The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurat...The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.展开更多
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These co...In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.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
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
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
A new type of displacement pile, the X-section cast-in-place concrete (XCC) pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance a...A new type of displacement pile, the X-section cast-in-place concrete (XCC) pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance and quantify the non-uniform deforma- tion effect (NUDE) of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index (CFI), and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates applica- tion of the newly developed XCC pile technique in geotechnical engineering.展开更多
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
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 the paper, the solution of Saint-Venant problem is obtained through assumption of principal stress curves by means of the equilibrium equations which were deduced in paper [1]. The results show that the speed of sh...In the paper, the solution of Saint-Venant problem is obtained through assumption of principal stress curves by means of the equilibrium equations which were deduced in paper [1]. The results show that the speed of shear approaching to zero is a(3)/y(3) and axial stress approaching to constant is a(2)/y(2).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
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
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
We study electromechanical felds in the anti-plane deformation of an infnite medium of piezoelectric materials of 6 mm symmetry with a circular cylindrical hole. The theory of electro- elastic dielectrics with electri...We study electromechanical felds in the anti-plane deformation of an infnite medium of piezoelectric materials of 6 mm symmetry with a circular cylindrical hole. The theory of electro- elastic dielectrics with electric feld gradient in the constitutive relations is used. Special attention is paid to the felds near the surface of the hole.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
In this paper, the problem of the periodic welding of an anisotropic elastic half_plane and a strip with different materials is studied. By means of the complex variable method for plane elasticity and the theory of b...In this paper, the problem of the periodic welding of an anisotropic elastic half_plane and a strip with different materials is studied. By means of the complex variable method for plane elasticity and the theory of boundary value problems for analytic function, the stress distribution is given in closed forms.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
In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, a...In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.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
基金the National Natural Science Foundation of China(No.11572210).
文摘The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.
文摘In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.
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.
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.
基金supported by the National Natural Science Foundation of China(No.51420105013)the State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology(No.SKLGDUEK1713)the Fundamental Research Funds for the Central Universities(Nos.106112017CDJXY200003 and 106112017CDJPT200001)
文摘A new type of displacement pile, the X-section cast-in-place concrete (XCC) pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance and quantify the non-uniform deforma- tion effect (NUDE) of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index (CFI), and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates applica- tion of the newly developed XCC pile technique in geotechnical engineering.
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
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.
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 the paper, the solution of Saint-Venant problem is obtained through assumption of principal stress curves by means of the equilibrium equations which were deduced in paper [1]. The results show that the speed of shear approaching to zero is a(3)/y(3) and axial stress approaching to constant is a(2)/y(2).
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.
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.
基金Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State EducationMinistry.
文摘We study electromechanical felds in the anti-plane deformation of an infnite medium of piezoelectric materials of 6 mm symmetry with a circular cylindrical hole. The theory of electro- elastic dielectrics with electric feld gradient in the constitutive relations is used. Special attention is paid to the felds near the surface of the hole.
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In this paper, the problem of the periodic welding of an anisotropic elastic half_plane and a strip with different materials is studied. By means of the complex variable method for plane elasticity and the theory of boundary value problems for analytic function, the stress distribution is given in closed forms.
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.
基金supported by the National Natural Science Foundation of China(Nos.10772106 and11072138)the Shanghai Leading Academic Discipline Project(No.S30106)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(No.20113108110005)the Natural Science Foundation Project of Shanghai(No.15ZR1416100)
文摘In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.
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.