Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ <em>x</em>)</span>, has been resolved and extended to complex valued functio...Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ <em>x</em>)</span>, has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup><em>x</em> </sup>)</span> . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(<em>i</em> + <em>x</em>)</span> are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.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
The 300 msw Simulated Saturation Diving Chamber Complex was designed and built by ourselves. It was completed at the end of 1985. A 300 msw trimixed saturation diving experiment was successfully conducted in the compl...The 300 msw Simulated Saturation Diving Chamber Complex was designed and built by ourselves. It was completed at the end of 1985. A 300 msw trimixed saturation diving experiment was successfully conducted in the complex by Chinese Underwater Technology Institute(CUTI) from May 22 to June 12 of 1987. During the experiment, 4 divers habitated in the complex for 20 days, and they performed 16 person-time excursion dives and 8 other tests. The result of the experiment indicates that the complex is well designed, suitably configurated, wholly integrated and steadily run, as well as of low leakage. The main functions of the complex have approached to those of the same kind in the world. The complex can be used as a basic facility for serving the nation's saturation diving technology, underwater operation, personnel training, etc.展开更多
Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts ...Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.展开更多
This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ab...This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.展开更多
In order to measure complex structure transfer function and calculate inner sound field, transfer function of integration is mentioned. By establishing virtual system, transfer function of integration can be measured ...In order to measure complex structure transfer function and calculate inner sound field, transfer function of integration is mentioned. By establishing virtual system, transfer function of integration can be measured and the inner sound field can also be calculated. In the experiment, automobile body transfer function of integration is measured and experimental method of establishing virtual system is very valid.展开更多
The molecular structures of fifteen possible 2-thioxanthine(2TX) complexes with one Hg^2+ and two Cl-ions were fully optimized using density functional theory B3PW91/6-311++G^** method. The effective pseudo pot...The molecular structures of fifteen possible 2-thioxanthine(2TX) complexes with one Hg^2+ and two Cl-ions were fully optimized using density functional theory B3PW91/6-311++G^** method. The effective pseudo potential LANL2DZ basis set was used for metal Hg^2+ion. The vibrational analysis was also carried out at the same level. The bond lengths, bond angles, zero point energies, Gibbs free energies, thermodynamic energies and relative energies of all the complexes were obtained. The NBO analysis for natural charge and the second order perturbation energy values was carried out for three stable complexes and the IR spectroscopy of the two complexes was assigned to the experimental data. The results show that the 2-thioxanthine complexes with one Hg^2+ and two Cl^-ions were formed and the complexes resulting from the thione tautomer are more stable than that of the thiol ones. The order of three complexes with relative lower energy is 2TX(1,3,7)-Hg^2+-2, 2 TX(1,3,7)-Hg^2+-1 and 2 TX(1,3,9)-Hg^2+. The calculated IR spectroscopy of the two complexes agreed with the experimental data.展开更多
Formulated in 1859 by the mathematician Bernhard Riemann, the Riemann hypothesis is a conjecture. She says that the Riemann’s Zeta function non-trivial zeros of all have real part . This demonstration would impr...Formulated in 1859 by the mathematician Bernhard Riemann, the Riemann hypothesis is a conjecture. She says that the Riemann’s Zeta function non-trivial zeros of all have real part . This demonstration would improve the prime numbers distribution knowledge. This conjecture constitutes one of the most important mathematics unsolved problems of the 21st century: it is one of the famous Hilbert problems proposed in 1900. In this article, a method for solving this conjecture is given. This work has been started by finding an analytical function which gives a best accurate 10<sup>-8</sup> of particular zeros sample that this number has increased gradually and finally prooving that this function is always irrational. This demonstration is important as allows Riemann’s zeta function to be a model function in the Dirichlet series theory and be at the crossroads of many other theories. Also, it is going to serve as a motivation and guideline for new studies.展开更多
In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can sa...In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.展开更多
In this paper problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces are dealt with. General solutions of the problems are formulated by applying extended Schwarz principl...In this paper problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces are dealt with. General solutions of the problems are formulated by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions. Closed-form solutions of several typical problems are obtained and the stress intensity factors are given. These solutions include a series of original results and some results of previous researches. It is found that under symmetrical loads the solutions for the dissimilar materials are the same as those for the homogeneous materia[7]展开更多
By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approa...By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.展开更多
With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads are investigated. General representations of analytical solutions are obta...With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads are investigated. General representations of analytical solutions are obtained with self-similar functions. The problems can be easily converted into Riemann-Hilbert problems using this technique. Analytical solutions to stress, displacement and dynamic stress intensity factor under constant and unit-step moving loads on the surfaces of asymmetrical extension crack, respectively, are obtained. By applying these solutions, together with the superposition principle, solutions of discretionarily intricate problems can be found.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 influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordina...The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordinates and auxiliary functions. First, the model is divided into two domains: a scalene triangular hill with a semi-circular bottom; and a half space with a semi-circular canyon. Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains. Then, considering the displacement continuity and stress equilibrium, algebraic equations are established. Finally, numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.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
In this paper,the dynamic stress concentration and scattering of SH-waves by bi-material structures that possess an interface elliptic cavity are investigated.First,by using the complex function method,the Green's...In this paper,the dynamic stress concentration and scattering of SH-waves by bi-material structures that possess an interface elliptic cavity are investigated.First,by using the complex function method,the Green's function is constructed.This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface.Then,the problem is divided into an upper and lower half space along the horizontal interface,regarded as a harmony model.In order to satisfy the integral continuity condition, the unknown anti-plane forces are applied to the interface.The integral equations with unknown forces can be established through the continuity condition,and after transformation,the algebraic equations are solved numerically.Finally,the distribution of the dynamic stress concentration factor(DSCF)around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.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
Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variab...Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variables. The functions can satisfy a series of basic equations and governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces and stress singularity at the crack tips. Thus, it is only necessary to consider the boundary conditions on the external boundaries of the plate, which can be approximately satisfied by the collocation method and least square technique. Different boundary conditions and loading cases of the cracked plates are analyzed and calculated. Compared to other methods, the numerical examples show that the present method has many advantages such as good accuracy and less computer time. This is an effective semi_analytical and semi_numerical method.展开更多
文摘Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ <em>x</em>)</span>, has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup><em>x</em> </sup>)</span> . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(<em>i</em> + <em>x</em>)</span> are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.
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The 300 msw Simulated Saturation Diving Chamber Complex was designed and built by ourselves. It was completed at the end of 1985. A 300 msw trimixed saturation diving experiment was successfully conducted in the complex by Chinese Underwater Technology Institute(CUTI) from May 22 to June 12 of 1987. During the experiment, 4 divers habitated in the complex for 20 days, and they performed 16 person-time excursion dives and 8 other tests. The result of the experiment indicates that the complex is well designed, suitably configurated, wholly integrated and steadily run, as well as of low leakage. The main functions of the complex have approached to those of the same kind in the world. The complex can be used as a basic facility for serving the nation's saturation diving technology, underwater operation, personnel training, etc.
基金partially supported by the JSPS KAKENHI(JP22H03643,JP19K22891)。
文摘Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.
文摘This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.
文摘In order to measure complex structure transfer function and calculate inner sound field, transfer function of integration is mentioned. By establishing virtual system, transfer function of integration can be measured and the inner sound field can also be calculated. In the experiment, automobile body transfer function of integration is measured and experimental method of establishing virtual system is very valid.
基金supported by the National Natural Science Foundation of China(No.21643014)the Special Natural Science Foundation of Science and Technology Bureau of Xi’an City Government(No.2016CXWL02)
文摘The molecular structures of fifteen possible 2-thioxanthine(2TX) complexes with one Hg^2+ and two Cl-ions were fully optimized using density functional theory B3PW91/6-311++G^** method. The effective pseudo potential LANL2DZ basis set was used for metal Hg^2+ion. The vibrational analysis was also carried out at the same level. The bond lengths, bond angles, zero point energies, Gibbs free energies, thermodynamic energies and relative energies of all the complexes were obtained. The NBO analysis for natural charge and the second order perturbation energy values was carried out for three stable complexes and the IR spectroscopy of the two complexes was assigned to the experimental data. The results show that the 2-thioxanthine complexes with one Hg^2+ and two Cl^-ions were formed and the complexes resulting from the thione tautomer are more stable than that of the thiol ones. The order of three complexes with relative lower energy is 2TX(1,3,7)-Hg^2+-2, 2 TX(1,3,7)-Hg^2+-1 and 2 TX(1,3,9)-Hg^2+. The calculated IR spectroscopy of the two complexes agreed with the experimental data.
文摘Formulated in 1859 by the mathematician Bernhard Riemann, the Riemann hypothesis is a conjecture. She says that the Riemann’s Zeta function non-trivial zeros of all have real part . This demonstration would improve the prime numbers distribution knowledge. This conjecture constitutes one of the most important mathematics unsolved problems of the 21st century: it is one of the famous Hilbert problems proposed in 1900. In this article, a method for solving this conjecture is given. This work has been started by finding an analytical function which gives a best accurate 10<sup>-8</sup> of particular zeros sample that this number has increased gradually and finally prooving that this function is always irrational. This demonstration is important as allows Riemann’s zeta function to be a model function in the Dirichlet series theory and be at the crossroads of many other theories. Also, it is going to serve as a motivation and guideline for new studies.
文摘In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.
文摘In this paper problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces are dealt with. General solutions of the problems are formulated by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions. Closed-form solutions of several typical problems are obtained and the stress intensity factors are given. These solutions include a series of original results and some results of previous researches. It is found that under symmetrical loads the solutions for the dissimilar materials are the same as those for the homogeneous materia[7]
基金Project supported by the Postdoctoral Science Foundation of China (No.2005038199)the Natural Science Foundation of Heilongjiang Province of China (No.ZJG04-08)
文摘By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.
基金the Post-Doctoral Science Foundation of China(No.2005038199)the Natural Science Foundation of Heilongjiang Province of China(No.ZJG04-08)
文摘With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads are investigated. General representations of analytical solutions are obtained with self-similar functions. The problems can be easily converted into Riemann-Hilbert problems using this technique. Analytical solutions to stress, displacement and dynamic stress intensity factor under constant and unit-step moving loads on the surfaces of asymmetrical extension crack, respectively, are obtained. By applying these solutions, together with the superposition principle, solutions of discretionarily intricate problems can be found.
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.
文摘The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordinates and auxiliary functions. First, the model is divided into two domains: a scalene triangular hill with a semi-circular bottom; and a half space with a semi-circular canyon. Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains. Then, considering the displacement continuity and stress equilibrium, algebraic equations are established. Finally, numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.
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.
文摘In this paper,the dynamic stress concentration and scattering of SH-waves by bi-material structures that possess an interface elliptic cavity are investigated.First,by using the complex function method,the Green's function is constructed.This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface.Then,the problem is divided into an upper and lower half space along the horizontal interface,regarded as a harmony model.In order to satisfy the integral continuity condition, the unknown anti-plane forces are applied to the interface.The integral equations with unknown forces can be established through the continuity condition,and after transformation,the algebraic equations are solved numerically.Finally,the distribution of the dynamic stress concentration factor(DSCF)around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.
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.
文摘Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variables. The functions can satisfy a series of basic equations and governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces and stress singularity at the crack tips. Thus, it is only necessary to consider the boundary conditions on the external boundaries of the plate, which can be approximately satisfied by the collocation method and least square technique. Different boundary conditions and loading cases of the cracked plates are analyzed and calculated. Compared to other methods, the numerical examples show that the present method has many advantages such as good accuracy and less computer time. This is an effective semi_analytical and semi_numerical method.