary have been obtained near the crack line. The solutions of this paper are sufficiently precise near the crack line region because the roughly qualitative assumptions of the small scale yielding theory have not been used and no other roughly qualitative assumptions have been taken, either. The analysis of this paper shows that the assumingly 'steady-state case' for stable crack growth, which has been discussed attentively in previous works, do not exist, and the plastic strains near the crack line do not have singularities, Two most important cases for stable crack growth have been discussed.
文摘The quasistatic axial magnetic fields in plasmas produced by ultrashort laser pulses were measured by measuring the Faraday rotation angle of the backscattered emission. The spatial distribution of the axial magnetic field was obtained with a peak value as high as 170 Tesla. Theory suggests that the axial magnetic field is generated by dynamo effect in laser-plasma interaction.