In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hy...In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.展开更多
This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational funct...This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.展开更多
An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primar...An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as 'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as 'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.展开更多
An extended multiscale finite element method (EMsFEM) is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multi...An extended multiscale finite element method (EMsFEM) is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.展开更多
In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or micr...In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.展开更多
For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mi...For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.展开更多
The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations (K-G-S equations) by the aid of the symbolic computation system Mathematica. ...The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations (K-G-S equations) by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.展开更多
In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study...In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study show that by applying the new direct algebraic method to the pKP equation,the behavior of the obliquely interacting surface waves in two dimensions can be analyzed.This article fairly clarifies the behaviors of surface waves in shallow waters.In the literature,several mathematical models have been developed in attempt to study these behaviors,with nonlinear mathematics being one of the most important steps;however,the investigations are still at a level that can be called‘baby steps’.Therefore,every study to be carried out in this context is of great importance.Thus,this study will serve as a reference to guide scientists working in this field.展开更多
Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete cr...Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete crack propagation under a constant hydration and hardening condition during the construction period, and a corresponding programming code was developed. The experimental investigation shows that initial crack propagation caused by self-deformation loads can be analyzed by this program. This improved algorithm was a preliminary application of the XFEM to the problem of the concrete self-deformation cracking during the hydration and hardening period. However, room for improvement exists for this algorithm in terms of matching calculation programs with mass concrete temperature fields containing cooling pipes and the influence of creep or damage on crack propagation.展开更多
In the paper the extended modelling method with serial sands is used in an experimental research on the erosion patterns at the discharge outlet of a beach Hua-Neng power plant. The theoretical basis for the extended ...In the paper the extended modelling method with serial sands is used in an experimental research on the erosion patterns at the discharge outlet of a beach Hua-Neng power plant. The theoretical basis for the extended modelling method with serial sands is systematically presented in the paper and the method has been successfully employed in the sediment experiment of coastal works. According to the Froude Law, the model is designed to be a normal one with movable bed, the geometric scale lambda(L) = lambda(H) = 15, and three scales of sediment grain size are chosen, i.e., lambda(d1) = 0.207; lambda(d2) = 0.393; and lambda(d3) = 0.656. The median particle diameter of sea beach prototype sand d(50p) = 0.059 mm and the dis-changed water flow of the power plant is 21.7 m(3) / s. Three types of natural sea sands have been chosen as the serial modelling sands to extend the simulation of the prototype, thus replacing the conventional test in which artificial lightweight sands are used. As a result, this method can not only reduce the cost significantly, but also it is an advanced technique easy to use. Upon a series of tests, satisfactory results have been obtained.展开更多
An approach for joint direction of arrival(DOA) angle and frequency estimation for a linear array is investigated in this paper. Specifically, we make the utmost of the autocorrelation and cross-correlation informatio...An approach for joint direction of arrival(DOA) angle and frequency estimation for a linear array is investigated in this paper. Specifically, we make the utmost of the autocorrelation and cross-correlation information to propose an extended DOAmatrix(EDOAM) method. Subsequently, we obtain the autopaired angle and frequency estimates by the eigenvalues and the corresponding eigenvectors of the novel DOA matrix. Furthermore, the proposed method surpasses the DOA-matrix method which partly ignores the autocorrelation and cross-correlation information. Finally, the proposed method works well for both uniform and non-uniform linear arrays. The simulation consequences indicate the superiority of our proposed approach.展开更多
This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and ...This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and then coupled with the extended finite element method to simulate the heterogeneities and discontinuities present in the meso-structure of concrete. The proposed procedure is verified and exemplified by a series of numerical simulations. The simulation results show that microcracks can exert considerable impact on the fracture performance of concrete. More broadly, this work provides valuable insight into the initiation and propagation mechanism of microcracks in concrete and helps to foster a better understanding of the micro-mechanical behavior of cementitious materials.展开更多
In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed ext...In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.展开更多
In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Ca...In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Calogero-Degasperis (VCCD) equation. New soliton and periodic solutions of many types are obtained. Furthermore, the soliton propagation is discussed under the effect of the variable coefficients.展开更多
An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function...An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.展开更多
In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions ...In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.展开更多
Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order, a new matrix method is presented for steady-state vibration analysis of a nonc...Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order, a new matrix method is presented for steady-state vibration analysis of a noncircular cylindrical shell simply sup- ported at two ends and circumferentially stiffened by rings under harmonic pressure. Its difference from the existing works by Yamada and Irie is that the matrix differential equation is solved by using the extended homogeneous capacity precision integration' approach other than the Runge-Kutta-Gill integration method. The transfer matrix can easily be determined by a high precision integration scheme. In addition, besides the normal interacting forces, which were commonly adopted by researchers earlier, the tangential interacting forces between the cylindrical shell and the rings are considered at the same time by means of the Dirac-δ function. The effects of the exciting frequencies on displacements and stresses responses have been investigated. Numerical results show that the proposed method is more efficient than the aforementioned method.展开更多
Pre-driven longwall retracement roadway(PLRR)is commonly used in large mine shaft.The support crushing disasters occur frequently during the retracement,and roof management is necessary.Taking the 31107 panel as resea...Pre-driven longwall retracement roadway(PLRR)is commonly used in large mine shaft.The support crushing disasters occur frequently during the retracement,and roof management is necessary.Taking the 31107 panel as research background,the roof breaking structure of PLRR is analyzed.It is concluded that the roof cutting with vertical hydraulic fracture(HF)at a specified position,that is,fixed-length roof cutting,can reduce support load and keep immediate roof intact.The extended finite element method(XFEM)is applied to simulate hydraulic fracturing.The results show that both the axial and transverse hydraulic fracturing cannot effectively create vertical HFs.Therefore,a novel construction method of vertical HF based on the stress shadow effect(SSE)is proposed.The stress reversal region and HF orientation caused by the prefabricated hydraulic fracture(PF)are verified in simulation.The sub-vertical HFs are obtained between two PFs,the vertical extension range of which is much larger than that of directional hydraulic fracturing.The new construction method was used to determine the field plan for fixed-length roof cutting.The roof formed a stable suspended structure and deformation of the main PLRR was improved after hydraulic fracturing.展开更多
A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate th...A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate the propagation of cracks at grain boundary. Simulation results show that the crystallographic orientation of PFZ has significant influence on crack propagation, which includes the crack growth direction and crack growth velocity. The fracture strain of soft orientation is larger than that of hard orientation due to the role of reducing the stress intensity at grain boundary in intergranular brittle fracture. But in intergranular ductile fracture, the fracture strain of soft orientation may be smaller than that of hard orientation due to the roles of deformation localization.展开更多
Mechanical degradation, especially fractures in active particles in an electrode, is a major reason why the capacity of lithiumion batteries fades. This paper proposes a model that couples Li-ion diffusion, stress evo...Mechanical degradation, especially fractures in active particles in an electrode, is a major reason why the capacity of lithiumion batteries fades. This paper proposes a model that couples Li-ion diffusion, stress evolution, and damage mechanics to simulate the growth of central cracks in cathode particles(Li Mn_2 O_4) by an extended finite element method by considering the influence of multiple factors. The simulation shows that particles are likely to crack at a high discharge rate, when the particle radius is large, or when the initial central crack is longer. It also shows that the maximum principal tensile stress decreases and cracking becomes more difficult when the influence of crack surface diffusion is considered. The fracturing process occurs according to the following stages: no crack growth, stable crack growth, and unstable crack growth. Changing the charge/discharge strategy before unstable crack growth sets in is beneficial to prevent further capacity fading during electrochemical cycling.展开更多
文摘In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.
基金Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010B17914) and the National Natural Science Foundation of China (Grant No. 10926162).
文摘This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.
文摘An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as 'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as 'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.
基金supported by the National Natural Science Foundation(10721062,11072051,90715037,10728205,91015003, 51021140004)the Program of Introducing Talents of Discipline to Universities(B08014)the National Key Basic Research Special Foundation of China(2010CB832704).
文摘An extended multiscale finite element method (EMsFEM) is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.
基金supported by the National Natural Science Foundation of China (Grants 11471262, 50976003, 51136005)
文摘In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.
文摘For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.
基金Project supported by the National Nature Science Foundation of China (Grant No 49894190) of the Chinese Academy of Science (Grant No KZCXI-sw-18), and Knowledge Innovation Program.
文摘The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations (K-G-S equations) by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.
文摘In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study show that by applying the new direct algebraic method to the pKP equation,the behavior of the obliquely interacting surface waves in two dimensions can be analyzed.This article fairly clarifies the behaviors of surface waves in shallow waters.In the literature,several mathematical models have been developed in attempt to study these behaviors,with nonlinear mathematics being one of the most important steps;however,the investigations are still at a level that can be called‘baby steps’.Therefore,every study to be carried out in this context is of great importance.Thus,this study will serve as a reference to guide scientists working in this field.
基金Funded by the National Natural Science Foundation of China(Nos.51409264,51509020,51209219)Zhejiang Provincial Natural Science Foundation(No.LQ15E090003)
文摘Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete crack propagation under a constant hydration and hardening condition during the construction period, and a corresponding programming code was developed. The experimental investigation shows that initial crack propagation caused by self-deformation loads can be analyzed by this program. This improved algorithm was a preliminary application of the XFEM to the problem of the concrete self-deformation cracking during the hydration and hardening period. However, room for improvement exists for this algorithm in terms of matching calculation programs with mass concrete temperature fields containing cooling pipes and the influence of creep or damage on crack propagation.
文摘In the paper the extended modelling method with serial sands is used in an experimental research on the erosion patterns at the discharge outlet of a beach Hua-Neng power plant. The theoretical basis for the extended modelling method with serial sands is systematically presented in the paper and the method has been successfully employed in the sediment experiment of coastal works. According to the Froude Law, the model is designed to be a normal one with movable bed, the geometric scale lambda(L) = lambda(H) = 15, and three scales of sediment grain size are chosen, i.e., lambda(d1) = 0.207; lambda(d2) = 0.393; and lambda(d3) = 0.656. The median particle diameter of sea beach prototype sand d(50p) = 0.059 mm and the dis-changed water flow of the power plant is 21.7 m(3) / s. Three types of natural sea sands have been chosen as the serial modelling sands to extend the simulation of the prototype, thus replacing the conventional test in which artificial lightweight sands are used. As a result, this method can not only reduce the cost significantly, but also it is an advanced technique easy to use. Upon a series of tests, satisfactory results have been obtained.
基金supported by the National Natural Science Foundation of China (61971217,61971218,61631020)Jiangsu Natural Science Foundation (BK20200444)+1 种基金Jiangsu Key Research and Development Project (BE2020101)the Fund of Sonar Technology Key Laboratory。
文摘An approach for joint direction of arrival(DOA) angle and frequency estimation for a linear array is investigated in this paper. Specifically, we make the utmost of the autocorrelation and cross-correlation information to propose an extended DOAmatrix(EDOAM) method. Subsequently, we obtain the autopaired angle and frequency estimates by the eigenvalues and the corresponding eigenvectors of the novel DOA matrix. Furthermore, the proposed method surpasses the DOA-matrix method which partly ignores the autocorrelation and cross-correlation information. Finally, the proposed method works well for both uniform and non-uniform linear arrays. The simulation consequences indicate the superiority of our proposed approach.
基金supported by the National Basic Research Program of China(2014CB046904)the Hubei Provincial Key Laboratory of Safety for Geotechnical and Structural Engineering at Wuhan University(HBKLCIV201207)the China Postdoctoral Science Foundation(2013M540604)
文摘This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and then coupled with the extended finite element method to simulate the heterogeneities and discontinuities present in the meso-structure of concrete. The proposed procedure is verified and exemplified by a series of numerical simulations. The simulation results show that microcracks can exert considerable impact on the fracture performance of concrete. More broadly, this work provides valuable insight into the initiation and propagation mechanism of microcracks in concrete and helps to foster a better understanding of the micro-mechanical behavior of cementitious materials.
文摘In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.
文摘In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Calogero-Degasperis (VCCD) equation. New soliton and periodic solutions of many types are obtained. Furthermore, the soliton propagation is discussed under the effect of the variable coefficients.
基金Project supported by the Natural Science Foundation of Henan Province of China (Grant No 0111050200) and the Science Foundation of Henan University of Science and Technology (Grant Nos 2004ZY040 and 2004ZD002).
文摘An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.
文摘In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.
基金Project supported by the Doctoral Foundation of the National Education Ministry of China(No.20040487013)
文摘Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order, a new matrix method is presented for steady-state vibration analysis of a noncircular cylindrical shell simply sup- ported at two ends and circumferentially stiffened by rings under harmonic pressure. Its difference from the existing works by Yamada and Irie is that the matrix differential equation is solved by using the extended homogeneous capacity precision integration' approach other than the Runge-Kutta-Gill integration method. The transfer matrix can easily be determined by a high precision integration scheme. In addition, besides the normal interacting forces, which were commonly adopted by researchers earlier, the tangential interacting forces between the cylindrical shell and the rings are considered at the same time by means of the Dirac-δ function. The effects of the exciting frequencies on displacements and stresses responses have been investigated. Numerical results show that the proposed method is more efficient than the aforementioned method.
基金financially supported by the Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX21_2358)the National Key Research and Development Program of China(2020YFB1314204)National Natural Science Foundation of China(No.52074239)。
文摘Pre-driven longwall retracement roadway(PLRR)is commonly used in large mine shaft.The support crushing disasters occur frequently during the retracement,and roof management is necessary.Taking the 31107 panel as research background,the roof breaking structure of PLRR is analyzed.It is concluded that the roof cutting with vertical hydraulic fracture(HF)at a specified position,that is,fixed-length roof cutting,can reduce support load and keep immediate roof intact.The extended finite element method(XFEM)is applied to simulate hydraulic fracturing.The results show that both the axial and transverse hydraulic fracturing cannot effectively create vertical HFs.Therefore,a novel construction method of vertical HF based on the stress shadow effect(SSE)is proposed.The stress reversal region and HF orientation caused by the prefabricated hydraulic fracture(PF)are verified in simulation.The sub-vertical HFs are obtained between two PFs,the vertical extension range of which is much larger than that of directional hydraulic fracturing.The new construction method was used to determine the field plan for fixed-length roof cutting.The roof formed a stable suspended structure and deformation of the main PLRR was improved after hydraulic fracturing.
基金Projects(51475162,51405153)supported by the National Natural Science Foundation of ChinaProject(14JJ5015)supported by the Hunan Provincial Natural Science Foundation,China
文摘A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate the propagation of cracks at grain boundary. Simulation results show that the crystallographic orientation of PFZ has significant influence on crack propagation, which includes the crack growth direction and crack growth velocity. The fracture strain of soft orientation is larger than that of hard orientation due to the role of reducing the stress intensity at grain boundary in intergranular brittle fracture. But in intergranular ductile fracture, the fracture strain of soft orientation may be smaller than that of hard orientation due to the roles of deformation localization.
基金support of the National Natural Science Foundation of China (11472165 and 11332005)
文摘Mechanical degradation, especially fractures in active particles in an electrode, is a major reason why the capacity of lithiumion batteries fades. This paper proposes a model that couples Li-ion diffusion, stress evolution, and damage mechanics to simulate the growth of central cracks in cathode particles(Li Mn_2 O_4) by an extended finite element method by considering the influence of multiple factors. The simulation shows that particles are likely to crack at a high discharge rate, when the particle radius is large, or when the initial central crack is longer. It also shows that the maximum principal tensile stress decreases and cracking becomes more difficult when the influence of crack surface diffusion is considered. The fracturing process occurs according to the following stages: no crack growth, stable crack growth, and unstable crack growth. Changing the charge/discharge strategy before unstable crack growth sets in is beneficial to prevent further capacity fading during electrochemical cycling.