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
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
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
By means of the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals is investig...By means of the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals is investigated. The solution of the stress intensity factor （SIF） for mode III problem has been found. Under the condition of limitation, both the known results and the SIF solution at the crack tip of a circular hole with two straight cracks and cross crack in one-dimensional hexagonal quasicrystals can be obtained.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
Sliding mode control(SMC)is a widely adopted control technology known for its robustness and simplicity.The essence of SMC is to use discontinuous control to drive a system into a pre-defined motion,called the sliding...Sliding mode control(SMC)is a widely adopted control technology known for its robustness and simplicity.The essence of SMC is to use discontinuous control to drive a system into a pre-defined motion,called the sliding mode,which is designed with desirable dynamical properties.In the sliding mode,the controlled system is insensitive to the matched uncertainties and disturbances.Most SMC theory and methods have been developed based on the dynamical systems in the continuous-time domain,where switching functions play a critical role.Ideal switching is supposed to be instantaneous,activating as soon as the switching condition is met.However,in practice,switching mechanisms are affected by imperfections such as time delays,unmodeled dynamics,defects,digitization effects,and actuation limitations,which can degrade the salient properties of SMC.Understanding these effects and developing mitigation strategies are essential for industrial applications.Furthermore,the advent of networked control environments presents new challenges like limited communication bandwidth,latency and cyberattack,which have seen the emergence of the event-triggered SMC recently.Despite these significant advances,there is a lack of comprehensive studies which examine the commonalities and distinctions of utilizing switching in SMC across the continuous-time and discrete-time domains and beyond.This paper investigates the role of switching in SMC from a spatio-temporal perspective,considering both state-space and time aspects.The aim is to facilitate better understanding of its effects and misbehaviors,and to unlock its full potential for future applications.The interplay between SMC methods in the continuous-time and discrete-time domains is analyzed,and their shared principles and unique challenges are identified.Furthermore,important technical issues relating to switching across these time domains are explored,and several myths and pitfalls in their theory and applications are depicted.The relationships of SMC with other switching-based control systems such as switched control systems,fuzzy control systems,and event-triggered control systems are discussed.The impact of networked control environments on SMC in the continuous-time and discrete-time domains is also examined.Finally,key challenges and opportunities are outlined for future work in SMC and beyond.展开更多
On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM)is discussed in this paper.The advantage of the CVRKPM is that the ...On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM)is discussed in this paper.The advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is formed.Then the CVRKPM is applied to solve two-dimensional elasto-plasticity problems.The Galerkin weak form is employed to obtain the discretized system equation,the penalty method is used to apply the essential boundary conditions.And then,the CVRKPM for two-dimensional elasto-plasticity problems is formed,the corresponding formulae are obtained,and the Newton-Raphson method is used in the numerical implementation.Three numerical examples are given to show that this method in this paper is effective for elasto-plasticity analysis.展开更多
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.
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(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Project supported by the National Natural Science Foundation of China(No.10761005)the Natural Science Foundation of Inner Mongolia Autonomous Region(No.200607010104)
文摘By means of the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals is investigated. The solution of the stress intensity factor （SIF） for mode III problem has been found. Under the condition of limitation, both the known results and the SIF solution at the crack tip of a circular hole with two straight cracks and cross crack in one-dimensional hexagonal quasicrystals can be obtained.
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.
基金supported in part by the Australian Research Council(DP240100830)。
文摘Sliding mode control(SMC)is a widely adopted control technology known for its robustness and simplicity.The essence of SMC is to use discontinuous control to drive a system into a pre-defined motion,called the sliding mode,which is designed with desirable dynamical properties.In the sliding mode,the controlled system is insensitive to the matched uncertainties and disturbances.Most SMC theory and methods have been developed based on the dynamical systems in the continuous-time domain,where switching functions play a critical role.Ideal switching is supposed to be instantaneous,activating as soon as the switching condition is met.However,in practice,switching mechanisms are affected by imperfections such as time delays,unmodeled dynamics,defects,digitization effects,and actuation limitations,which can degrade the salient properties of SMC.Understanding these effects and developing mitigation strategies are essential for industrial applications.Furthermore,the advent of networked control environments presents new challenges like limited communication bandwidth,latency and cyberattack,which have seen the emergence of the event-triggered SMC recently.Despite these significant advances,there is a lack of comprehensive studies which examine the commonalities and distinctions of utilizing switching in SMC across the continuous-time and discrete-time domains and beyond.This paper investigates the role of switching in SMC from a spatio-temporal perspective,considering both state-space and time aspects.The aim is to facilitate better understanding of its effects and misbehaviors,and to unlock its full potential for future applications.The interplay between SMC methods in the continuous-time and discrete-time domains is analyzed,and their shared principles and unique challenges are identified.Furthermore,important technical issues relating to switching across these time domains are explored,and several myths and pitfalls in their theory and applications are depicted.The relationships of SMC with other switching-based control systems such as switched control systems,fuzzy control systems,and event-triggered control systems are discussed.The impact of networked control environments on SMC in the continuous-time and discrete-time domains is also examined.Finally,key challenges and opportunities are outlined for future work in SMC and beyond.
基金supported by the National Natural Science Foundation of China(Grant Nos.10571118 and 10871124)Innovation Program of Shanghai Municipal Education Commission(Grant No.09ZZ99)
文摘On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM)is discussed in this paper.The advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is formed.Then the CVRKPM is applied to solve two-dimensional elasto-plasticity problems.The Galerkin weak form is employed to obtain the discretized system equation,the penalty method is used to apply the essential boundary conditions.And then,the CVRKPM for two-dimensional elasto-plasticity problems is formed,the corresponding formulae are obtained,and the Newton-Raphson method is used in the numerical implementation.Three numerical examples are given to show that this method in this paper is effective for elasto-plasticity analysis.
