With the development of satellite structure technology, more and more design parameters will affect its structural performance. It is desirable to obtain an optimal structure design with a minimum weight, including op...With the development of satellite structure technology, more and more design parameters will affect its structural performance. It is desirable to obtain an optimal structure design with a minimum weight, including optimal configuration and sizes. The present paper aims to describe an optimization analysis for a satellite structure, including topology optimization and size optimization. Based on the homogenization method, the topology optimization is carried out for the main supporting frame of service module under given constraints and load conditions, and then the sensitivity analysis is made of 15 structural size parameters of the whole satellite and the optimal sizes are obtained. The numerical result shows that the present optimization design method is very effective.展开更多
The objective of this study was to determine the overall thermal elastic behavior of composites by homogenization method. The results obtained were compared with those by other well-known methods such as mean field me...The objective of this study was to determine the overall thermal elastic behavior of composites by homogenization method. The results obtained were compared with those by other well-known methods such as mean field method , self-consistent method and etc. A good agreement is achieved and thus a reliable nwthod for predicting the effective behavior of composite is presented. It is very easy to extend this method to multi-phase composite. The materiol properties determined here include elastic modulus, Poisson ratio and thermal expansion coefficient (CTE).展开更多
The objective of this study is to investigate the local stress fluctuation in two-phase composite by homogenization method. The composite was described by homogeneous macro structure and periodical micro structure sin...The objective of this study is to investigate the local stress fluctuation in two-phase composite by homogenization method. The composite was described by homogeneous macro structure and periodical micro structure sinudtaneously and the mechanical response of the composite can be described based on both macro and micro dimensional scales. Micro and mocro homogenization problems can be formulated. The effective material properties of the composite and the local stress field in the microstructure of the composite can be determined by solving these equntions.展开更多
In this study,a homogenization method is employed to determine the values of effective elastic modulus for BaZrO3 which is a promising candidate material for electrolyte in solid oxide fuel cell (SOFC).Comparison betw...In this study,a homogenization method is employed to determine the values of effective elastic modulus for BaZrO3 which is a promising candidate material for electrolyte in solid oxide fuel cell (SOFC).Comparison between the homogenization and the analysis data reveals that the difference becomes significant with increasing of porosity when upper 20%.The empire mechanic behavior in a typical planar fuel cell is evaluated using finite element method (FEM).Large stress gradient occurs in vicinity of the interface of the electrolyte and the cathode due to theirs mismatch of thermal expansion coefficient (TEC).Moreover,local processing results reveal that microscopic stress concentration around pore near the interface of the electrolyte and the cathode in the cell perhaps produces cracks which may lead to the fail of the electrolyte and the lower energy convention efficiency.展开更多
Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing e...Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing efficiency and simplified programming. Both the dual convex programming method and perimeter constraint scheme are used to optimize the 2D and 3D microstructures. Numerical results indicate that the strain energy-based method has the same effectiveness as that of homogenization method for orthotropic materials.展开更多
Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solutio...Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.展开更多
A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale met...A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.展开更多
A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding ...A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method(RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.展开更多
Y2O3: Er^3+, Yb^3+ nanoparticles were synthesized by a homogeneous precipitation method without and with different concentrations of EDTA 2Na. Upconversion luminescence spectra of the samples were studied under 980...Y2O3: Er^3+, Yb^3+ nanoparticles were synthesized by a homogeneous precipitation method without and with different concentrations of EDTA 2Na. Upconversion luminescence spectra of the samples were studied under 980 nm laser excitation. The results of XRD showed that the obtained Y2O3:Er^3+,Yb^3+ nanoparticles were of a cubic structure. The average crystallite sizes calculated were in the range of 28-40 nm. Green and red upconversion emission were observed, and attributed to ^2H11/2,^4S3/2→^4I15/2 and ^4F9/2→^4I15/2 transitions of the ion, respectively. The ratio of the intensity of green emission to that of red emission drastically changed with a change in the EDTA 2Na concentration. In the sample synthesized without EDTA, the relative intensity of the green emission was weaker than that of the red emission. The relative intensities of green emission increased with the increased amount of EDTA 2Na used. The possible upconversion luminescence mechanisms were discussed.展开更多
In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which...In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.展开更多
This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method (IFM) and the homoge...This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method (IFM) and the homogenized initial system method (HISM). In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods.展开更多
The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-sc...The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.展开更多
The fuel-air cloud resulting from an accidental discharge event is normally irregular in shape and varying in concentration. Performance of dispersion simulations using the computational fluid dynamics (CFD)-based t...The fuel-air cloud resulting from an accidental discharge event is normally irregular in shape and varying in concentration. Performance of dispersion simulations using the computational fluid dynamics (CFD)-based tool FLACS can get an uneven and irregular cloud. For the performance of gas explosion study with FLACS, the equivalent stoichiometric fuel-air cloud concept is widely applied to get a representative distribution of explosion loads. The Q9 cloud model that is employed in FLACS is an equivalent fuel-air cloud representation, in which the laminar burning velocity with first order SL and volume expansion ratio are taken into consideration. However, during an explosion in congested areas, the main part of the combustion involves turbulent flame propagation. Hence, to give a more reasonable equivalent fuel-air size, the turbulent burning velocity must be taken into consideration. The paper presents a new equivalent cloud method using the turbulent burning velocity, which is described as a function of SL, deduced from the TNO multi- energy method.展开更多
The (G'/G, 1/G)-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the (G'/G)-expansion method proposed recently, is present...The (G'/G, 1/G)-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the (G'/G)-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.展开更多
Hydroxyapatite whilkers were prepared by the homogeneousprecipitation method. Soluble calci- um ion and phosphate ion wereused as initial materials, they were refluxed respectively at 85 deg.C, 90 deg. C and 95 deg. C...Hydroxyapatite whilkers were prepared by the homogeneousprecipitation method. Soluble calci- um ion and phosphate ion wereused as initial materials, they were refluxed respectively at 85 deg.C, 90 deg. C and 95 deg. C for various lengths of time. A properprecipitation agent was selected to control the releasing speed ofions in the system; it induced the hydroxyapatite crystal to grow indesired way. The pH each solutions were mea- sured continuouslyduring the reaction.展开更多
In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.W...In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.We also add the average classification as an approximate solution to the nonlinear operator part,without requiring to cope with nonlinear equations to resolve the weighting coefficients because these constructions are owned many conditions about the true solution.The unknown boundary conditions and the result can be retrieved straightway by coping with a small-scale linear system when the outcome is described by a new 3D homogenization function,which is right to find the numerical solutions with the errors smaller than the level of noise being put on the over-specified Neumann conditions on the bottom of the cuboid.Besides,note that the new homogenization functions method(HFM)does not require dealing with the regularization and highly nonlinear equations.The robustness and accuracy of the HFM are verified by comparing the recovered results of several numerical experiments to the exact solutions in the entire region,even though a very large level of noise 50%is imposed on the over specified Neumann conditions.The numerical errors of our scheme are in the order of O(10^(−1))-O(10^(−4)).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
By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential...By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.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
文摘With the development of satellite structure technology, more and more design parameters will affect its structural performance. It is desirable to obtain an optimal structure design with a minimum weight, including optimal configuration and sizes. The present paper aims to describe an optimization analysis for a satellite structure, including topology optimization and size optimization. Based on the homogenization method, the topology optimization is carried out for the main supporting frame of service module under given constraints and load conditions, and then the sensitivity analysis is made of 15 structural size parameters of the whole satellite and the optimal sizes are obtained. The numerical result shows that the present optimization design method is very effective.
文摘The objective of this study was to determine the overall thermal elastic behavior of composites by homogenization method. The results obtained were compared with those by other well-known methods such as mean field method , self-consistent method and etc. A good agreement is achieved and thus a reliable nwthod for predicting the effective behavior of composite is presented. It is very easy to extend this method to multi-phase composite. The materiol properties determined here include elastic modulus, Poisson ratio and thermal expansion coefficient (CTE).
基金Funded by National High-Tech Foundation(State 863 Plan)(No.2003AA305920)
文摘The objective of this study is to investigate the local stress fluctuation in two-phase composite by homogenization method. The composite was described by homogeneous macro structure and periodical micro structure sinudtaneously and the mechanical response of the composite can be described based on both macro and micro dimensional scales. Micro and mocro homogenization problems can be formulated. The effective material properties of the composite and the local stress field in the microstructure of the composite can be determined by solving these equntions.
基金the support by the Medicine and Engineering Project
文摘In this study,a homogenization method is employed to determine the values of effective elastic modulus for BaZrO3 which is a promising candidate material for electrolyte in solid oxide fuel cell (SOFC).Comparison between the homogenization and the analysis data reveals that the difference becomes significant with increasing of porosity when upper 20%.The empire mechanic behavior in a typical planar fuel cell is evaluated using finite element method (FEM).Large stress gradient occurs in vicinity of the interface of the electrolyte and the cathode due to theirs mismatch of thermal expansion coefficient (TEC).Moreover,local processing results reveal that microscopic stress concentration around pore near the interface of the electrolyte and the cathode in the cell perhaps produces cracks which may lead to the fail of the electrolyte and the lower energy convention efficiency.
基金National Natural Science Foundation of China (90405016, 10676028) 973 Program (2006CB601205)+1 种基金 863 Project (2006AA04Z 122) Aeronautical Science Foundation (04B53080, 2006ZA 53006) and 111 Project (B07050)
文摘Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing efficiency and simplified programming. Both the dual convex programming method and perimeter constraint scheme are used to optimize the 2D and 3D microstructures. Numerical results indicate that the strain energy-based method has the same effectiveness as that of homogenization method for orthotropic materials.
基金supported by the National Natural Science Foundation of China (Grants 11332004, 11572071)the Program for Changjiang Scholars and Innovative Research Team in Dalian University of Technology (PCSIRT)+2 种基金111 Project (Grant B14013)the CATIC Industrial Production Projects (Grant CXY2013DLLG32)the Fundamental Research Funds for the Central Universities (Grant DUT15ZD101)
文摘Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.
基金Supported by the National Natural Science Foundation of China(51105195,51075204)the Aeronautical Science Foundation of China(2011ZB52024)
文摘A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.
基金Project supported by the Desenvolvimento e Aplicaoes de Mtodos Matemticos de Homogeneizaao(CAPES)(No.88881.030424/2013-01)the Homogeneizao Reiterada Aplicada a Meios Dependentes de Múltiplas Escalas con Contato Imperfeito Entre as Fases(CNPq)(Nos.450892/2016-6and 303208/2014-7)the Caracterizacin de Propiedades Efectivas de Tejidos Biolgicos Sanos y Cancerosos(CONACYT)(No.2016–01–3212)
文摘A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method(RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.
基金the Foundation for the University by Educational Department of Liaoning (05L337)Key Laboratory of Rare Earth Chemistry and Physics, Chinese Academy of Sciences
文摘Y2O3: Er^3+, Yb^3+ nanoparticles were synthesized by a homogeneous precipitation method without and with different concentrations of EDTA 2Na. Upconversion luminescence spectra of the samples were studied under 980 nm laser excitation. The results of XRD showed that the obtained Y2O3:Er^3+,Yb^3+ nanoparticles were of a cubic structure. The average crystallite sizes calculated were in the range of 28-40 nm. Green and red upconversion emission were observed, and attributed to ^2H11/2,^4S3/2→^4I15/2 and ^4F9/2→^4I15/2 transitions of the ion, respectively. The ratio of the intensity of green emission to that of red emission drastically changed with a change in the EDTA 2Na concentration. In the sample synthesized without EDTA, the relative intensity of the green emission was weaker than that of the red emission. The relative intensities of green emission increased with the increased amount of EDTA 2Na used. The possible upconversion luminescence mechanisms were discussed.
基金supported by the National Natural Science Foundation of China (No.10461005)the Ph.D.Programs Foundation of Ministry of Education of China (No.20070128001)the High Education Science Research Program of Inner Mongolia (No.NJZY08057)
文摘In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.
基金Hunan Provincial Natural Science Foundation Under Grant No.02JJY2085
文摘This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method (IFM) and the homogenized initial system method (HISM). In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods.
基金supported by the National Natural Science Foundation of China(Nos.10801042 and 11171257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20104410120001)
文摘The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.
文摘The fuel-air cloud resulting from an accidental discharge event is normally irregular in shape and varying in concentration. Performance of dispersion simulations using the computational fluid dynamics (CFD)-based tool FLACS can get an uneven and irregular cloud. For the performance of gas explosion study with FLACS, the equivalent stoichiometric fuel-air cloud concept is widely applied to get a representative distribution of explosion loads. The Q9 cloud model that is employed in FLACS is an equivalent fuel-air cloud representation, in which the laminar burning velocity with first order SL and volume expansion ratio are taken into consideration. However, during an explosion in congested areas, the main part of the combustion involves turbulent flame propagation. Hence, to give a more reasonable equivalent fuel-air size, the turbulent burning velocity must be taken into consideration. The paper presents a new equivalent cloud method using the turbulent burning velocity, which is described as a function of SL, deduced from the TNO multi- energy method.
基金Supported by the International Cooperation and Exchanges Foundation of Henan Province (084300510060)the Youth Science Foundation of Henan University of Science and Technology of China (2008QN026)
文摘The (G'/G, 1/G)-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the (G'/G)-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.
基金Funded by Nature Science Foundation of Hubei Provence (No.99J076)
文摘Hydroxyapatite whilkers were prepared by the homogeneousprecipitation method. Soluble calci- um ion and phosphate ion wereused as initial materials, they were refluxed respectively at 85 deg.C, 90 deg. C and 95 deg. C for various lengths of time. A properprecipitation agent was selected to control the releasing speed ofions in the system; it induced the hydroxyapatite crystal to grow indesired way. The pH each solutions were mea- sured continuouslyduring the reaction.
基金This work was financially supported by the National United University[Grant Numbers T110M20600].
文摘In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.We also add the average classification as an approximate solution to the nonlinear operator part,without requiring to cope with nonlinear equations to resolve the weighting coefficients because these constructions are owned many conditions about the true solution.The unknown boundary conditions and the result can be retrieved straightway by coping with a small-scale linear system when the outcome is described by a new 3D homogenization function,which is right to find the numerical solutions with the errors smaller than the level of noise being put on the over-specified Neumann conditions on the bottom of the cuboid.Besides,note that the new homogenization functions method(HFM)does not require dealing with the regularization and highly nonlinear equations.The robustness and accuracy of the HFM are verified by comparing the recovered results of several numerical experiments to the exact solutions in the entire region,even though a very large level of noise 50%is imposed on the over specified Neumann conditions.The numerical errors of our scheme are in the order of O(10^(−1))-O(10^(−4)).
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.
文摘By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.
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.