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
Nanocrystalline Gd3Ga5O12:Eu3+ with cubic phase was prepared by a urea homogeneous precipitation method. X-ray diffraction (XRD), field emission scanning electron microscopy (SEM), Fourier transform infrared spectrosc...Nanocrystalline Gd3Ga5O12:Eu3+ with cubic phase was prepared by a urea homogeneous precipitation method. X-ray diffraction (XRD), field emission scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FT-IR), thermo-gravimetric and differential thermal analysis (TG-DTA) and photoluminescence spectra were used to characterize the samples. The effects of the initial solution pH value and urea content on the structure of the sample were studied. The XRD results show that pure phase Gd3Ga5O12 can be obtained at pH =6 and pH =8 of the initial solution. The average crystallite size can be calculated as in the range of 24~33 nm. The average crystallite size decreases with increasing molar ratio of urea to metal ion. The results of excitation spectra and emission spectra show that the emission peaks are ascribed to 5D0→7FJ transitions of Eu3+, and the magnetic dipole transition originated from 5D0 →7F1 of Eu3+ is the strongest; the broad excitation bands belong to change transfer band of Eu?O and the host absorption of Gd3Ga5O12. An efficient energy transfer occurs from Gd3+ to Eu3+.展开更多
A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbala...A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations.展开更多
Homogeneous and dispersed Y3 Al5 O12（yttrium aluminum garnet,YAG） nanopowders were synthesized via a homogeneous co-precipitation method from the mixed solutions of yttrium nitrate,aluminum nitrate and a small amoun...Homogeneous and dispersed Y3 Al5 O12（yttrium aluminum garnet,YAG） nanopowders were synthesized via a homogeneous co-precipitation method from the mixed solutions of yttrium nitrate,aluminum nitrate and a small amount of ammonium sulfate using hot urea as the precipitant.The method has the superiorities that co-precipitation of cations is ensured and continuous decomposition of the hot urea is achieved to obtain the narrow size distribution particles.The addition of small amount of ammonium sulfate surfactant,although has no influence on YAG garnet phase formation,has significant effect on dispersion,particles distribution and sinterability of the resultant YAG and Yb：YAG powders.Compared with the undoped sample,the green body of Yb：YAG doped with ammonium sulfate has higher total shrinkage,linear shrinkage rate and relative density through sintering at 1600 ℃.The resultant Yb：YAG powders can be sintered into transparent ceramics at 1700 ℃ through vacuum sintering.The influence of the sulfate ions on characteristics of the resultant powders was thoroughly studied.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
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 present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several ki...In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact（new） solutions of the generalized KdV equation are obtained.展开更多
The activity of the Ab-bound enzyme(HRP)changed after immunochemical reaction,and can be indicated by a sensitive fluorimetric kinetic method.The finding set the stage for developing sensitive homogeneous immunoassay....The activity of the Ab-bound enzyme(HRP)changed after immunochemical reaction,and can be indicated by a sensitive fluorimetric kinetic method.The finding set the stage for developing sensitive homogeneous immunoassay.AFP was measured as an example.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
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
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 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
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
Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and...Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.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
In this article, the analytical homogenization method of periodic discrete media（HPDM）and the numerical condensed wave finite element method（CWFEM） are employed to study the longitudinal and transverse vibrations ...In this article, the analytical homogenization method of periodic discrete media（HPDM）and the numerical condensed wave finite element method（CWFEM） are employed to study the longitudinal and transverse vibrations of framed structures. The valid frequency range of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. The relative error of the wavenumber by the HPDM compared to that by the CWFEM is illustrated in functions of frequency and scale ratio. A parametric study on the thickness of the structure is carried out where the dispersion relation and the relative error are given for three different thicknesses. The dynamics of a finite structure such as natural frequency and forced response are also investigated using the HPDM and the CWFEM.展开更多
A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinfo...A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous matrix.This framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact conditions.The mathematical formulation of the local problems and the effective coefficients are presented by the AHM.The local problems obtained from the AHM are solved by the FEM,which is denoted as the SAFEM.The numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.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
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
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financially supported by the Science and Technology Research Project of Department of Education of Liaoning Province,China(No.L2011063)
文摘Nanocrystalline Gd3Ga5O12:Eu3+ with cubic phase was prepared by a urea homogeneous precipitation method. X-ray diffraction (XRD), field emission scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FT-IR), thermo-gravimetric and differential thermal analysis (TG-DTA) and photoluminescence spectra were used to characterize the samples. The effects of the initial solution pH value and urea content on the structure of the sample were studied. The XRD results show that pure phase Gd3Ga5O12 can be obtained at pH =6 and pH =8 of the initial solution. The average crystallite size can be calculated as in the range of 24~33 nm. The average crystallite size decreases with increasing molar ratio of urea to metal ion. The results of excitation spectra and emission spectra show that the emission peaks are ascribed to 5D0→7FJ transitions of Eu3+, and the magnetic dipole transition originated from 5D0 →7F1 of Eu3+ is the strongest; the broad excitation bands belong to change transfer band of Eu?O and the host absorption of Gd3Ga5O12. An efficient energy transfer occurs from Gd3+ to Eu3+.
基金Supported by the National Natural Science Foundation of China under Grant No. 11071209the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province under Grant No. 10KJBll0011
文摘A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations.
基金National Natural Science Foundation of China(51602042,51602045)the Fundamental Research Funds for the Central Universities(N162304004,N162304013)+1 种基金the Natural Science Foundation of Hebei Province(E2017501082)the Scientific Research Foundation of Northeastern University at Qinhuangdao(XNB201715)
文摘Homogeneous and dispersed Y3 Al5 O12（yttrium aluminum garnet,YAG） nanopowders were synthesized via a homogeneous co-precipitation method from the mixed solutions of yttrium nitrate,aluminum nitrate and a small amount of ammonium sulfate using hot urea as the precipitant.The method has the superiorities that co-precipitation of cations is ensured and continuous decomposition of the hot urea is achieved to obtain the narrow size distribution particles.The addition of small amount of ammonium sulfate surfactant,although has no influence on YAG garnet phase formation,has significant effect on dispersion,particles distribution and sinterability of the resultant YAG and Yb：YAG powders.Compared with the undoped sample,the green body of Yb：YAG doped with ammonium sulfate has higher total shrinkage,linear shrinkage rate and relative density through sintering at 1600 ℃.The resultant Yb：YAG powders can be sintered into transparent ceramics at 1700 ℃ through vacuum sintering.The influence of the sulfate ions on characteristics of the resultant powders was thoroughly studied.
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Foundation item： Supported by the National Natural Science Foundation of China（10671182） Supported by the Foundation and Frontier Technology Research of Henan（082300410060）
文摘In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact（new） solutions of the generalized KdV equation are obtained.
文摘The activity of the Ab-bound enzyme(HRP)changed after immunochemical reaction,and can be indicated by a sensitive fluorimetric kinetic method.The finding set the stage for developing sensitive homogeneous immunoassay.AFP was measured as an example.
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 (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.
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.
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.
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 Nature Science Foundation of China(10371070)Supported by the Nature Science Foundation of Educational Committee of Liaoning Province(2021401157)
文摘Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.
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.
文摘In this article, the analytical homogenization method of periodic discrete media（HPDM）and the numerical condensed wave finite element method（CWFEM） are employed to study the longitudinal and transverse vibrations of framed structures. The valid frequency range of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. The relative error of the wavenumber by the HPDM compared to that by the CWFEM is illustrated in functions of frequency and scale ratio. A parametric study on the thickness of the structure is carried out where the dispersion relation and the relative error are given for three different thicknesses. The dynamics of a finite structure such as natural frequency and forced response are also investigated using the HPDM and the CWFEM.
基金Project supported by the National Council of Humanities,Sciences,and Technologies of Mexico(Nos.CF-2023-G-792 and CF-2023-G-1458)the National Council for Scientific and Technological Development of Brazil(No.09/2023)the Research on Productivity of Brazil(No.307188/2023-0)。
文摘A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous matrix.This framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact conditions.The mathematical formulation of the local problems and the effective coefficients are presented by the AHM.The local problems obtained from the AHM are solved by the FEM,which is denoted as the SAFEM.The numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.
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.
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.
