In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
The structural system failure probability(SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams.Traditional methods for estimating the failure probabilities are based on defined mathe...The structural system failure probability(SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams.Traditional methods for estimating the failure probabilities are based on defined mathematical descriptions,namely,limit state functions of failure modes.Several problems are to be solved in the use of traditional methods for gravity dams.One is how to define the limit state function really reflecting the mechanical mechanism of the failure mode;another is how to understand the relationship among failure modes and enable the probability of the whole structure to be determined.Performing SFP analysis for a gravity dam system is a challenging task.This work proposes a novel nonlinear finite-element-based SFP analysis method for gravity dams.Firstly,reasonable nonlinear constitutive modes for dam concrete,concrete/rock interface and rock foundation are respectively introduced according to corresponding mechanical mechanisms.Meanwhile the response surface(RS) method is used to model limit state functions of main failure modes through the Monte Carlo(MC) simulation results of the dam-interface-foundation interaction finite element(FE) analysis.Secondly,a numerical SFP method is studied to compute the probabilities of several failure modes efficiently by simple matrix integration operations.Then,the nonlinear FE-based SFP analysis methodology for gravity dams considering correlated failure modes with the additional sensitivity analysis is proposed.Finally,a comprehensive computational platform for interfacing the proposed method with the open source FE code Code Aster is developed via a freely available MATLAB software tool(FERUM).This methodology is demonstrated by a case study of an existing gravity dam analysis,in which the dominant failure modes are identified,and the corresponding performance functions are established.Then,the dam failure probability of the structural system is obtained by the proposed method considering the correlation relationship of main failure modes on the basis of the mechanical mechanism analysis with the MC-FE simulations.展开更多
The paper presents some problems of lightning overvoltage modeling in transmission lines with nonlinear elements.The presented results were obtained mostly for fast front transients of subsequent lightning return stro...The paper presents some problems of lightning overvoltage modeling in transmission lines with nonlinear elements.The presented results were obtained mostly for fast front transients of subsequent lightning return stroke currents.The effectiveness of numerical algorithms of nonlinear models and possibilities of their development for such transients are analyzed.Computer simulations carried out by application of EMTP show that nonlinear models of back-flashover and ZnO arresters work properly,while the implemented corona model can not be used for relatively large peak values of subsequent lightning return-stroke currents.展开更多
This article demonstrates a novel approach for material nonlinear analysis.This analysis procedure eliminates tedious and lengthy step by step incremental and then iterative procedure adopted classically and gives dir...This article demonstrates a novel approach for material nonlinear analysis.This analysis procedure eliminates tedious and lengthy step by step incremental and then iterative procedure adopted classically and gives direct results in the linear as well as in nonlinear range of the material behavior.Use of elastic moduli is eliminated.Instead,stress and strain functions are used as the material input in the analysis procedure.These stress and strain functions are directly derived from the stress-strain behavior of the material by the method of curve fitting.This way,the whole stress-strain diagram is utilized in the analysis which naturally exposes the response of structure when loading is in nonlinear range of the material behavior.It is found that it is an excellent computational procedure adopted so far for material nonlinear analysis which gives very accurate results,easy to adopt and simple in calculations.The method eliminates all types of linearity assumptions in basic derivations of equations and hence,eliminates all types of possibility of errors in the analysis procedure as well.As it is required to know stress distribution in the structural body by proper modelling and structural idealization,the proposed analysis approach can be regarded as stress-based analysis procedure.Basic problems such as uniaxial problem,beam bending,and torsion problems are solved.It is found that approach is very suitable for solving the problems of fracture mechanics.Energy release rate for plate with center crack and double cantilever beam specimen is also evaluated.The approach solves the fracture problem with relative ease in strength of material style calculations.For all problems,results are compared with the classical displacement-based liner theory.展开更多
Based on a variety of geometric observations for location of solutions, a general and unified region analysis framework for developing constructive solvability of nonlinear operator equations are proposed. Within this...Based on a variety of geometric observations for location of solutions, a general and unified region analysis framework for developing constructive solvability of nonlinear operator equations are proposed. Within this framework, the methods including interval, ball and ellipsoid methods can be studied in a unified way. The ball algorithm, as a typical example, is in particular analysed.展开更多
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
基金Projects(51409167,51139001,51179066)supported by the National Natural Science Foundation of ChinaProjects(201401022,201501036)supported by the Ministry of Water Resources Public Welfare Industry Research Special Fund,ChinaProjects(GG201532,GG201546)supported by the Scientific and Technological Research for Water Conservancy,Henan Province,China
文摘The structural system failure probability(SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams.Traditional methods for estimating the failure probabilities are based on defined mathematical descriptions,namely,limit state functions of failure modes.Several problems are to be solved in the use of traditional methods for gravity dams.One is how to define the limit state function really reflecting the mechanical mechanism of the failure mode;another is how to understand the relationship among failure modes and enable the probability of the whole structure to be determined.Performing SFP analysis for a gravity dam system is a challenging task.This work proposes a novel nonlinear finite-element-based SFP analysis method for gravity dams.Firstly,reasonable nonlinear constitutive modes for dam concrete,concrete/rock interface and rock foundation are respectively introduced according to corresponding mechanical mechanisms.Meanwhile the response surface(RS) method is used to model limit state functions of main failure modes through the Monte Carlo(MC) simulation results of the dam-interface-foundation interaction finite element(FE) analysis.Secondly,a numerical SFP method is studied to compute the probabilities of several failure modes efficiently by simple matrix integration operations.Then,the nonlinear FE-based SFP analysis methodology for gravity dams considering correlated failure modes with the additional sensitivity analysis is proposed.Finally,a comprehensive computational platform for interfacing the proposed method with the open source FE code Code Aster is developed via a freely available MATLAB software tool(FERUM).This methodology is demonstrated by a case study of an existing gravity dam analysis,in which the dominant failure modes are identified,and the corresponding performance functions are established.Then,the dam failure probability of the structural system is obtained by the proposed method considering the correlation relationship of main failure modes on the basis of the mechanical mechanism analysis with the MC-FE simulations.
文摘The paper presents some problems of lightning overvoltage modeling in transmission lines with nonlinear elements.The presented results were obtained mostly for fast front transients of subsequent lightning return stroke currents.The effectiveness of numerical algorithms of nonlinear models and possibilities of their development for such transients are analyzed.Computer simulations carried out by application of EMTP show that nonlinear models of back-flashover and ZnO arresters work properly,while the implemented corona model can not be used for relatively large peak values of subsequent lightning return-stroke currents.
文摘This article demonstrates a novel approach for material nonlinear analysis.This analysis procedure eliminates tedious and lengthy step by step incremental and then iterative procedure adopted classically and gives direct results in the linear as well as in nonlinear range of the material behavior.Use of elastic moduli is eliminated.Instead,stress and strain functions are used as the material input in the analysis procedure.These stress and strain functions are directly derived from the stress-strain behavior of the material by the method of curve fitting.This way,the whole stress-strain diagram is utilized in the analysis which naturally exposes the response of structure when loading is in nonlinear range of the material behavior.It is found that it is an excellent computational procedure adopted so far for material nonlinear analysis which gives very accurate results,easy to adopt and simple in calculations.The method eliminates all types of linearity assumptions in basic derivations of equations and hence,eliminates all types of possibility of errors in the analysis procedure as well.As it is required to know stress distribution in the structural body by proper modelling and structural idealization,the proposed analysis approach can be regarded as stress-based analysis procedure.Basic problems such as uniaxial problem,beam bending,and torsion problems are solved.It is found that approach is very suitable for solving the problems of fracture mechanics.Energy release rate for plate with center crack and double cantilever beam specimen is also evaluated.The approach solves the fracture problem with relative ease in strength of material style calculations.For all problems,results are compared with the classical displacement-based liner theory.
文摘Based on a variety of geometric observations for location of solutions, a general and unified region analysis framework for developing constructive solvability of nonlinear operator equations are proposed. Within this framework, the methods including interval, ball and ellipsoid methods can be studied in a unified way. The ball algorithm, as a typical example, is in particular analysed.
