We review theoretical results on anti-plane motions of polarized ceramics based on the linear theory of piezoelectricity. Solutions to dynamic problems of the propagation of bulk acoustic waves （BAW） and surface aco...We review theoretical results on anti-plane motions of polarized ceramics based on the linear theory of piezoelectricity. Solutions to dynamic problems of the propagation of bulk acoustic waves （BAW） and surface acoustic waves （SAW）, vibrations of finite bodies, and applications to various piezoelectric devices including piezoelectric waveguides, resonators, mass sensors, fluid sensors, actuators, nondestructive evaluation, power harvesters （generators）, transformers, and power transmission through an elastic wall by acoustic waves are discussed. Complications due to material inhomogeneity, initial stress, electromagnetic coupling, electric field gradient and semiconduction are also discussed. The paper cites 82 references.展开更多
The present paper is exposed theoretically to the influence on the dynamic stress intensity factor （DSIF） in the piezoelectric bi-materials model with two symmet- rically permeable interracial cracks near the edges ...The present paper is exposed theoretically to the influence on the dynamic stress intensity factor （DSIF） in the piezoelectric bi-materials model with two symmet- rically permeable interracial cracks near the edges of a circular cavity, subjected to the dynamic incident anti-plane shearing wave （SH-wave）. An available theoretical method to dynamic analysis in the related research field is provided. The formulations are based on Green＇s function method. The DSIFs at the inner and outer tips of the left crack are obtained by solving the boundary value problems with the conjunction and crack- simulation technique. The numerical results are obtained by the FORTRAN language program and plotted to show the influence of the variations of the physical parameters, the structural geometry, and the wave frequencies of incident wave on the dimensionless DSIFs. Comparisons with previous work and between the inner and outer tips are con- cluded.展开更多
The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with c...The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with contour integral of the Laplace inverse transform specifically,the general analytical expressions of the soil displacement and stress are obtained in the time domain,respectively.And the numerical solutions of the problem computed by analytical expressions are presented.In the time domain,the dynamic responses of the infinite elastic soil are analyzed,and the calculation results are compared with those from numerical inversion proposed by Durbin and the static results.One observes good agreement between analytical and numerical inversion results,lending the further support to the method presented.Finally,some valuable shear wave propagation laws are gained: the displacement of the soil remains zero before the wave arrival,and after the shear wave arrival,the stress and the displacement at this point increase abruptly,then reduce and tend to the static value gradually at last.The wave attenuates along the radial,therefore the farther the wave is from the source,the smaller the stress and the displacement are,and the stress and the displacement are just functions of the radial distance from the axis.展开更多
Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-pla...Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.展开更多
For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions （or between the derivatives of eig...For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions （or between the derivatives of eigenfunctions） of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors （SIFs）, so any order SIF can be extracted based on a certain known solution of displacement （an analytic result or a numerical result）. Many numerical examples based on the finite element method of lines （FEMOL） show that the present method is very powerful and efficient.展开更多
Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface condi...Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface conditions. Taking the advantage of the knowledge of the variation forms of the eigen-functions, a series of numerical techniques are proposed to simplify the computation and speed up the convergence rare of the inverse iteration. A number of numerical examples are given to demonstrate the excellent accuracy, efficiency and reliability of the proposed approach.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
Anti-plane electroelastic problems are studied by the Trefftz boundary element method （BEM） in this paper. The Trefftz BEM is based on a weighted residual formulation and indirect boundary approach. In particular th...Anti-plane electroelastic problems are studied by the Trefftz boundary element method （BEM） in this paper. The Trefftz BEM is based on a weighted residual formulation and indirect boundary approach. In particular the point-collocation and Galerkin techniques, in which the basic unknowns are the retained expansion coefficients in the system of complete equations, are considered. Furthermore, special Trefftz functions and auxiliary functions which satisfy exactly the specified boundary conditions along the slit boundaries are also used to derive a special purpose element with local defects. The path-independent integral is evaluated at the tip of a crack to determine the energy release rate for a mode Ⅲ fracture problem. In final, the accuracy and efficiency of the Trefftz boundary element method are illustrated by an example and the comparison is made with other methods.展开更多
The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By usin...The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.展开更多
Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four Cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving ...Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four Cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate we obtained, The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate h --> infinity.展开更多
The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors ...The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric displacement around the crack tip are dependent on the speed of the Griffith crack as well as the material coefficients. When the two piezoelectric materials are identical, the present result will be reduced to the result far the problem of an anti-plane moving Griffith crack in homogeneous piezoelectric materials.展开更多
This paper contains a theoretical formulations and solutions of multiple cracks sub- jected to an anti-plane time-harmonic point load in a functionally graded strip. The distributed dislocation technique is used to co...This paper contains a theoretical formulations and solutions of multiple cracks sub- jected to an anti-plane time-harmonic point load in a functionally graded strip. The distributed dislocation technique is used to construct integral equations for a functionally graded material strip weakened by several cracks under anti-plane time-harmonic load. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to evaluate the stress intensity factor and strain energy density factors （SEDFs） for multiple cracks with differ- ent configurations. Numerical calculations are presented to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded strip with multiple curved cracks.展开更多
The transient and static anti-plane problem of a rigid line inclusion pulled out from an elastic medium is studied.The singular integral equation method is used to solve the stress field.Under the static load,the stre...The transient and static anti-plane problem of a rigid line inclusion pulled out from an elastic medium is studied.The singular integral equation method is used to solve the stress field.Under the static load,the stress intensity factor(SIF)at the inclusion tips increases with the medium length.The problem becomes equivalent to an inclusion in a medium with an infinite length when the length of the medium is 3.5times longer than that of the inclusion.However,under the transient load,the maximum value of the SIF occurs when the medium length is about two times the inclusion length.Besides,the relation between the pull-out force and the anti-plane displacement is given.The conclusions are useful in guiding the design of fiber reinforced composite materials.展开更多
Based on the theoretical representation of piezoelectric quasicrystal,a generalized dynamic model is built to represent the transmission of wave aspects in surface acoustic pulse nano-devices.Surface elasticity,surfac...Based on the theoretical representation of piezoelectric quasicrystal,a generalized dynamic model is built to represent the transmission of wave aspects in surface acoustic pulse nano-devices.Surface elasticity,surface piezoelectricity,and surface permittivity help to include the surface effect,which equals additional thin sheets.It is shown that,under certain assumptions,this generalized dynamic model may be simplified to a few classical examples that are appropriate for both macro and nano-scale applications.In the current work,surface piezoelectricity is used to develop a theoretical model for shear horizontal(SH)waves where it contains the surface piezoelectricity theory and a linear spring model to quantitatively and qualitatively explore SH waves in an orthotropic piezoelectric quasicrystal layer overlying an elastic framework(Model I),a piezoelectric quasi-crystal nano substrate,and an orthotropic piezoelectric quasicrystal half-space(Model II).The theoretical model stimulates the numerical results,which establish the critical thickness.As the piezoelectric layer’s thickness gets closer to nanometres,surface energy must be included when analyzing dispersion properties.Furthermore,the effects of surface elasticity and density on wave velocity are investigated individually.The authors establish a parameter,precisely the ratio of the physical modulus along the width direction to along the direction of wave travel.The surface effect’s impact on the general char-acteristics of piezoelectric structures is seen as a spring force acting on bulk boundaries.Analytical presentation of frequency equations for both symmetric and anti-symmetric waves pertains to the case of an electrical short circuit in Model II.The project aims to analyze SH waves in orthogonal anisotropic,transversely isotropic piezoelectric layered nanostructures,providing a practical mathematical tool for surface effects analysis and adaptability to other wave types,including Rayleigh waves and acoustic surface waves.展开更多
Based on the gist of anti-planning,evaluation standards and methods of intensive land utilization were re-examined according to the inverse planning procedures.Significant role of compulsory non-development zone(simil...Based on the gist of anti-planning,evaluation standards and methods of intensive land utilization were re-examined according to the inverse planning procedures.Significant role of compulsory non-development zone(similar to the traditional"non-construction land")among the planning fruits in the intensive utilization of urban land resources and relevant index weights in the evaluation system were re-weighed.In land evaluation,relevant control indexes of compulsory non-development zone were first calculated and evaluated,healthy and sustainable development coefficients of land were obtained and regarded as the core content of the whole evaluation system.展开更多
基金the National Natural Science Foundation of China (No. 10572065) a grant from the Scienceand Technology Division of Zhejiang Province, China, under the Key Technological Initiative Program (No. 2006C14021).
文摘We review theoretical results on anti-plane motions of polarized ceramics based on the linear theory of piezoelectricity. Solutions to dynamic problems of the propagation of bulk acoustic waves （BAW） and surface acoustic waves （SAW）, vibrations of finite bodies, and applications to various piezoelectric devices including piezoelectric waveguides, resonators, mass sensors, fluid sensors, actuators, nondestructive evaluation, power harvesters （generators）, transformers, and power transmission through an elastic wall by acoustic waves are discussed. Complications due to material inhomogeneity, initial stress, electromagnetic coupling, electric field gradient and semiconduction are also discussed. The paper cites 82 references.
基金supported by the National Natural Science Foundation of China(No.51108113)
文摘The present paper is exposed theoretically to the influence on the dynamic stress intensity factor （DSIF） in the piezoelectric bi-materials model with two symmet- rically permeable interracial cracks near the edges of a circular cavity, subjected to the dynamic incident anti-plane shearing wave （SH-wave）. An available theoretical method to dynamic analysis in the related research field is provided. The formulations are based on Green＇s function method. The DSIFs at the inner and outer tips of the left crack are obtained by solving the boundary value problems with the conjunction and crack- simulation technique. The numerical results are obtained by the FORTRAN language program and plotted to show the influence of the variations of the physical parameters, the structural geometry, and the wave frequencies of incident wave on the dimensionless DSIFs. Comparisons with previous work and between the inner and outer tips are con- cluded.
文摘The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with contour integral of the Laplace inverse transform specifically,the general analytical expressions of the soil displacement and stress are obtained in the time domain,respectively.And the numerical solutions of the problem computed by analytical expressions are presented.In the time domain,the dynamic responses of the infinite elastic soil are analyzed,and the calculation results are compared with those from numerical inversion proposed by Durbin and the static results.One observes good agreement between analytical and numerical inversion results,lending the further support to the method presented.Finally,some valuable shear wave propagation laws are gained: the displacement of the soil remains zero before the wave arrival,and after the shear wave arrival,the stress and the displacement at this point increase abruptly,then reduce and tend to the static value gradually at last.The wave attenuates along the radial,therefore the farther the wave is from the source,the smaller the stress and the displacement are,and the stress and the displacement are just functions of the radial distance from the axis.
基金supported by the National Natural Science Foundation of China(11072060)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.
基金Project supported by the National Natural Science Foundation of China (Nos. 59525813 and 19872066).
文摘For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions （or between the derivatives of eigenfunctions） of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors （SIFs）, so any order SIF can be extracted based on a certain known solution of displacement （an analytic result or a numerical result）. Many numerical examples based on the finite element method of lines （FEMOL） show that the present method is very powerful and efficient.
基金The project is supported by the Natural Science Foundation of China.
文摘Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface conditions. Taking the advantage of the knowledge of the variation forms of the eigen-functions, a series of numerical techniques are proposed to simplify the computation and speed up the convergence rare of the inverse iteration. A number of numerical examples are given to demonstrate the excellent accuracy, efficiency and reliability of the proposed approach.
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.
基金Project supported by the National Natural Science Foundation of China (No. 10472086).
文摘Anti-plane electroelastic problems are studied by the Trefftz boundary element method （BEM） in this paper. The Trefftz BEM is based on a weighted residual formulation and indirect boundary approach. In particular the point-collocation and Galerkin techniques, in which the basic unknowns are the retained expansion coefficients in the system of complete equations, are considered. Furthermore, special Trefftz functions and auxiliary functions which satisfy exactly the specified boundary conditions along the slit boundaries are also used to derive a special purpose element with local defects. The path-independent integral is evaluated at the tip of a crack to determine the energy release rate for a mode Ⅲ fracture problem. In final, the accuracy and efficiency of the Trefftz boundary element method are illustrated by an example and the comparison is made with other methods.
基金Project supported by the National Natural Science Foundation of China (No.90305023)
文摘The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.
文摘Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four Cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate we obtained, The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate h --> infinity.
基金the National Natural Science Foundationthe National Post-doctoral Science Foundation of China
文摘The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric displacement around the crack tip are dependent on the speed of the Griffith crack as well as the material coefficients. When the two piezoelectric materials are identical, the present result will be reduced to the result far the problem of an anti-plane moving Griffith crack in homogeneous piezoelectric materials.
文摘This paper contains a theoretical formulations and solutions of multiple cracks sub- jected to an anti-plane time-harmonic point load in a functionally graded strip. The distributed dislocation technique is used to construct integral equations for a functionally graded material strip weakened by several cracks under anti-plane time-harmonic load. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to evaluate the stress intensity factor and strain energy density factors （SEDFs） for multiple cracks with differ- ent configurations. Numerical calculations are presented to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded strip with multiple curved cracks.
基金Project supported by the Guangdong Basic and Applied Basic Research Foundation of China(Nos.2022A1515010801 and 2023A1515012641)the Shenzhen Science and Technology Program of China(Nos.JCYJ20220818102409020 and GXWD20220811165158003)。
文摘The transient and static anti-plane problem of a rigid line inclusion pulled out from an elastic medium is studied.The singular integral equation method is used to solve the stress field.Under the static load,the stress intensity factor(SIF)at the inclusion tips increases with the medium length.The problem becomes equivalent to an inclusion in a medium with an infinite length when the length of the medium is 3.5times longer than that of the inclusion.However,under the transient load,the maximum value of the SIF occurs when the medium length is about two times the inclusion length.Besides,the relation between the pull-out force and the anti-plane displacement is given.The conclusions are useful in guiding the design of fiber reinforced composite materials.
文摘Based on the theoretical representation of piezoelectric quasicrystal,a generalized dynamic model is built to represent the transmission of wave aspects in surface acoustic pulse nano-devices.Surface elasticity,surface piezoelectricity,and surface permittivity help to include the surface effect,which equals additional thin sheets.It is shown that,under certain assumptions,this generalized dynamic model may be simplified to a few classical examples that are appropriate for both macro and nano-scale applications.In the current work,surface piezoelectricity is used to develop a theoretical model for shear horizontal(SH)waves where it contains the surface piezoelectricity theory and a linear spring model to quantitatively and qualitatively explore SH waves in an orthotropic piezoelectric quasicrystal layer overlying an elastic framework(Model I),a piezoelectric quasi-crystal nano substrate,and an orthotropic piezoelectric quasicrystal half-space(Model II).The theoretical model stimulates the numerical results,which establish the critical thickness.As the piezoelectric layer’s thickness gets closer to nanometres,surface energy must be included when analyzing dispersion properties.Furthermore,the effects of surface elasticity and density on wave velocity are investigated individually.The authors establish a parameter,precisely the ratio of the physical modulus along the width direction to along the direction of wave travel.The surface effect’s impact on the general char-acteristics of piezoelectric structures is seen as a spring force acting on bulk boundaries.Analytical presentation of frequency equations for both symmetric and anti-symmetric waves pertains to the case of an electrical short circuit in Model II.The project aims to analyze SH waves in orthogonal anisotropic,transversely isotropic piezoelectric layered nanostructures,providing a practical mathematical tool for surface effects analysis and adaptability to other wave types,including Rayleigh waves and acoustic surface waves.
文摘Based on the gist of anti-planning,evaluation standards and methods of intensive land utilization were re-examined according to the inverse planning procedures.Significant role of compulsory non-development zone(similar to the traditional"non-construction land")among the planning fruits in the intensive utilization of urban land resources and relevant index weights in the evaluation system were re-weighed.In land evaluation,relevant control indexes of compulsory non-development zone were first calculated and evaluated,healthy and sustainable development coefficients of land were obtained and regarded as the core content of the whole evaluation system.
