In this paper,we establish characterizations of α-Bloch functions and little α-Bloch functions on the unit ball as well as the unit polydisk of C^(m),which generalize and improve results of Aulaskari-Lappan,Minda,Au...In this paper,we establish characterizations of α-Bloch functions and little α-Bloch functions on the unit ball as well as the unit polydisk of C^(m),which generalize and improve results of Aulaskari-Lappan,Minda,Aulaskari-Wulan,and Wu.Some examples are also given to complement our theory.展开更多
In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of C^n＋l, so-called complex holomorphic Cli...In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of C^n＋l, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D△^mf= 0, obtain the integral representation formula for the complex holo-morphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of C^n＋1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.展开更多
We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the auth...We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.展开更多
Extension of classical Mandelbrojt’s criterion for normality to several complex variables is given. Some inequalities for holomorphic functions which omit values 0 and 1 are obtained.
Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate...Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate method and a suitable numerical scheme are used to solve such integrals numerically for the unknown function, which are later used to find the stress intensity factor, SIF.展开更多
Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception o...Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception of a finite number of isolated singularities, and for P>o, if then where z=Rei and CR is the open semicircle in the upper half of the z plane.With the extended Jordan's lemma one can find that Laplace transform and Fourier transform are a pair of integral transforms which relate to each other.展开更多
In this paper, the complex variable function method is used to obtain the hypersingular integral equations for the interaction between straight and curved cracks problem in plane elasticity. The curved length coordina...In this paper, the complex variable function method is used to obtain the hypersingular integral equations for the interaction between straight and curved cracks problem in plane elasticity. The curved length coordinate method and suitable quadrature rule are used to solve the integrals for the unknown function, which are later used to evaluate the stress intensity factor, SIF. Three types of stress modes are presented for the numerical results.展开更多
Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single...Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.展开更多
A basic solution in series form for the three-phase composite cylindrical model in antiplane piezoelectricity subjected to the action of a singularity in the intermediate matrix region is presented. The solution is ob...A basic solution in series form for the three-phase composite cylindrical model in antiplane piezoelectricity subjected to the action of a singularity in the intermediate matrix region is presented. The solution is obtained through the complex potential approach in conjunction with the techniques of analytical continuation, singularity analysis, Laurent series expansion in an annular region and Cauchy integral formulae, etc. Based on the complex potentials obtained, explicit expressions for the distribution of stress and electric displacement in the three regions are also derived.展开更多
In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems a...In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.展开更多
The element-free Galerkin(EFG)method,which constructs shape functions via moving least squares(MLS)approximation,represents a fundamental and widely studied meshless method in numerical computation.Although it achieve...The element-free Galerkin(EFG)method,which constructs shape functions via moving least squares(MLS)approximation,represents a fundamental and widely studied meshless method in numerical computation.Although it achieves high computational accuracy,the shape functions are more complex than those in the conventional finite element method(FEM),resulting in great computational requirements.Therefore,improving the computational efficiency of the EFG method represents an important research direction.This paper systematically reviews significant contributions fromdomestic and international scholars in advancing the EFGmethod.Including the improved element-free Galerkin(IEFG)method,various interpolating EFG methods,four distinct complex variable EFG methods,and a series of dimension splitting meshless methods.In the numerical examples,the effectiveness and efficiency of the three methods are validated by analyzing the solutions of the IEFG method for 3D steadystate anisotropic heat conduction,3D elastoplasticity,and large deformation problems,as well as the performance of two-dimensional splitting meshless methods in solving the 3D Helmholtz equation.展开更多
Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classic...Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.展开更多
Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solv...Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.展开更多
The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common...The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.展开更多
Two boundary value problems are investigated for an over-determined elliptic system with several complex variables in polydisc. Necessary and sufficient conditions for the existence of finitely many linearly independe...Two boundary value problems are investigated for an over-determined elliptic system with several complex variables in polydisc. Necessary and sufficient conditions for the existence of finitely many linearly independent solutions and finitely many solvability conditions are derived. Moreover, the boundary value problem for any number of complex variables is treated in a unified way and the essential difference between the case of one complex variable and that of several complex variables is revealed.展开更多
In this work, we used the complex variable methods to derive the Goursat functions for the first and second fundamental problem of an infinite plate with a curvilinear hole C. The hole is mapped in the domain inside a...In this work, we used the complex variable methods to derive the Goursat functions for the first and second fundamental problem of an infinite plate with a curvilinear hole C. The hole is mapped in the domain inside a unit circle by means of the rational mapping function. Many special cases are discussed and established of these functions. Also, many applications and examples are considered. The results indicate that the infinite plate with a curvilinear hole inside the unit circle is very pronounced.展开更多
A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions....A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions.Fundamental solution was prepared for solving these types of problems with boundary element method.展开更多
基金Supported by Natural Science Research Project for Colleges and Universities of Anhui Province(Grant No.2022AH050329)Yunnan Provincial Department of Education Fund(Grant No.2025J0376).
文摘In this paper,we establish characterizations of α-Bloch functions and little α-Bloch functions on the unit ball as well as the unit polydisk of C^(m),which generalize and improve results of Aulaskari-Lappan,Minda,Aulaskari-Wulan,and Wu.Some examples are also given to complement our theory.
基金Supported by NNSF of China (6087349, 10871150)863Project of China (2008AA01Z419)+1 种基金RFDP of Higher Education (20060486001)Post-Doctor Foundation ofChina (20090460316)
文摘In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of C^n＋l, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D△^mf= 0, obtain the integral representation formula for the complex holo-morphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of C^n＋1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.
文摘We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.
文摘Extension of classical Mandelbrojt’s criterion for normality to several complex variables is given. Some inequalities for holomorphic functions which omit values 0 and 1 are obtained.
基金Ministry of Science,Technology and Innovation(MOSTI),Malaysia for the Science Fund,Vot No.5450657
文摘Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate method and a suitable numerical scheme are used to solve such integrals numerically for the unknown function, which are later used to find the stress intensity factor, SIF.
文摘Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception of a finite number of isolated singularities, and for P>o, if then where z=Rei and CR is the open semicircle in the upper half of the z plane.With the extended Jordan's lemma one can find that Laplace transform and Fourier transform are a pair of integral transforms which relate to each other.
文摘In this paper, the complex variable function method is used to obtain the hypersingular integral equations for the interaction between straight and curved cracks problem in plane elasticity. The curved length coordinate method and suitable quadrature rule are used to solve the integrals for the unknown function, which are later used to evaluate the stress intensity factor, SIF. Three types of stress modes are presented for the numerical results.
基金Project supported by the National Natural Science Foundation of China(Nos.10702071 and 11090334)the China Postdoctoral Science Foundation(No.201003281)+2 种基金the Shanghai Postdoctoral Scientific Program(No.10R21415800)the Shanghai Leading Academic Discipline Project(No.B302)sponsored by the"Sino-German Center for Research Promotion"under a project of"Crack Growth in Ferroelectrics Driven by Cyclic Electric Loading"
文摘Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.
文摘A basic solution in series form for the three-phase composite cylindrical model in antiplane piezoelectricity subjected to the action of a singularity in the intermediate matrix region is presented. The solution is obtained through the complex potential approach in conjunction with the techniques of analytical continuation, singularity analysis, Laurent series expansion in an annular region and Cauchy integral formulae, etc. Based on the complex potentials obtained, explicit expressions for the distribution of stress and electric displacement in the three regions are also derived.
基金supported by the NSF of Henan Province(222300420397,242300421394)Xie’s research was supported by the NSFC(11571089,11871191).
文摘In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.
基金supported by the National Natural Science Foundation of China(Grant No.12271341).
文摘The element-free Galerkin(EFG)method,which constructs shape functions via moving least squares(MLS)approximation,represents a fundamental and widely studied meshless method in numerical computation.Although it achieves high computational accuracy,the shape functions are more complex than those in the conventional finite element method(FEM),resulting in great computational requirements.Therefore,improving the computational efficiency of the EFG method represents an important research direction.This paper systematically reviews significant contributions fromdomestic and international scholars in advancing the EFGmethod.Including the improved element-free Galerkin(IEFG)method,various interpolating EFG methods,four distinct complex variable EFG methods,and a series of dimension splitting meshless methods.In the numerical examples,the effectiveness and efficiency of the three methods are validated by analyzing the solutions of the IEFG method for 3D steadystate anisotropic heat conduction,3D elastoplasticity,and large deformation problems,as well as the performance of two-dimensional splitting meshless methods in solving the 3D Helmholtz equation.
文摘Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.
基金supported by the National Natural Science Foundation of China (Grant No 10761005)the Inner Mongolia Natural Science Foundation of China (Grant No 200607010104)
文摘Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.
基金Projects(50874047,51074014,51174014)supported by the National Natural Science Foundation of China
文摘The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.
文摘Two boundary value problems are investigated for an over-determined elliptic system with several complex variables in polydisc. Necessary and sufficient conditions for the existence of finitely many linearly independent solutions and finitely many solvability conditions are derived. Moreover, the boundary value problem for any number of complex variables is treated in a unified way and the essential difference between the case of one complex variable and that of several complex variables is revealed.
文摘In this work, we used the complex variable methods to derive the Goursat functions for the first and second fundamental problem of an infinite plate with a curvilinear hole C. The hole is mapped in the domain inside a unit circle by means of the rational mapping function. Many special cases are discussed and established of these functions. Also, many applications and examples are considered. The results indicate that the infinite plate with a curvilinear hole inside the unit circle is very pronounced.
文摘A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions.Fundamental solution was prepared for solving these types of problems with boundary element method.
