The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear li...The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.展开更多
Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to a pair of normal point loads moving in a direction perpendicular to the crack edge on its face...Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to a pair of normal point loads moving in a direction perpendicular to the crack edge on its faces. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Some features of the solution are discussed through numerical results.展开更多
In this paper,the growth of analytic function defined by L-S transforms convergent in the right half plane is studied and some properties on the L-S transform F(s)and its relative transforms f(s)are obtained.
In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condit...In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condition. Optimal error bounds for this fully discrete scheme are obtained.展开更多
Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant s...Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.展开更多
The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subj...The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.展开更多
An exact and complete solution of the problem of a half-planecrack in an infinite transversely isotropic piezoelectric body ispresented. The upper and lower crack faces are assumed to be loadedantisym- metrically by a...An exact and complete solution of the problem of a half-planecrack in an infinite transversely isotropic piezoelectric body ispresented. The upper and lower crack faces are assumed to be loadedantisym- metrically by a couple of tangential point forces inopposite directions. The solution is derived through a lim- itingprocedure from that of a penny-shaped crack. The expressions for theelectroelastic field are given in terms of elementary functions.Finally, the numerical results of the second and third mode stressintensity factors k_2 and k_3 of piezoelectric materials and elasticmaterials are compared in figures.展开更多
This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the d...This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.展开更多
This paper investigates in detail the nature of diffraction of plane P waves around a canyon in poroelastic half-space, and studies the effects of incident frequency, drainage condition, porosity, etc, on the diffract...This paper investigates in detail the nature of diffraction of plane P waves around a canyon in poroelastic half-space, and studies the effects of incident frequency, drainage condition, porosity, etc, on the diffraction of waves. It is shown that the surface displacement amplitudes of the drained case are close to those of the undrained case, however, the surface displacement amplitudes of the dry case are very different from those of the saturated （either drained or undrained） cases. There are large phase shift between the dry case and the saturated cases, as well as slightly longer resultant wavelengths for the undrained case than those for the drained case and longer resultant wavelengths for the drained case than those for the dry case. For small porosity the surface displacement amplitudes for the saturated cases are almost identical to those for the dry case; while for large porosity, the effect of drainage condition becomes significant, and the surface displacement amplitudes for the undrained case are larger than those for the drained case. As the incident frequency increases, the effect of porosity becomes significant, and more significant for the undrained case than that for the drained case. As the porosity increases, the pore pressures increase significantly but their oscillations become smoother. As the incident frequency increases, the pore pressures become more complicated.展开更多
This paper presents an indirect boundary integration equation method for diffraction of plane P waves by a two-dimensional canyon of arbitrary shape in poroelastic half-space. The Green＇s functions of compressional a...This paper presents an indirect boundary integration equation method for diffraction of plane P waves by a two-dimensional canyon of arbitrary shape in poroelastic half-space. The Green＇s functions of compressional and shear wave sources in poroelastic half-space are derived based on Biot＇s theory. The scattered waves are constructed using the fictitious wave sources close to the boundary of the canyon, and magnitude of the fictitious wave sources are determined by the boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, the comparison between the degenerated solutions of single-phased half-space and the well-known solutions, and the numerical stability of the method.展开更多
In this paper,we connsider the plane crack problem of the compound orthotropic material for loads applied symmetrically with respect to the crack plane by means of method of complex variable.
A general solution which can be expressed by three "harmonic functions" is derived. Then using this general solution as well as the trial-and-error method, the Green’s functions for point forces and point c...A general solution which can be expressed by three "harmonic functions" is derived. Then using this general solution as well as the trial-and-error method, the Green’s functions for point forces and point charge acting in the interior of a piezoelectric half plane are obtained. The point force solutions of an infinite piezoelectric plane can be derived as a special case of the results presented in this paper.展开更多
This investigation evaluates, by the dislocation method, the dynamic stress intensity factors of cracked orthotropic half-plane and functionally graded material coating of a coating- substrate material due to the acti...This investigation evaluates, by the dislocation method, the dynamic stress intensity factors of cracked orthotropic half-plane and functionally graded material coating of a coating- substrate material due to the action of anti-plane traction on the crack surfaces. First, by using the complex Fourier transform, the dislocation problem can be solved and the stress fields are obtained with Cauchy singularity at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks in the orthotropic half-plane with functionally graded orthotropic coating. Several examples are solved and dynamic stress intensity factors are obtained.展开更多
The dynamic stress intensity factors in a half-plane weakened by several finite moving cracks are investigated by employing the Fourier complex transformation. Stress analysis is performed in a half-plane containing a...The dynamic stress intensity factors in a half-plane weakened by several finite moving cracks are investigated by employing the Fourier complex transformation. Stress analysis is performed in a half-plane containing a single dislocation and without dislocation. An exact solution in a closed form to the stress fields and displacement is ob- tained. The Galilean transformation is used to transform between coordinates connected to the cracks. The stress components are of the Cauchy singular kind at the location of dislocation and the point of application of the the influence of crack length and crack running force. Numerical examples demonstrate velocity on the stress intensity factor.展开更多
The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform...The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.展开更多
This paper derives explicit expressions for the propagation of Gaussian beams carrying two vortices of equal charges m = ±1diffracted at a half-plane screen, which enables the study of the dynamic evolution of vo...This paper derives explicit expressions for the propagation of Gaussian beams carrying two vortices of equal charges m = ±1diffracted at a half-plane screen, which enables the study of the dynamic evolution of vortices in the diffraction field. It shows that there may be no vortices, a pair or several pairs of vortices of opposite charges m -=±, -1 in the diffraction field. Pair creation, annihilation and motion of vortices may appear upon propagation. The off-axis distance additionally affects the evolutionary behaviour. In the process the total topological charge is equal to zero, which is unequal to that of the vortex beam at the source plane. A comparison with the free-space propagation of two vortices of equal charges and a further extension are made.展开更多
The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation.The elastic shear modulus of the medium is considered to vary ex-ponentially.The dislocation solution is util...The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation.The elastic shear modulus of the medium is considered to vary ex-ponentially.The dislocation solution is utilized to formulate integral equations for the half-plane weakened by multiple smooth cracks under anti-plane deformation.The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically.Several examples are solved and the stress intensity factors are obtained.展开更多
We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the b...We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for nonhomogeneous half-plane problems with the Young’s modulus E(x)-E_0θxp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.展开更多
Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line sourc...Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.展开更多
基金The project supported by the National Natural Science Foundation of China
文摘The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.
基金The project supported by the Guangdong Provincial Natural Science Foundationthe Science Foundation of Shantou University
文摘Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to a pair of normal point loads moving in a direction perpendicular to the crack edge on its faces. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Some features of the solution are discussed through numerical results.
基金Foundation item： the National Natural Science Foundation of China （No. 10471048） Specialized Research Fund for the Doctoral Program of Higher Education （No. 20050574002）.
文摘In this paper,the growth of analytic function defined by L-S transforms convergent in the right half plane is studied and some properties on the L-S transform F(s)and its relative transforms f(s)are obtained.
文摘In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condition. Optimal error bounds for this fully discrete scheme are obtained.
基金Project supported by the National Natural Science Foundation of China (No. 10172075)the Yu-Ying Foundation of Hunan University.
文摘Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.
基金National Natural Science Foundation of China under Grant 51378384Key Project of Natural Science Foundation of Tianjin Municipality under Grant 12JCZDJC29000
文摘The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.
基金the National Natural Science Foundation of China(No.19872060 and 69982009)the Postdoctoral Foundation of China
文摘An exact and complete solution of the problem of a half-planecrack in an infinite transversely isotropic piezoelectric body ispresented. The upper and lower crack faces are assumed to be loadedantisym- metrically by a couple of tangential point forces inopposite directions. The solution is derived through a lim- itingprocedure from that of a penny-shaped crack. The expressions for theelectroelastic field are given in terms of elementary functions.Finally, the numerical results of the second and third mode stressintensity factors k_2 and k_3 of piezoelectric materials and elasticmaterials are compared in figures.
基金National Natural Science Foundation of China Under Grant No.50908156 and 50978183Tianjin Natural Science Foundation Under Grant No. 07JCZDJC10100
文摘This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.
基金support from the Program for New Century Excellent Talents in University (NCET-05-0248)the Key Program for Applied Basic Research of Tianjin Municipality (07JCZDJC10100)
文摘This paper investigates in detail the nature of diffraction of plane P waves around a canyon in poroelastic half-space, and studies the effects of incident frequency, drainage condition, porosity, etc, on the diffraction of waves. It is shown that the surface displacement amplitudes of the drained case are close to those of the undrained case, however, the surface displacement amplitudes of the dry case are very different from those of the saturated （either drained or undrained） cases. There are large phase shift between the dry case and the saturated cases, as well as slightly longer resultant wavelengths for the undrained case than those for the drained case and longer resultant wavelengths for the drained case than those for the dry case. For small porosity the surface displacement amplitudes for the saturated cases are almost identical to those for the dry case; while for large porosity, the effect of drainage condition becomes significant, and the surface displacement amplitudes for the undrained case are larger than those for the drained case. As the incident frequency increases, the effect of porosity becomes significant, and more significant for the undrained case than that for the drained case. As the porosity increases, the pore pressures increase significantly but their oscillations become smoother. As the incident frequency increases, the pore pressures become more complicated.
基金support from the Program for New Century Excellent Talents in University (NCET-05-0248)the Key Program for Applied Basic Research of Tianjin Municipality (07JCZDJC10100)
文摘This paper presents an indirect boundary integration equation method for diffraction of plane P waves by a two-dimensional canyon of arbitrary shape in poroelastic half-space. The Green＇s functions of compressional and shear wave sources in poroelastic half-space are derived based on Biot＇s theory. The scattered waves are constructed using the fictitious wave sources close to the boundary of the canyon, and magnitude of the fictitious wave sources are determined by the boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, the comparison between the degenerated solutions of single-phased half-space and the well-known solutions, and the numerical stability of the method.
文摘In this paper,we connsider the plane crack problem of the compound orthotropic material for loads applied symmetrically with respect to the crack plane by means of method of complex variable.
文摘A general solution which can be expressed by three "harmonic functions" is derived. Then using this general solution as well as the trial-and-error method, the Green’s functions for point forces and point charge acting in the interior of a piezoelectric half plane are obtained. The point force solutions of an infinite piezoelectric plane can be derived as a special case of the results presented in this paper.
文摘This investigation evaluates, by the dislocation method, the dynamic stress intensity factors of cracked orthotropic half-plane and functionally graded material coating of a coating- substrate material due to the action of anti-plane traction on the crack surfaces. First, by using the complex Fourier transform, the dislocation problem can be solved and the stress fields are obtained with Cauchy singularity at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks in the orthotropic half-plane with functionally graded orthotropic coating. Several examples are solved and dynamic stress intensity factors are obtained.
文摘The dynamic stress intensity factors in a half-plane weakened by several finite moving cracks are investigated by employing the Fourier complex transformation. Stress analysis is performed in a half-plane containing a single dislocation and without dislocation. An exact solution in a closed form to the stress fields and displacement is ob- tained. The Galilean transformation is used to transform between coordinates connected to the cracks. The stress components are of the Cauchy singular kind at the location of dislocation and the point of application of the the influence of crack length and crack running force. Numerical examples demonstrate velocity on the stress intensity factor.
基金supported by the National Natural Science Foundation of China (50908156,50978183)Tianjin Research Program of Application Foundation and Advanced Technology (12JCQNJC04700)
文摘The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.
基金supported by the National Natural Science Foundation of China (Grant No. 10874125)the Foundation of Education Department of Sichuan Province of China (Grant No. 10ZA063)
文摘This paper derives explicit expressions for the propagation of Gaussian beams carrying two vortices of equal charges m = ±1diffracted at a half-plane screen, which enables the study of the dynamic evolution of vortices in the diffraction field. It shows that there may be no vortices, a pair or several pairs of vortices of opposite charges m -=±, -1 in the diffraction field. Pair creation, annihilation and motion of vortices may appear upon propagation. The off-axis distance additionally affects the evolutionary behaviour. In the process the total topological charge is equal to zero, which is unequal to that of the vortex beam at the source plane. A comparison with the free-space propagation of two vortices of equal charges and a further extension are made.
文摘The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation.The elastic shear modulus of the medium is considered to vary ex-ponentially.The dislocation solution is utilized to formulate integral equations for the half-plane weakened by multiple smooth cracks under anti-plane deformation.The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically.Several examples are solved and the stress intensity factors are obtained.
文摘We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for nonhomogeneous half-plane problems with the Young’s modulus E(x)-E_0θxp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.
基金supported by National Natural Science Foundation of China (50978183)
文摘Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.
