This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara...This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.展开更多
The optical potential ambiguity is a long-standing problem in the analysis of elastic scattering data.For a specific collid-ing system,ambiguous potential families can lead to different behaviors in the nearside and f...The optical potential ambiguity is a long-standing problem in the analysis of elastic scattering data.For a specific collid-ing system,ambiguous potential families can lead to different behaviors in the nearside and farside scattering components.By contrast,the envelope method can decompose the experimental data into two components with negative and positive deflection angles,respectively.Hence,a question arises as to whether the comparison between the calculated nearside(or farside)component and the derived positive-deflection-angle(or negative-deflection-angle)component can help analyze the potential ambiguity problem.In this study,we conducted a trial application of the envelope method to the potential ambiguity problem.The envelope method was improved by including uncertainties in the experimental data.The colliding systems of 16O+28Si at 215.2 MeV and 12C+12C at 1016 MeV were considered in the analyses.For each colliding system,the angular distribution experimental data were described nearly equally well by two potential sets,one of which is“surface transpar-ent”and the other is refractive.The calculated angular distributions were decomposed into nearside and farside scattering components.Using the improved envelope method,the experimental data were decomposed into the positive-deflection-angle and negative-deflection-angle components,which were then compared with the calculated nearside and farside components.The capability of the envelope method to analyze the potential ambiguities was also discussed.展开更多
In this paper, an improved interpolating moving least-square （IIMLS） method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker 5 function. The weight function used in the II...In this paper, an improved interpolating moving least-square （IIMLS） method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker 5 function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. The number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square （MLS） approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin （IIEFG） method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin （EFG） method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.展开更多
The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （B...The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （BEFM）, combining the boundary integral equation （BIE） method with the IMLS method, the improved boundary element-free method （IBEFM） for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker ~ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.展开更多
In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This st...In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.展开更多
In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-f...In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-free Galerkin （ICVEFG） method for two-dimensional potential problems, is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square （CVMLS） approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.展开更多
In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also con...In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.展开更多
Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential proble...Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.展开更多
In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the d...In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the discrete Korn＇s second inequality valid.In this paper,a triangular element is presented.We prove that this element is locking-free,the discrete Korn＇s second inequality holds and the convergence order is two.展开更多
The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so t...The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.展开更多
In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorp...In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorphic property and exponential stability of the semigroups associated with these systems via inclusion relation of the domains of A and B.展开更多
The problems of equilibrium of an elastic half-plane with loads on some intervals of the boundary and zero displacements on its other parts are discussed. The solutions of such problems are expressed in terms of integ...The problems of equilibrium of an elastic half-plane with loads on some intervals of the boundary and zero displacements on its other parts are discussed. The solutions of such problems are expressed in terms of integrals by reducing them to Riemann boundary value problems. The analytic expressions of the solutions are obtained in cases of uniform loads. In particular, the solution is written in detail for the important case when uniform pressure is given on a single interval or two equal intervals.展开更多
We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by usin...We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.展开更多
The experiments were carried out under the conditions of controlled soil water potential in a greenhouse. The effects of water stress on tissue elasticity were studied in 1 - 3 year-old seedlings Pinus tabulaeformis, ...The experiments were carried out under the conditions of controlled soil water potential in a greenhouse. The effects of water stress on tissue elasticity were studied in 1 - 3 year-old seedlings Pinus tabulaeformis, Platycladus orientalis, Quercus variabilis, Acer truncatum , Robinia psendoacacia, Fraxinus americana , Amorpha fruticosa, Hip-pophea rahmnoides and Cotinus coggygria ,using the pressure-volume method. Tissue elasticity was characterized using graphs of the modulus of elasticity plotted as a function of turgor pressure and maximum values of the elastic modulus. Changes in tissue elasticity may be an important characteristic allowing low water potentials to be reached and maintained without the development of detrimental water stress. The results show that tissue e-lasticity in needle-leaved tree species is higher than in broad-leaved tree species,but the modulus of elasticity of the tree species tend to increase following development of water stress. Increases in elastic modulus展开更多
This paper evaluates the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. It finds tha...This paper evaluates the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. It finds that the H-H interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of r ～ 6a.u. and a barrier rising at τ ≤5a.u.展开更多
In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to ...In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G3.展开更多
Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,ar...Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.展开更多
Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With th...Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With the aid of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is obtained. The solution of the mode II Griffith crack as a special case is constructed. The stress intensity factor and energy release rate have been also obtained as a direct result of the crack solution.展开更多
In this article, we focus on the eigenvalue problem of the following linear biharmonic equation in R^N：△^2u-αu＋λg（x）u=0 with u ∈H^2（R^N）,u≠0,N≥5Note that there are two parameters α and λ in it, which is ...In this article, we focus on the eigenvalue problem of the following linear biharmonic equation in R^N：△^2u-αu＋λg（x）u=0 with u ∈H^2（R^N）,u≠0,N≥5Note that there are two parameters α and λ in it, which is different from the usual eigenvalue problems. Here, we consider λ as an eigenvalue and seek Ior a sulble range of parameter α, which ensures that problem （＊） has a maximal eigenvalue. As the loss of strong maximum principle for our problem, we can only get the existence of non-trivial solutions, not positive solutions, in this article. As an application, by using these results, we studied also the existence of non-trivial solutions for an asymptotically linear biharmonic equation in R^N.展开更多
基金supported by the Tianjin Municipal Science and Technology Program of China(No.23JCZDJC00070)。
文摘This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.
基金This work was supported by the National Natural Science Foundation of China(Nos.12005047 and U1832105).
文摘The optical potential ambiguity is a long-standing problem in the analysis of elastic scattering data.For a specific collid-ing system,ambiguous potential families can lead to different behaviors in the nearside and farside scattering components.By contrast,the envelope method can decompose the experimental data into two components with negative and positive deflection angles,respectively.Hence,a question arises as to whether the comparison between the calculated nearside(or farside)component and the derived positive-deflection-angle(or negative-deflection-angle)component can help analyze the potential ambiguity problem.In this study,we conducted a trial application of the envelope method to the potential ambiguity problem.The envelope method was improved by including uncertainties in the experimental data.The colliding systems of 16O+28Si at 215.2 MeV and 12C+12C at 1016 MeV were considered in the analyses.For each colliding system,the angular distribution experimental data were described nearly equally well by two potential sets,one of which is“surface transpar-ent”and the other is refractive.The calculated angular distributions were decomposed into nearside and farside scattering components.Using the improved envelope method,the experimental data were decomposed into the positive-deflection-angle and negative-deflection-angle components,which were then compared with the calculated nearside and farside components.The capability of the envelope method to analyze the potential ambiguities was also discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Shanghai Leading Academic Discipline Project, China (Grant No. S30106)
文摘In this paper, an improved interpolating moving least-square （IIMLS） method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker 5 function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. The number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square （MLS） approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin （IIEFG） method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin （EFG） method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.
基金Project supported by the National Natural Science Foundation of China (Grant No 10871124)Innovation Program of Shanghai Municipal Education Commission (Grant No 09ZZ99)Shanghai Leading Academic Discipline Project (Grant No J50103)
文摘The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （BEFM）, combining the boundary integral equation （BIE） method with the IMLS method, the improved boundary element-free method （IBEFM） for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker ~ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.10902076)the Natural Science Foundation of Shanxi Province of China(Grant No.2007011009)+1 种基金the Scientific Research and Development Program of the Shanxi Higher Education Institutions(Grant No.20091131)the Doctoral Startup Foundation of Taiyuan University of Science and Technology(Grant No.200708)
文摘In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Shanghai Leading Academic Discipline Project, China (Grant No. S30106)the Innovation Fund Project for Graduate Student of Shanghai University,China (Grant No. SHUCX112359)
文摘In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-free Galerkin （ICVEFG） method for two-dimensional potential problems, is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square （CVMLS） approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.
文摘In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11102125)
文摘Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.
文摘In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the discrete Korn＇s second inequality valid.In this paper,a triangular element is presented.We prove that this element is locking-free,the discrete Korn＇s second inequality holds and the convergence order is two.
文摘The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.
文摘In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorphic property and exponential stability of the semigroups associated with these systems via inclusion relation of the domains of A and B.
文摘The problems of equilibrium of an elastic half-plane with loads on some intervals of the boundary and zero displacements on its other parts are discussed. The solutions of such problems are expressed in terms of integrals by reducing them to Riemann boundary value problems. The analytic expressions of the solutions are obtained in cases of uniform loads. In particular, the solution is written in detail for the important case when uniform pressure is given on a single interval or two equal intervals.
文摘We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.
文摘The experiments were carried out under the conditions of controlled soil water potential in a greenhouse. The effects of water stress on tissue elasticity were studied in 1 - 3 year-old seedlings Pinus tabulaeformis, Platycladus orientalis, Quercus variabilis, Acer truncatum , Robinia psendoacacia, Fraxinus americana , Amorpha fruticosa, Hip-pophea rahmnoides and Cotinus coggygria ,using the pressure-volume method. Tissue elasticity was characterized using graphs of the modulus of elasticity plotted as a function of turgor pressure and maximum values of the elastic modulus. Changes in tissue elasticity may be an important characteristic allowing low water potentials to be reached and maintained without the development of detrimental water stress. The results show that tissue e-lasticity in needle-leaved tree species is higher than in broad-leaved tree species,but the modulus of elasticity of the tree species tend to increase following development of water stress. Increases in elastic modulus
基金supported in part by the National Natural Science Foundation of China (Grant No 10575024)in part by the Division of Nuclear Physics, Department of Energy (Grant No DE-AC05-00OR22725) managed by UT-Battelle, LLC
文摘This paper evaluates the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. It finds that the H-H interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of r ～ 6a.u. and a barrier rising at τ ≤5a.u.
文摘In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G3.
基金NASI (National Academy of Sciences, India) for providing financial support
文摘Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.
基金Project supported by the National Natural Science Foundation of China(Grant No.10761005)the Natural Science Foundation of Inner Mongolia of China(Grant Nos.2009MS0102,2009BS0101 and 2009BS0104)+1 种基金the Natural Science Foundation of Inner Mongolia Normal University(Grant No.QN07034)the Natural Science Foundation of Inner Mongolia Department of Public Education(Grant No.NJzy08024)
文摘Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With the aid of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is obtained. The solution of the mode II Griffith crack as a special case is constructed. The stress intensity factor and energy release rate have been also obtained as a direct result of the crack solution.
基金supported by the National Science Foundation of China (11071245)
文摘In this article, we focus on the eigenvalue problem of the following linear biharmonic equation in R^N：△^2u-αu＋λg（x）u=0 with u ∈H^2（R^N）,u≠0,N≥5Note that there are two parameters α and λ in it, which is different from the usual eigenvalue problems. Here, we consider λ as an eigenvalue and seek Ior a sulble range of parameter α, which ensures that problem （＊） has a maximal eigenvalue. As the loss of strong maximum principle for our problem, we can only get the existence of non-trivial solutions, not positive solutions, in this article. As an application, by using these results, we studied also the existence of non-trivial solutions for an asymptotically linear biharmonic equation in R^N.
