Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenienc...Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods.展开更多
This paper is devoted to the analysis of the nonlinear Stability of a clamped rodcarrying electric current in the magnetic field which is produced by the current frowingin a pair of inifinitely long parallel rigid wi...This paper is devoted to the analysis of the nonlinear Stability of a clamped rodcarrying electric current in the magnetic field which is produced by the current frowingin a pair of inifinitely long parallel rigid wires. The natural State of the rod is in theplane of the wires and is equidistant from them.Firstly under the assumption of apatial deformation, the governing equations of the problem are derived, and the linearizedproblem and critical currents are discussed. Secondly, it ls proved that the buckledstates of the rod are always in planes. Finally. the global responses of the bifurcationproblem of the rod are compuled numerically and the distributions of the deflections.axial forces and bending monents are obtained. The results show that the buckledslates of the rod may be either supercritical or Subcritical. depending on the distancebetween the rod and the wires. Furthermore, it is found that -there exists a limit pointon the branch solution of the supercritical buckled State. This is distinctively differentfrom the buckled slate of the elastic compressive rods.展开更多
The upper bound limit analysis(UBLA)is one of the key research directions in geotechnical engineering and is widely used in engineering practice.UBLA assumes that the slip surface with the minimum factor of safety(FSm...The upper bound limit analysis(UBLA)is one of the key research directions in geotechnical engineering and is widely used in engineering practice.UBLA assumes that the slip surface with the minimum factor of safety(FSmin)is the critical slip surface,and then applies it to slope stability analysis.However,the hypothesis of UBLA has not been systematically verified,which may be due to the fact that the traditional numerical method is difficult to simulate the large deformation.In this study,in order to systematically verify the assumption of UBLA,material point method(MPM),which is suitable to simulate the large deformation of continuous media,is used to simulate the whole process of the slope failure,including the large-scale transportation and deposition of soil mass after slope failure.And a series of comparative studies are conducted on the stability of cohesive slopes using UBLA and MPM.The proposed study indicated that the slope angle,internal friction angle and cohesion have a remarkable effect on the slip surface of the cohesive slope.Also,for stable slopes,the calculation results of the two are relatively close.However,for unstable slopes,the slider volume determined by the UBLA is much smaller than the slider volume determined by the MPM.In other words,for unstable slopes,the critical slip surface of UBLA is very different from the slip surface when the slope failure occurs,and when the UBLA is applied to the stability analysis of unstable slope,it will lead to extremely unfavorable results.展开更多
The purpose of this paper is to solve the problem of determining the limits of multivariate rational functions.It is essential to decide whether or not limxˉ→0f g=0 for two non-zero polynomials f,g∈R[x1,...,xn]with...The purpose of this paper is to solve the problem of determining the limits of multivariate rational functions.It is essential to decide whether or not limxˉ→0f g=0 for two non-zero polynomials f,g∈R[x1,...,xn]with f(0,...,0)=g(0,...,0)=0.For two such polynomials f and g,we establish two necessary and sufcient conditions for the rational functionf g to have its limit 0 at the origin.Based on these theoretic results,we present an algorithm for deciding whether or not lim(x1,...,xn)→(0,...,0)f g=0,where f,g∈R[x1,...,xn]are two non-zero polynomials.The design of our algorithm involves two existing algorithms:one for computing the rational univariate representations of a complete chain of polynomials,another for catching strictly critical points in a real algebraic variety.The two algorithms are based on the well-known Wu’s method.With the aid of the computer algebraic system Maple,our algorithm has been made into a general program.In the final section of this paper,several examples are given to illustrate the efectiveness of our algorithm.展开更多
基金The project supported by the Special Research Fund for Doctor Program of Universities (9424702)
文摘Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods.
文摘This paper is devoted to the analysis of the nonlinear Stability of a clamped rodcarrying electric current in the magnetic field which is produced by the current frowingin a pair of inifinitely long parallel rigid wires. The natural State of the rod is in theplane of the wires and is equidistant from them.Firstly under the assumption of apatial deformation, the governing equations of the problem are derived, and the linearizedproblem and critical currents are discussed. Secondly, it ls proved that the buckledstates of the rod are always in planes. Finally. the global responses of the bifurcationproblem of the rod are compuled numerically and the distributions of the deflections.axial forces and bending monents are obtained. The results show that the buckledslates of the rod may be either supercritical or Subcritical. depending on the distancebetween the rod and the wires. Furthermore, it is found that -there exists a limit pointon the branch solution of the supercritical buckled State. This is distinctively differentfrom the buckled slate of the elastic compressive rods.
基金financially supported by the National Natural Science Foundation of China(No.51878668)the Guizhou Provincial Department of Transportation Foundation(Nos.2017-123-033,2018-123-040)+1 种基金the Innovation-Driven Project of Central South University(No.2016CX012)the Science and Technology Project Plan for Key Projects of Jiangxi Transportation Department(No.2019C0011)
文摘The upper bound limit analysis(UBLA)is one of the key research directions in geotechnical engineering and is widely used in engineering practice.UBLA assumes that the slip surface with the minimum factor of safety(FSmin)is the critical slip surface,and then applies it to slope stability analysis.However,the hypothesis of UBLA has not been systematically verified,which may be due to the fact that the traditional numerical method is difficult to simulate the large deformation.In this study,in order to systematically verify the assumption of UBLA,material point method(MPM),which is suitable to simulate the large deformation of continuous media,is used to simulate the whole process of the slope failure,including the large-scale transportation and deposition of soil mass after slope failure.And a series of comparative studies are conducted on the stability of cohesive slopes using UBLA and MPM.The proposed study indicated that the slope angle,internal friction angle and cohesion have a remarkable effect on the slip surface of the cohesive slope.Also,for stable slopes,the calculation results of the two are relatively close.However,for unstable slopes,the slider volume determined by the UBLA is much smaller than the slider volume determined by the MPM.In other words,for unstable slopes,the critical slip surface of UBLA is very different from the slip surface when the slope failure occurs,and when the UBLA is applied to the stability analysis of unstable slope,it will lead to extremely unfavorable results.
基金supported by National Natural Science Foundation of China(Grant No.11161034)the Science Foundation of the Eduction Department of Jiangxi Province(Grant No.Gjj12012)
文摘The purpose of this paper is to solve the problem of determining the limits of multivariate rational functions.It is essential to decide whether or not limxˉ→0f g=0 for two non-zero polynomials f,g∈R[x1,...,xn]with f(0,...,0)=g(0,...,0)=0.For two such polynomials f and g,we establish two necessary and sufcient conditions for the rational functionf g to have its limit 0 at the origin.Based on these theoretic results,we present an algorithm for deciding whether or not lim(x1,...,xn)→(0,...,0)f g=0,where f,g∈R[x1,...,xn]are two non-zero polynomials.The design of our algorithm involves two existing algorithms:one for computing the rational univariate representations of a complete chain of polynomials,another for catching strictly critical points in a real algebraic variety.The two algorithms are based on the well-known Wu’s method.With the aid of the computer algebraic system Maple,our algorithm has been made into a general program.In the final section of this paper,several examples are given to illustrate the efectiveness of our algorithm.
