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 paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing sm...In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.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
Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of o...Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of order σ（f）=1. Examples show that some of the results are sharp.展开更多
Applying the Nevanlinna theory of meromorphic function, we investigate the non-admissible meromorphic solutions of nonlinear complex algebraic differential equation and gain a general result. Meanwhile, we prove that ...Applying the Nevanlinna theory of meromorphic function, we investigate the non-admissible meromorphic solutions of nonlinear complex algebraic differential equation and gain a general result. Meanwhile, we prove that the meromorphic solutions of some types of the systems of nonlinear complex differential equations are non-admissible. Moreover, the form of the systems of equations with admissible solutions is discussed.展开更多
This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities...This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.展开更多
In this paper,we consider the truncated multiplicity finite range set problem of meromorphic functions on some complex disc.By using the value distribution theory of meromorphic functions,we establish a second main th...In this paper,we consider the truncated multiplicity finite range set problem of meromorphic functions on some complex disc.By using the value distribution theory of meromorphic functions,we establish a second main theorem for meromorphic functions with finite growth index which share meromorphic functions(may not be small functions).As its application,we also extend the result of a finite range set with truncated multiplicity.展开更多
For entire or meromorphic function f,a value θ∈[0,2π)is called a Julia limiting direction if there is an unbounded sequence{z_(n)}in the Julia set satisfying limn→∞ arg z_(n)=θ.Our main result is on the entire s...For entire or meromorphic function f,a value θ∈[0,2π)is called a Julia limiting direction if there is an unbounded sequence{z_(n)}in the Julia set satisfying limn→∞ arg z_(n)=θ.Our main result is on the entire solution f of P(z,f)+F(z)f^(s)=0,where P(z,f)is a differential polynomial of f with entire coefficients of growth smaller than that of the entire transcendental F,with the integer s being no more than the minimum degree of all differential monomials in P(z,f). We observe that Julia limiting directions of f partly come from the directions in which F grows quickly.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
Let q be a finite nonzero complex number,let the q-difference equation f(qz)f(z/p)=R(z,f(z))=P(z,f(z))/Q(z,f(z))=Σ_(j=0)^(p)=0aj(z)f^(j)(z)/Σ_(k=0)b_(k)(z)f^(k)(z)(+)admit a nonconstant meromorphic solution f,where ...Let q be a finite nonzero complex number,let the q-difference equation f(qz)f(z/p)=R(z,f(z))=P(z,f(z))/Q(z,f(z))=Σ_(j=0)^(p)=0aj(z)f^(j)(z)/Σ_(k=0)b_(k)(z)f^(k)(z)(+)admit a nonconstant meromorphic solution f,where p and q are nonnegative integers,a_(j)with 0≤j≤p and b_(k)with 0≤k≤q polynomials in zwith a_(p)≠0 and b_(q)≠0 such that P(z,f(z))and Q(z,f(z))are relatively prime polynomials in f(z)and let m=p-q≥3.Then,(+)has no transcendental meromorphic solution when|q|=1,and the lower bound of the lower order of f is obtained when m≥3 and |q|≠1.展开更多
This study is to determine the support mechanism of pre-stressed expandable props for the stope roof in room- and-pillar mining, which is crucial for maintaining stability and preventing roof collapse in mines. Utiliz...This study is to determine the support mechanism of pre-stressed expandable props for the stope roof in room- and-pillar mining, which is crucial for maintaining stability and preventing roof collapse in mines. Utilizing an engineering case from a gold mine in Dandong, China, a laboratory-based similar test is conducted to extract the actual roof characteristic curve. This test continues until the mining stope collapses due to a U-shaped failure. Concurrently, a semi-theoretical method for obtaining the roof characteristic curve is proposed and verified against the actual curve. The semi-theoretical method calculated that the support force and vertical displacement at the demarcation point between the elastic and plastic zones of the roof characteristic curve are 5.0 MPa and 8.20 mm, respectively, corroborating well with the laboratory-based similar test results of 0.22 MPa and 0.730 mm. The weakening factor for the plastic zone in the roof characteristic curve was semi-theoretically estimated to be 0.75. The intersection between the actual roof characteristic curve and the support characteristic curves of expandable props, natural pillars, and concrete props indicates that the expandable prop is the most effective “yielding support” for the stope roof in room-and-pillar mining. That is, the deformation and failure of the stope roof can be effectively controlled with proper release of roof stress. This study provides practical insights for optimizing support strategies in room-and-pillar mining, enhancing the safety and efficiency of mining operations.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
This paper deals with the problem of uniqueness of meromorphic functions with two deficient values and obtains a result which is an improvement of that of F.Gross and Yi Hongxun.
By applying rotated complex empirical orthogonal function (RCEOF) analysis on 1880-1999 summer rainfall at 28 selected stations over the east part of China, the spatio-temporal variations of China summer rainfall are ...By applying rotated complex empirical orthogonal function (RCEOF) analysis on 1880-1999 summer rainfall at 28 selected stations over the east part of China, the spatio-temporal variations of China summer rainfall are investigated. Six divisions are identified, showing strong temporal variability, the middle and lower reaches of the Yangtze River, the Huaihe River, Southeast China, North China, Southwest China, and Northeast China. The locations of all divisions except Southwest China are in a good agreement with those of the rainband which moves northward from Southeast China to Northeast China from June-August. The phase relationship revealed by the RCEOF analysis suggests that rainfall anomalies in the middle and lower reaches of the Yangtze River, Southeast China, and Northeast China are all characterized by a stationary wave, while a traveling wave is more pronounced in the Huaihe River division, North China, and Southwest China. The fourth RCEOF mode indicates that rainfall anomalies can propagate from south of Northeast China across lower reaches of the Huanghe River and the Huaihe River to the lower reaches of the Yangtze River. A 20-25-year oscillation is found at the middle and lower reaches of the Yangtze River, the Huaihe River valley, North China, and Northeast China. The middle and lower reaches of the Yangtze River and Northeast China also show an approximately-60-year oscillation. Northeast China and the Huaihe River division are dominated by a 36-year and a 70-80-year oscillation, respectively. An 11-year oscillation is also evident in North China, with a periodicity similar to sunspot activity. The interdecadal variability in the middle and lower reaches of the Yangtze River, the Huaihe River valley, and North China shows a significant positive correlation with the solar activity.展开更多
Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For th...Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.展开更多
Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-pla...Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.展开更多
Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the ...Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.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
The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material.The holes will lead to mutations and discontinuity to ...The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material.The holes will lead to mutations and discontinuity to the structure.So the hole-edge stress concentration is always a serious phenomenon.And the phenomenon makes the structure strength decrease very quickly to form dangerous weak points.Most partial damage begins from these weak points.According to the complex variable functions theory,the accurate boundary condition of composite plate with different hole-shapes is founded by conformal mapping method to settle the boundary condition problem of complex hole-shapes.Composite plate with commonly hole-shapes in engineering is studied by several complex variable stress fimction.The boundary integral equations are founded based on exact boundary conditions.Then the exact hole-edge stress analytic solution of composite plate with rectangle holes and wing manholes is resolved.Both of offset axis loadings and its influences on the stress concentration coefficient of the hole-edge are discussed.And comparisons of different loads along various offset axis on the hole-edge stress distribution of orthotropic plate with rectangle hole or wing manhole are made.It can be concluded that hole-edge with continuous variable curvatures might help to decrease the stress concentration coefficient;and smaller angle of outer load and fiber can decrease the stress peak value.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partially supported by the NSFC(11271227,11271161)the PCSIRT(IRT1264)the Fundamental Research Funds of Shandong University(2017JC019)。
文摘In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.
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.
基金supported by the NSF of Shandong Province, China (ZR2010AM030)the NNSF of China (11171013 & 11041005)
文摘Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of order σ（f）=1. Examples show that some of the results are sharp.
基金The NSF(11171013)of Chinathe NSF(KJ2015A323)of the Education Department of Anhui Provincethe Outstanding Young Talents Program(gxyq2017153)of the Education Department of Anhui Province
文摘Applying the Nevanlinna theory of meromorphic function, we investigate the non-admissible meromorphic solutions of nonlinear complex algebraic differential equation and gain a general result. Meanwhile, we prove that the meromorphic solutions of some types of the systems of nonlinear complex differential equations are non-admissible. Moreover, the form of the systems of equations with admissible solutions is discussed.
基金partially supported by the NSFC(12061042)the NSF of Jiangxi(20202BAB201003)+3 种基金the support of the National Science Center(Poland)via grant 2017/25/B/ST1/00931partially supported by the Project PID2021-124472NB-I00funded by MCIN/AEI/10.13039/501100011033by"EFDF A way of making Europe"。
文摘This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.
基金Supported by National Natural Science Foundation of China(12061041)Jiangxi Provincial Natural Science Foundation(20232BAB201003).
文摘In this paper,we consider the truncated multiplicity finite range set problem of meromorphic functions on some complex disc.By using the value distribution theory of meromorphic functions,we establish a second main theorem for meromorphic functions with finite growth index which share meromorphic functions(may not be small functions).As its application,we also extend the result of a finite range set with truncated multiplicity.
基金This work was supported by the National Natural Science Foundation of China(11771090,11901311)Natural Sciences Foundation of Shanghai(17ZR1402900).
文摘For entire or meromorphic function f,a value θ∈[0,2π)is called a Julia limiting direction if there is an unbounded sequence{z_(n)}in the Julia set satisfying limn→∞ arg z_(n)=θ.Our main result is on the entire solution f of P(z,f)+F(z)f^(s)=0,where P(z,f)is a differential polynomial of f with entire coefficients of growth smaller than that of the entire transcendental F,with the integer s being no more than the minimum degree of all differential monomials in P(z,f). We observe that Julia limiting directions of f partly come from the directions in which F grows quickly.
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 Nos.1226102311861023)the Foundation of Science and Technology Project of Guizhou Province of China(Grant No.[2018]5769-05).
文摘Let q be a finite nonzero complex number,let the q-difference equation f(qz)f(z/p)=R(z,f(z))=P(z,f(z))/Q(z,f(z))=Σ_(j=0)^(p)=0aj(z)f^(j)(z)/Σ_(k=0)b_(k)(z)f^(k)(z)(+)admit a nonconstant meromorphic solution f,where p and q are nonnegative integers,a_(j)with 0≤j≤p and b_(k)with 0≤k≤q polynomials in zwith a_(p)≠0 and b_(q)≠0 such that P(z,f(z))and Q(z,f(z))are relatively prime polynomials in f(z)and let m=p-q≥3.Then,(+)has no transcendental meromorphic solution when|q|=1,and the lower bound of the lower order of f is obtained when m≥3 and |q|≠1.
基金Project(2022YFC2903801) supported by the National Key Research and Development Program of ChinaProjects(52374117, 52274115) supported by the National Natural Science Foundation of China。
文摘This study is to determine the support mechanism of pre-stressed expandable props for the stope roof in room- and-pillar mining, which is crucial for maintaining stability and preventing roof collapse in mines. Utilizing an engineering case from a gold mine in Dandong, China, a laboratory-based similar test is conducted to extract the actual roof characteristic curve. This test continues until the mining stope collapses due to a U-shaped failure. Concurrently, a semi-theoretical method for obtaining the roof characteristic curve is proposed and verified against the actual curve. The semi-theoretical method calculated that the support force and vertical displacement at the demarcation point between the elastic and plastic zones of the roof characteristic curve are 5.0 MPa and 8.20 mm, respectively, corroborating well with the laboratory-based similar test results of 0.22 MPa and 0.730 mm. The weakening factor for the plastic zone in the roof characteristic curve was semi-theoretically estimated to be 0.75. The intersection between the actual roof characteristic curve and the support characteristic curves of expandable props, natural pillars, and concrete props indicates that the expandable prop is the most effective “yielding support” for the stope roof in room-and-pillar mining. That is, the deformation and failure of the stope roof can be effectively controlled with proper release of roof stress. This study provides practical insights for optimizing support strategies in room-and-pillar mining, enhancing the safety and efficiency of mining operations.
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.
文摘This paper deals with the problem of uniqueness of meromorphic functions with two deficient values and obtains a result which is an improvement of that of F.Gross and Yi Hongxun.
基金The authors wish to thank Professor Wang Shaowu from the Department of AtmosphericSciences of Peking University, who generously provided the China Summer Rainfall Station Data used in this study. This research was supported by the National Key Program
文摘By applying rotated complex empirical orthogonal function (RCEOF) analysis on 1880-1999 summer rainfall at 28 selected stations over the east part of China, the spatio-temporal variations of China summer rainfall are investigated. Six divisions are identified, showing strong temporal variability, the middle and lower reaches of the Yangtze River, the Huaihe River, Southeast China, North China, Southwest China, and Northeast China. The locations of all divisions except Southwest China are in a good agreement with those of the rainband which moves northward from Southeast China to Northeast China from June-August. The phase relationship revealed by the RCEOF analysis suggests that rainfall anomalies in the middle and lower reaches of the Yangtze River, Southeast China, and Northeast China are all characterized by a stationary wave, while a traveling wave is more pronounced in the Huaihe River division, North China, and Southwest China. The fourth RCEOF mode indicates that rainfall anomalies can propagate from south of Northeast China across lower reaches of the Huanghe River and the Huaihe River to the lower reaches of the Yangtze River. A 20-25-year oscillation is found at the middle and lower reaches of the Yangtze River, the Huaihe River valley, North China, and Northeast China. The middle and lower reaches of the Yangtze River and Northeast China also show an approximately-60-year oscillation. Northeast China and the Huaihe River division are dominated by a 36-year and a 70-80-year oscillation, respectively. An 11-year oscillation is also evident in North China, with a periodicity similar to sunspot activity. The interdecadal variability in the middle and lower reaches of the Yangtze River, the Huaihe River valley, and North China shows a significant positive correlation with the solar activity.
基金supported by the National Natural Science Foundation of China(Nos.11362018,11261045,and 11261401)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116401110002)
文摘Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.
基金Project supported by the National Natural Science Foundation of China(Nos.10932001 and 11072015)the Scientific Research Key Program of Beijing Municipal Commission of Education (No.KZ201010005003)the Ph.D.Innovation Foundation of Beijing University of Aeronautics and Astronautics(No.300351)
文摘Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.
基金Project supported by the National Natural Science Foundation of China(Nos.10932001 and 11072015)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20101102110016)
文摘Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.
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.
基金supported by National Natural Science Foundation of China(No.50675209)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education of China(No.200724).
文摘The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material.The holes will lead to mutations and discontinuity to the structure.So the hole-edge stress concentration is always a serious phenomenon.And the phenomenon makes the structure strength decrease very quickly to form dangerous weak points.Most partial damage begins from these weak points.According to the complex variable functions theory,the accurate boundary condition of composite plate with different hole-shapes is founded by conformal mapping method to settle the boundary condition problem of complex hole-shapes.Composite plate with commonly hole-shapes in engineering is studied by several complex variable stress fimction.The boundary integral equations are founded based on exact boundary conditions.Then the exact hole-edge stress analytic solution of composite plate with rectangle holes and wing manholes is resolved.Both of offset axis loadings and its influences on the stress concentration coefficient of the hole-edge are discussed.And comparisons of different loads along various offset axis on the hole-edge stress distribution of orthotropic plate with rectangle hole or wing manhole are made.It can be concluded that hole-edge with continuous variable curvatures might help to decrease the stress concentration coefficient;and smaller angle of outer load and fiber can decrease the stress peak value.
