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
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
The behavior of the stress intensity factor at the tips of cracks subjected to uniaxial tension σχ^∞= p with traction-free boundary condition in half-plane elasticity is investigated. The problem is formulated into...The behavior of the stress intensity factor at the tips of cracks subjected to uniaxial tension σχ^∞= p with traction-free boundary condition in half-plane elasticity is investigated. The problem is formulated into singular integral equations with the distribution dislocation function as unknown. In the formulation, we make used of a modified complex potential. Based on the appropriate quadrature formulas together with a suitable choice of collocation points, the singular integral equations are reduced to a system of linear equations for the unknown coefficients. Numerical examples show that the values of the stress intensity factor are influenced by the distance from the cracks to the boundary of the half-plane and the configuration of the cracks.展开更多
Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of resi...Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of residual surface stress and surface elasticity are included.Airy stress function method and Fourier integral transform technique are used.The solutions are provided in a compact manner that can easily reduce to special situations that take into account either one surface effect or none at all.Numerical results indicate that surface effects generally lower the stress levels and smooth the deformation profiles in the half-plane.Surface elasticity plays a dominant role in the in-plane elastic fields for a tangentially loaded half-plane,while the effect of residual surface stress is fundamentally crucial for the out-of-plane stress and displacement when the half-plane is normally loaded.In the remaining situations,combined effects of surface elasticity and residual surface stress should be considered.The results for a concentrated surface force serve essentially as fundamental solutions of the Flamant and the half-plane Cerruti problems with surface effects.The solutions presented in this work may be helpful for understanding the contact behaviors between solids at the nanoscale.展开更多
This paper presents a further development of the Boundary Contour Method (BCM) for half-plane piezoelectric media. Firstly, the divergence free property of the integrand of the half-plane piezoelectric boundary elemen...This paper presents a further development of the Boundary Contour Method (BCM) for half-plane piezoelectric media. Firstly, the divergence free property of the integrand of the half-plane piezoelectric boundary element is proven. Secondly, the boundary contour method formulation is derived and potential functions are obtained by introducing linear shape functions and Green's functions[1] for half-plane piezoelectric media. Finally, numerical solutions for illustrative example are compared with exact ones and that of conventional boundary element method (BEM) ones. The numerical results of BCM coincide very well with exact solution, and the feasibility and efficiency of the method are verified.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
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
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
This paper deals with the combination of point phonon and phason forces applied in the interior of infinite planes and half-planes of 1D quasicrystal bi-materials. Based on the general solution of quasicrystals, a ser...This paper deals with the combination of point phonon and phason forces applied in the interior of infinite planes and half-planes of 1D quasicrystal bi-materials. Based on the general solution of quasicrystals, a series of displacement functions are adopted to obtain Green's functions for infinite planes and bi-material planes composed of two half-planes in the closed form, when the two half-planes are supposed to be ideally bonded or to be in smooth contact. Since the physical quantities can be readily calculated without the need of performing any transform operations, Green's functions are very convenient to be used in the study of point defects and inhomogeneities in the quasicrystal materials.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
针对具有非最小相位特性的单电感双输出Buck-Boost变换器(SIDO Buck-Boost)输出两支路存在严重的交叉影响、控制困难以及系统暂态性能差等问题,提出一种基于扩张状态观测器(extended state observer,ESO)的主路微分平坦控制(differentia...针对具有非最小相位特性的单电感双输出Buck-Boost变换器(SIDO Buck-Boost)输出两支路存在严重的交叉影响、控制困难以及系统暂态性能差等问题,提出一种基于扩张状态观测器(extended state observer,ESO)的主路微分平坦控制(differential flatness based control,DFBC)和支路改进双闭环自抗扰控制(active disturbance rejection controller,ADRC)的控制策略.首先,根据主路微分平坦理论,在主路控制中设计微分平坦控制器,并对微分平坦系统进行误差反馈;设计ESO对主路的扰动项进行观测,将观测后的状态量反馈到微分平坦控制器中.其次,针对支路存在耦合以及右半平面零点的问题,设计改进型双闭环ADRC进行系统解耦,其中,电流内环选取基于模型补偿和前馈补偿的ADRC,电压外环选取普通ADRC,然后,利用Lyapunov理论证明系统的稳定性.最后,在Matlab/Simulink平台中搭建了仿真模型,并基于HIL搭建了实验平台.仿真及实验结果表明:所提控制策略减小了输出两支路之间的交叉影响,解决了非最小相位系统控制困难的问题,提高了系统的暂态响应性能.展开更多
In the theory of two-dimensional linear elasticity,an elliptical inclusion is known to attain a constant stress field when perfectly buried in an infinite homogeneous matrix if a uniform eigenstrain is applied to it.T...In the theory of two-dimensional linear elasticity,an elliptical inclusion is known to attain a constant stress field when perfectly buried in an infinite homogeneous matrix if a uniform eigenstrain is applied to it.The focus of this paper falls on the question:when the initially elliptical inclusion verges on a bi-material interface,what would happen to its configuration if it is required to retain the internal constant stress?Specifically,we explore the anti-plane shear version of this question(the version of plane deformations or three-dimensional deformations seems,however,insoluble at this stage),in which an inclusion undergoing a uniform(anti-plane shear)eigenstrain is embedded in a bi-material structure composed of two infinite elastic half-planes whose interface is straight and perfectly bonded,and the shape of the inclusion is to be determined such that the eigenstraininduced stress inside the inclusion appears to be a constant.Unlike most optimization methods-driven solution procedures for finding the shape of the inclusion approximately in which huge computation is required,we derive by a rigorous theoretical analysis an exact integral equation with respect to the boundary curve of the inclusion that is sufficiently and necessarily related to the existence of a constant stress inside the inclusion.We solve this integral equation via the use of some analytic techniques and present in several illustrative examples a variety of shapes of the inclusion achieving constant stresses.We discover some interesting phenomena for the evolution of the shape of the uniformly stressed inclusion relative to the stiffness of the nearby interface.展开更多
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.
文摘The behavior of the stress intensity factor at the tips of cracks subjected to uniaxial tension σχ^∞= p with traction-free boundary condition in half-plane elasticity is investigated. The problem is formulated into singular integral equations with the distribution dislocation function as unknown. In the formulation, we make used of a modified complex potential. Based on the appropriate quadrature formulas together with a suitable choice of collocation points, the singular integral equations are reduced to a system of linear equations for the unknown coefficients. Numerical examples show that the values of the stress intensity factor are influenced by the distance from the cracks to the boundary of the half-plane and the configuration of the cracks.
基金supported by the National Natural Science Foundation of China(12272126,12272127)the Doctoral Fund of HPU(B2015-64).
文摘Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of residual surface stress and surface elasticity are included.Airy stress function method and Fourier integral transform technique are used.The solutions are provided in a compact manner that can easily reduce to special situations that take into account either one surface effect or none at all.Numerical results indicate that surface effects generally lower the stress levels and smooth the deformation profiles in the half-plane.Surface elasticity plays a dominant role in the in-plane elastic fields for a tangentially loaded half-plane,while the effect of residual surface stress is fundamentally crucial for the out-of-plane stress and displacement when the half-plane is normally loaded.In the remaining situations,combined effects of surface elasticity and residual surface stress should be considered.The results for a concentrated surface force serve essentially as fundamental solutions of the Flamant and the half-plane Cerruti problems with surface effects.The solutions presented in this work may be helpful for understanding the contact behaviors between solids at the nanoscale.
文摘This paper presents a further development of the Boundary Contour Method (BCM) for half-plane piezoelectric media. Firstly, the divergence free property of the integrand of the half-plane piezoelectric boundary element is proven. Secondly, the boundary contour method formulation is derived and potential functions are obtained by introducing linear shape functions and Green's functions[1] for half-plane piezoelectric media. Finally, numerical solutions for illustrative example are compared with exact ones and that of conventional boundary element method (BEM) ones. The numerical results of BCM coincide very well with exact solution, and the feasibility and efficiency of the method are verified.
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.
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.
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.
基金Project supported by the National Natural Science Foundation of China (No 10702077)the Alexander von Humboldt Foundation in Germany
文摘This paper deals with the combination of point phonon and phason forces applied in the interior of infinite planes and half-planes of 1D quasicrystal bi-materials. Based on the general solution of quasicrystals, a series of displacement functions are adopted to obtain Green's functions for infinite planes and bi-material planes composed of two half-planes in the closed form, when the two half-planes are supposed to be ideally bonded or to be in smooth contact. Since the physical quantities can be readily calculated without the need of performing any transform operations, Green's functions are very convenient to be used in the study of point defects and inhomogeneities in the quasicrystal materials.
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.
文摘针对具有非最小相位特性的单电感双输出Buck-Boost变换器(SIDO Buck-Boost)输出两支路存在严重的交叉影响、控制困难以及系统暂态性能差等问题,提出一种基于扩张状态观测器(extended state observer,ESO)的主路微分平坦控制(differential flatness based control,DFBC)和支路改进双闭环自抗扰控制(active disturbance rejection controller,ADRC)的控制策略.首先,根据主路微分平坦理论,在主路控制中设计微分平坦控制器,并对微分平坦系统进行误差反馈;设计ESO对主路的扰动项进行观测,将观测后的状态量反馈到微分平坦控制器中.其次,针对支路存在耦合以及右半平面零点的问题,设计改进型双闭环ADRC进行系统解耦,其中,电流内环选取基于模型补偿和前馈补偿的ADRC,电压外环选取普通ADRC,然后,利用Lyapunov理论证明系统的稳定性.最后,在Matlab/Simulink平台中搭建了仿真模型,并基于HIL搭建了实验平台.仿真及实验结果表明:所提控制策略减小了输出两支路之间的交叉影响,解决了非最小相位系统控制困难的问题,提高了系统的暂态响应性能.
基金supported by the National Natural Science Foundation of China(Grant No.11902147)the Natural Science Foundation of Jiangsu Province(Grant No.BK20190393).
文摘In the theory of two-dimensional linear elasticity,an elliptical inclusion is known to attain a constant stress field when perfectly buried in an infinite homogeneous matrix if a uniform eigenstrain is applied to it.The focus of this paper falls on the question:when the initially elliptical inclusion verges on a bi-material interface,what would happen to its configuration if it is required to retain the internal constant stress?Specifically,we explore the anti-plane shear version of this question(the version of plane deformations or three-dimensional deformations seems,however,insoluble at this stage),in which an inclusion undergoing a uniform(anti-plane shear)eigenstrain is embedded in a bi-material structure composed of two infinite elastic half-planes whose interface is straight and perfectly bonded,and the shape of the inclusion is to be determined such that the eigenstraininduced stress inside the inclusion appears to be a constant.Unlike most optimization methods-driven solution procedures for finding the shape of the inclusion approximately in which huge computation is required,we derive by a rigorous theoretical analysis an exact integral equation with respect to the boundary curve of the inclusion that is sufficiently and necessarily related to the existence of a constant stress inside the inclusion.We solve this integral equation via the use of some analytic techniques and present in several illustrative examples a variety of shapes of the inclusion achieving constant stresses.We discover some interesting phenomena for the evolution of the shape of the uniformly stressed inclusion relative to the stiffness of the nearby interface.
