This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field couple...This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media. This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy, from which, however, the results for the isotropic case can be readily obtained.展开更多
To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy curre...To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.展开更多
The pursuit problem is a well-known problem in computer science. In this problem, a group of predator agents attempt to capture a prey agent in an environment with various obstacle types, partial observation, and an i...The pursuit problem is a well-known problem in computer science. In this problem, a group of predator agents attempt to capture a prey agent in an environment with various obstacle types, partial observation, and an infinite grid-world. Predator agents are applied algorithms that use the univector field method to reach the prey agent, strategies for avoiding obstacles and strategies for cooperation between predator agents. Obstacle avoidance strategies are generalized and presented through strategies called hitting and following boundary(HFB); trapped and following shortest path(TFSP); and predicted and following shortest path(PFSP). In terms of cooperation, cooperation strategies are employed to more quickly reach and capture the prey agent. Experimental results are shown to illustrate the efficiency of the method in the pursuit problem.展开更多
An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien＇s method, a pair of generalized variational principl...An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien＇s method, a pair of generalized variational principles （GVPs） are established, which directly leads to all four Maxwell＇s equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem.展开更多
The objective of this work is to present a boundary integral formulation for the static, linear plane strain problem of uncoupled magneto-elasticity for an infinite magnetizable cylinder in a transverse magnetic field...The objective of this work is to present a boundary integral formulation for the static, linear plane strain problem of uncoupled magneto-elasticity for an infinite magnetizable cylinder in a transverse magnetic field. This formulation allows to obtain analytical solutions in closed form for problems with relatively simple geometries, in addition to being particularly well-adapted to numerical approaches for more complicated cases. As an application, the first fundamental problem of Elasticity for the circular cylinder is investigated.展开更多
The notion of preordering, which is a generalization of the notion of ordering, has been introduced by Serre. On the other hand, the notion of round quadratic forms has been introduced by Witt. Based on these ideas, i...The notion of preordering, which is a generalization of the notion of ordering, has been introduced by Serre. On the other hand, the notion of round quadratic forms has been introduced by Witt. Based on these ideas, it is here shown that 1) a field F is formally real n-pythagorean iff the nth radical, RnF is a preordering (Theorem 2), and 2) a field F is n-pythagorean iff for any n-fold Pfister form ρ. There exists an odd integer l(>1) such that l×ρ is a round quadratic form (Theorem 8). By considering upper bounds for the number of squares on Pfister’s interpretation, these results finally lead to the main result (Theorem 10) such that the generalization of pythagorean fields coincides with the generalization of Hilbert’s 17th Problem.展开更多
Potential field due to line sources residing on slender heterogeneities is involved in various areas,such as heat conduction,potential flow,and electrostatics.Often dipolar line sources are either prescribed or induce...Potential field due to line sources residing on slender heterogeneities is involved in various areas,such as heat conduction,potential flow,and electrostatics.Often dipolar line sources are either prescribed or induced due to close interaction with other objects.Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect.In the present work,we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities.In a benchmark example of two parallel rods,we compare the line element solution with the boundary element solution to show the accuracy as a function in terms of rods distance.Furthermore,we use more complicated examples to demonstrate the capability of the line element technique.展开更多
Magnetic flux density around the weld area was used to reconstruct the current density distribution during resistance spot welding(RSW) of aluminum alloy according to inverse problem theory. A current-magnetic field m...Magnetic flux density around the weld area was used to reconstruct the current density distribution during resistance spot welding(RSW) of aluminum alloy according to inverse problem theory. A current-magnetic field model was established and the conjugate gradient method was used to solve this model. The results showed that the current density was low at the center of nugget while high on the edge of nugget. Moreover, the welding time of 30ms—60 ms is a key period for nucleation. The current density distribution can reflect whether the weld nugget is formed or splashed, therefore it has the potential to monitor the weld quality of RSW.展开更多
A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization.The enthalpy method was applied to solve this two-phase ax...A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization.The enthalpy method was applied to solve this two-phase axisymmetrical mehing problem.Computational results of tempera ture fields were obtained,which provide useful information to practical lair treatment processing. The validity of enthalpy method in solving such problems is presented.展开更多
Non-contact magnetic measurement method is an effective way to study the air arc behavior experimentally. One of the crucial techniques is to solve an inverse problem for the electromagnetic field. This study is devot...Non-contact magnetic measurement method is an effective way to study the air arc behavior experimentally. One of the crucial techniques is to solve an inverse problem for the electromagnetic field. This study is devoted to investigating different algorithms for this kind of inverse problem preliminarily, including the preconditioned conjugate gradient method, penalty function method and genetic algorithm. The feasibility of each algorithm is analyzed. It is shown that the preconditioned conjugate gradient method is valid only for few arc segments, the estimation accuracy of the penalty function method is dependent on the initial conditions, and the convergence of genetic algorithm should be studied further for more segments in an arc current.展开更多
基金Project (No. 10372088) supported by the National Natural Science Foundation of China
文摘This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media. This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy, from which, however, the results for the isotropic case can be readily obtained.
基金supported by the National Defense Basic Technology Research Program of China(Grant No.Z132013T001)
文摘To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.
基金the Basic Science Research Program through the National Research Foundation of Korea (NRF-2014R1A1A2057735)the Kyung Hee University in 2016 [KHU-20160601]
文摘The pursuit problem is a well-known problem in computer science. In this problem, a group of predator agents attempt to capture a prey agent in an environment with various obstacle types, partial observation, and an infinite grid-world. Predator agents are applied algorithms that use the univector field method to reach the prey agent, strategies for avoiding obstacles and strategies for cooperation between predator agents. Obstacle avoidance strategies are generalized and presented through strategies called hitting and following boundary(HFB); trapped and following shortest path(TFSP); and predicted and following shortest path(PFSP). In terms of cooperation, cooperation strategies are employed to more quickly reach and capture the prey agent. Experimental results are shown to illustrate the efficiency of the method in the pursuit problem.
基金Project supported by the National Natural Science Foundation of China （No. 60304009） and the Natural Science Foundation of Hebei Province of China （No. F2005000385）
文摘An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien＇s method, a pair of generalized variational principles （GVPs） are established, which directly leads to all four Maxwell＇s equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem.
文摘The objective of this work is to present a boundary integral formulation for the static, linear plane strain problem of uncoupled magneto-elasticity for an infinite magnetizable cylinder in a transverse magnetic field. This formulation allows to obtain analytical solutions in closed form for problems with relatively simple geometries, in addition to being particularly well-adapted to numerical approaches for more complicated cases. As an application, the first fundamental problem of Elasticity for the circular cylinder is investigated.
文摘The notion of preordering, which is a generalization of the notion of ordering, has been introduced by Serre. On the other hand, the notion of round quadratic forms has been introduced by Witt. Based on these ideas, it is here shown that 1) a field F is formally real n-pythagorean iff the nth radical, RnF is a preordering (Theorem 2), and 2) a field F is n-pythagorean iff for any n-fold Pfister form ρ. There exists an odd integer l(>1) such that l×ρ is a round quadratic form (Theorem 8). By considering upper bounds for the number of squares on Pfister’s interpretation, these results finally lead to the main result (Theorem 10) such that the generalization of pythagorean fields coincides with the generalization of Hilbert’s 17th Problem.
文摘Potential field due to line sources residing on slender heterogeneities is involved in various areas,such as heat conduction,potential flow,and electrostatics.Often dipolar line sources are either prescribed or induced due to close interaction with other objects.Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect.In the present work,we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities.In a benchmark example of two parallel rods,we compare the line element solution with the boundary element solution to show the accuracy as a function in terms of rods distance.Furthermore,we use more complicated examples to demonstrate the capability of the line element technique.
基金Supported by the National Natural Science Foundation of China(No.51275342 and No.51275338)
文摘Magnetic flux density around the weld area was used to reconstruct the current density distribution during resistance spot welding(RSW) of aluminum alloy according to inverse problem theory. A current-magnetic field model was established and the conjugate gradient method was used to solve this model. The results showed that the current density was low at the center of nugget while high on the edge of nugget. Moreover, the welding time of 30ms—60 ms is a key period for nucleation. The current density distribution can reflect whether the weld nugget is formed or splashed, therefore it has the potential to monitor the weld quality of RSW.
基金the National Natural Science Foundation of China and the Chinese Academy of Sciences
文摘A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization.The enthalpy method was applied to solve this two-phase axisymmetrical mehing problem.Computational results of tempera ture fields were obtained,which provide useful information to practical lair treatment processing. The validity of enthalpy method in solving such problems is presented.
基金supported by National Natural Science Foundation of China (No.50977072)the key project of Chinese Ministry of Education (No.109141)
文摘Non-contact magnetic measurement method is an effective way to study the air arc behavior experimentally. One of the crucial techniques is to solve an inverse problem for the electromagnetic field. This study is devoted to investigating different algorithms for this kind of inverse problem preliminarily, including the preconditioned conjugate gradient method, penalty function method and genetic algorithm. The feasibility of each algorithm is analyzed. It is shown that the preconditioned conjugate gradient method is valid only for few arc segments, the estimation accuracy of the penalty function method is dependent on the initial conditions, and the convergence of genetic algorithm should be studied further for more segments in an arc current.
