The universal practices have been centralizing on the research of regularization to the direct boundary integal equations （DBIEs）. The character is elimination of singularities by using the simple solutions. However...The universal practices have been centralizing on the research of regularization to the direct boundary integal equations （DBIEs）. The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value （CPV） and Hadamard-finite-part （HFP） integrals are established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system.展开更多
In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem...In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.展开更多
On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials ar...On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials are obtained. Two parametersbased on material constants a_1, a_2 are used to derive the rele-vant expressions in a real variable form. Additionally, an analyticalmethod of solving the singular integral for the internal stresses isintroduced, and the corresponding result are given. If a_1=a_2=1, allthe expres- sions obtained for orthotropy can be reduced to thecorresponding ones for isotropy. Because all these expres- sions andresults can be directly used for both isotropic problems andorthotropic problems, it is convenient to use them in engineeringwith the boundary element method (BEM).展开更多
In this paper.the boundary value problems of plane problems with a simply-ormultiply-connected domain for isotropic linear visca-elosticity are first established byterms of Airy stress function F(Xu t). Secondly some ...In this paper.the boundary value problems of plane problems with a simply-ormultiply-connected domain for isotropic linear visca-elosticity are first established byterms of Airy stress function F(Xu t). Secondly some identity relations betweendisplacements and stresses for plane problems of sisco-and elasticity are discussed indetait and some meaningful conclusions are obtained As an example the deformationresponse for viscoelastic plate with a small circular hote at the center is analyzed undera uniasial uniform extension.展开更多
Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious...Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.展开更多
This paper expresses potential function of complex variable in Fabere series and the solution in closed form is provided for the plane stress problems in piezoelectric media with elliptic inclusion. It is shown from t...This paper expresses potential function of complex variable in Fabere series and the solution in closed form is provided for the plane stress problems in piezoelectric media with elliptic inclusion. It is shown from the solution that the stress, strain, electric field intensity and electric displacement in inclusion are all constant. In addition, the electromechanical behavior of piezoelectric influence at the elliptic rim of the infinite matrix with only acting mechanical or electric load is discussed with numerical examples.展开更多
Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex str...Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex stress functions and stress-intensity tactors expressed in terms of series, and to these problems disiusses three sposial cases,i.e.the cases of the crack under a uniform pressure, a uniform shear stress and the use of the dise rotating uniformly. In these cases the approximate formulas calcidating the stress-intensity factors are also presented. The calculated results shun that for the middle and.small orachs situated inside the disc and not near the external boundary,these approximate formulas give good or better approximation.展开更多
In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residu...In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual- spectrum of the operators are symmetric with respect to real axis and imaginary axis. Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state spac,3. At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.展开更多
The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cra...The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.展开更多
In this paper, the author obtains the more general displacement solutions for the isotropic plane elasticity problems. The general solution obtained in ref. [ 1 ] is merely the particular case of this paper, In compar...In this paper, the author obtains the more general displacement solutions for the isotropic plane elasticity problems. The general solution obtained in ref. [ 1 ] is merely the particular case of this paper, In comparison with ref. [1], the general solutions of this paper contain more arbitrary constants. Thus they may satisfy more boundary conditions.展开更多
By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be dire...By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which does not include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.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
The structure damage detection with spatial wavelets was approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, was investigated. The displac...The structure damage detection with spatial wavelets was approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, was investigated. The displacement response data along the parallel and perpendicular lines at different positions from the crack were analyzed with the Haar wavelet. The peak in the spatial variations of the wavelets indicates the direction of the crack. In addition, a transverse crack in a cantilever beam was also investigated in the same ways. For these problems, the different crack positions were also simulated to testify the effectiveness of the technique. All the above numerical simulations were processed by the finite element analysis code, ABACUS. The results show that the spatial wavelet is a powerful tool for damage detection, and this new technique sees wide application fields with broad prospects. (Edited author abstract) 14 Refs.展开更多
The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement a...The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region.The completeness of the eigenfunctions is then proved,providing the feasibility of using separation of variables to solve the problems.A general solution is obtained with the symplectic eigenfunction expansion theorem.展开更多
First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the gener...First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three 'harmonic functions'. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.展开更多
This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained...This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.展开更多
An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from ...An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that: (i) the stress intensify factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i.e., it is always positive, and independent of the electric loads. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.展开更多
By means of the generalized variable principle of magnetoelectroelastic solids, the plane magnetoelectroelastic solids problem was derived to Hamiltonian system. In symplectic geometry space, which consists of origina...By means of the generalized variable principle of magnetoelectroelastic solids, the plane magnetoelectroelastic solids problem was derived to Hamiltonian system. In symplectic geometry space, which consists of original variables, displacements, electric potential and magnetic potential, and their duality variables, lengthways stress, electric displacement and magnetic induction, the effective methods of separation of variables and symplectic eigenfunction expansion were applied to solve the problem. Then all the eigen-solutions and the eigen-solutions in Jordan form on eigenvalue zero can be given, and their specific physical significations were shown clearly. At last, the special solutions were presented with uniform loader, constant electric displacement and constant magnetic induction on two sides of the rectangle domain.展开更多
The first fundamental problems in the infinite plane with cracks and boundary values cyclically symmetric are considered. They are reduced to singular integral equations on a single crack, which would considerably sim...The first fundamental problems in the infinite plane with cracks and boundary values cyclically symmetric are considered. They are reduced to singular integral equations on a single crack, which would considerably simplify the process of method of solution for such problems. Some special cases are illustrated.展开更多
In this paper, the equilibrium equations on orthogonal curve coordinates made of curves of principal stresses are disscused and their properties in process of solution are presented through a simple example. Therefore...In this paper, the equilibrium equations on orthogonal curve coordinates made of curves of principal stresses are disscused and their properties in process of solution are presented through a simple example. Therefore, it is deduced that there is another way to solve problems in elasticity, i.e., by assumption of orthogonal curves of principal stresses.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10571110)the Natural Science Foundation of Shandong Province of China (No.2003ZX12)
文摘The universal practices have been centralizing on the research of regularization to the direct boundary integal equations （DBIEs）. The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value （CPV） and Hadamard-finite-part （HFP） integrals are established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system.
文摘In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.
文摘On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials are obtained. Two parametersbased on material constants a_1, a_2 are used to derive the rele-vant expressions in a real variable form. Additionally, an analyticalmethod of solving the singular integral for the internal stresses isintroduced, and the corresponding result are given. If a_1=a_2=1, allthe expres- sions obtained for orthotropy can be reduced to thecorresponding ones for isotropy. Because all these expres- sions andresults can be directly used for both isotropic problems andorthotropic problems, it is convenient to use them in engineeringwith the boundary element method (BEM).
文摘In this paper.the boundary value problems of plane problems with a simply-ormultiply-connected domain for isotropic linear visca-elosticity are first established byterms of Airy stress function F(Xu t). Secondly some identity relations betweendisplacements and stresses for plane problems of sisco-and elasticity are discussed indetait and some meaningful conclusions are obtained As an example the deformationresponse for viscoelastic plate with a small circular hote at the center is analyzed undera uniasial uniform extension.
文摘Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.
文摘This paper expresses potential function of complex variable in Fabere series and the solution in closed form is provided for the plane stress problems in piezoelectric media with elliptic inclusion. It is shown from the solution that the stress, strain, electric field intensity and electric displacement in inclusion are all constant. In addition, the electromechanical behavior of piezoelectric influence at the elliptic rim of the infinite matrix with only acting mechanical or electric load is discussed with numerical examples.
文摘Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex stress functions and stress-intensity tactors expressed in terms of series, and to these problems disiusses three sposial cases,i.e.the cases of the crack under a uniform pressure, a uniform shear stress and the use of the dise rotating uniformly. In these cases the approximate formulas calcidating the stress-intensity factors are also presented. The calculated results shun that for the middle and.small orachs situated inside the disc and not near the external boundary,these approximate formulas give good or better approximation.
基金supported by the National Natural Science Foundation of China under Grant No.10562002the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070126002+1 种基金the Natural Science Foundation of Inner Mongolia under Grant No.200508010103the Inner Mongolia University Scientific Research Starting Foundation for Talented Scholars under Grant No.207066
文摘In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual- spectrum of the operators are symmetric with respect to real axis and imaginary axis. Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state spac,3. At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.
基金Project supported by the Science Fund of the Chinese Academy of Sciences
文摘The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.
文摘In this paper, the author obtains the more general displacement solutions for the isotropic plane elasticity problems. The general solution obtained in ref. [ 1 ] is merely the particular case of this paper, In comparison with ref. [1], the general solutions of this paper contain more arbitrary constants. Thus they may satisfy more boundary conditions.
文摘By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which does not include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.
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.
基金The project supported by the National Natural Science Foundation of China
文摘The structure damage detection with spatial wavelets was approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, was investigated. The displacement response data along the parallel and perpendicular lines at different positions from the crack were analyzed with the Haar wavelet. The peak in the spatial variations of the wavelets indicates the direction of the crack. In addition, a transverse crack in a cantilever beam was also investigated in the same ways. For these problems, the different crack positions were also simulated to testify the effectiveness of the technique. All the above numerical simulations were processed by the finite element analysis code, ABACUS. The results show that the spatial wavelet is a powerful tool for damage detection, and this new technique sees wide application fields with broad prospects. (Edited author abstract) 14 Refs.
基金supported by the National Natural Science Foundation of China(No.10962004)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20070126002)the Natural Science Foundation of Inner Mongolia of China(No.20080404MS0104)
文摘The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region.The completeness of the eigenfunctions is then proved,providing the feasibility of using separation of variables to solve the problems.A general solution is obtained with the symplectic eigenfunction expansion theorem.
文摘First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three 'harmonic functions'. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.
文摘This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.
文摘An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that: (i) the stress intensify factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i.e., it is always positive, and independent of the electric loads. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.
基金Project supported by the National Natural Science Foundation of China (No.10172021)
文摘By means of the generalized variable principle of magnetoelectroelastic solids, the plane magnetoelectroelastic solids problem was derived to Hamiltonian system. In symplectic geometry space, which consists of original variables, displacements, electric potential and magnetic potential, and their duality variables, lengthways stress, electric displacement and magnetic induction, the effective methods of separation of variables and symplectic eigenfunction expansion were applied to solve the problem. Then all the eigen-solutions and the eigen-solutions in Jordan form on eigenvalue zero can be given, and their specific physical significations were shown clearly. At last, the special solutions were presented with uniform loader, constant electric displacement and constant magnetic induction on two sides of the rectangle domain.
文摘The first fundamental problems in the infinite plane with cracks and boundary values cyclically symmetric are considered. They are reduced to singular integral equations on a single crack, which would considerably simplify the process of method of solution for such problems. Some special cases are illustrated.
文摘In this paper, the equilibrium equations on orthogonal curve coordinates made of curves of principal stresses are disscused and their properties in process of solution are presented through a simple example. Therefore, it is deduced that there is another way to solve problems in elasticity, i.e., by assumption of orthogonal curves of principal stresses.
