Recently, stratospheric airships prefer to employ a vectored tail rotor or differential main propellers for the yaw control, rather than the control surfaces like common low-altitude airship. The load capacity of vect...Recently, stratospheric airships prefer to employ a vectored tail rotor or differential main propellers for the yaw control, rather than the control surfaces like common low-altitude airship. The load capacity of vectored mechanism and propellers are always limited by the weight and strength, which bring challenges for the attitude controller. In this paper, the yaw channel of airship dynamics is firstly rewritten as a simplified two-order dynamics equation and the dynamic charac- teristics is analyzed with a phase plane method. Analysis shows that when ignoring damping, the yaw control channel is available to the minimum principle of Pontryagin for optimal control, which can obtain a Bang-Bang controller. But under this controller, the control output could he bouncing around the theoretical switch curve due to the presence of disturbance and damping, which makes adverse effects for the servo structure. Considering the structure requirements of actuators, a phase plane method controller is employed, with a dead zone surrounded by several phase switch curve. Thus, the controller outputs are limited to finite values. Finally, through the numerical simulation and actual flight experiment, the method is proved to be effective.展开更多
The steady calculation based on the mixing-plane method is still the most widely-used three-dimensional flow analysis tool for multistage turbomachines. For modern turbomachines,the trend of design is to reach higher ...The steady calculation based on the mixing-plane method is still the most widely-used three-dimensional flow analysis tool for multistage turbomachines. For modern turbomachines,the trend of design is to reach higher aerodynamic loading but with still further compact size. In such a case, the traditional mixing-plane method has to be revised to give a more physically meaningful prediction. In this paper, a novel mixing-plane method was proposed, and three representative test cases including a transonic compressor, a highly-loaded centrifugal compressor and a highpressure axial turbine were performed for validation purpose. This novel mixing-plane method can satisfy the flux conservation perfectly. Reverse flow across the mixing-plane interface can be resolved naturally, thus making this method numerically robust. Artificial reflection at the mixing-plane interface is almost eliminated, and then its detrimental impact on the flow field is minimized. Generally, this mixing-plane method is suitable to simulate steady flows in highly-loaded multistage turbomachines.展开更多
The prediction of the fracture plane orientation in fatigue is a scientific topic and remains relevant for every type of material. However, in this work, we compared the orientation of the fracture plane obtained expe...The prediction of the fracture plane orientation in fatigue is a scientific topic and remains relevant for every type of material. However, in this work, we compared the orientation of the fracture plane obtained experimentally through tests on specimens under multiaxial loading with that calculated by the variance method. In the statistical approach criteria, several methods have been developed but we have presented only one method, namely the variance method using the equivalent stress. She assumes that the fracture plane orientation is the one on which the variance of the equivalent stress is maximum. Three types of equivalent stress are defined for this method [1]: normal stress, shear stress and combined normal and shear stress. The results obtained were compared with experimental results for multiaxial cyclic stress states, and it emerges that the variance method for the case of combined loading is conservative as it gives a better prediction of the fracture plane.展开更多
The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of pla...The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.展开更多
Although concern has been recently expressed with regard to the solution to the non-convex problem, convex optimization is still important in machine learning, especially when the situation requires an interpretable m...Although concern has been recently expressed with regard to the solution to the non-convex problem, convex optimization is still important in machine learning, especially when the situation requires an interpretable model. Solution to the convex problem is a global minimum, and the final model can be explained mathematically. Typically, the convex problem is re-casted as a regularized risk minimization problem to prevent overfitting. The cutting plane method (CPM) is one of the best solvers for the convex problem, irrespective of whether the objective function is differentiable or not. However, CPM and its variants fail to adequately address large-scale data-intensive cases because these algorithms access the entire dataset in each iteration, which substantially increases the computational burden and memory cost. To alleviate this problem, we propose a novel algorithm named the mini-batch cutting plane method (MBCPM), which iterates with estimated cutting planes calculated on a small batch of sampled data and is capable of handling large-scale problems. Furthermore, the proposed MBCPM adopts a "sink" operation that detects and adjusts noisy estimations to guarantee convergence. Numerical experiments on extensive real-world datasets demonstrate the effectiveness of MBCPM, which is superior to the bundle methods for regularized risk minimization as well as popular stochastic gradient descent methods in terms of convergence speed.展开更多
The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point wit...The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point with cutting plane （IP/CP） method is proposed to solve the mixed-integer optimization problem of the electrical power generation expansion planning. The IP/CP method could improve the overall efficiency of the solution and reduce the computational time. Proposed method is combined with the Bender＇s decomposition technique in order to decompose the generation expansion problem into a master investment problem and a slave operational problem. The numerical example is presented to compare with the effectiveness of the proposed algorithm.展开更多
In this paper, the basic principles and mathematical process of the Second-order Imaginary Plane Method (IPM) for modeling the radiative heat transfer are analysed and proved in detail. Through the numerical computati...In this paper, the basic principles and mathematical process of the Second-order Imaginary Plane Method (IPM) for modeling the radiative heat transfer are analysed and proved in detail. Through the numerical computation for the real process of the radiative heat transfer using the Second-order IPM,the previous IPM (the first-order), the Analytic Method and the Zone Method, it was shown that the calculation accuracy of the Secondr-order IPM is much higher than that of the first-order IPM, and its demand to computer capacity and time consuming is much lower than that of the Zone Method or the Analytic Method. It is verilied that the method is more effective and has a higher accuracy for modeling radiative heat transfer in engineering.展开更多
A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the l...A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.展开更多
VARTM (Vacuum Assisted Resin Transfer Molding) is a popular method for manufacturing large-scaled, single-sided mold composite structures, such as wind turbine blades and yachts. Simulation to find the proper infusion...VARTM (Vacuum Assisted Resin Transfer Molding) is a popular method for manufacturing large-scaled, single-sided mold composite structures, such as wind turbine blades and yachts. Simulation to find the proper infusion scenario before manufacturing is essential to avoid dry spots as well as incomplete saturation and various fiber weaves with different permeability affect numerical simulation tremendously. This study focused on deriving the in-plane permeability prediction method for FRP (Fiber Reinforced Plastics) laminates in the VARTM process by experimental measurements and numerical analysis. The method provided an efficient way to determine the permeability of laminates without conducting lots of experiments in the future. In-plane permeability imported into the software, RTM-Worx, to simulate resin flowing pattern before the infusion experiments of a 3D ship hull with two different infusion scenarios. The close agreement between experiments and simulations proved the correctness and applicability of the prediction method for the in-plane permeability.展开更多
In this papert a cutting planelnethod is presented for solving the linear BLPP.An optimality criterion for the linear BLPP is derived from two related linear programsconstructed by using the complementarity conditions...In this papert a cutting planelnethod is presented for solving the linear BLPP.An optimality criterion for the linear BLPP is derived from two related linear programsconstructed by using the complementarity conditions for the second level problem. Twotypes of cutting planes are developed in order to deal with different situations and to obtaina maximal efficiency. The method makes use of the special cuts and the implicit vertexenumeration idea to avoid some drawbacks in some existing cuttillg plane methods. Thealgorithm can be proved to be finitely convergent.展开更多
In this paper, we are concerned with a positive solution of the non-homogeneous A-Laplacian equation in an open bounded connected domain. We use moving planes method to prove that the domain is a ball and the solution...In this paper, we are concerned with a positive solution of the non-homogeneous A-Laplacian equation in an open bounded connected domain. We use moving planes method to prove that the domain is a ball and the solution is radially symmetric.展开更多
When solving the complex radiative heat transfer problems in reheating furnaces, there are a number of difficulties with the traditional zonal methods. To circumvent these difficulties, a new simplified method was pro...When solving the complex radiative heat transfer problems in reheating furnaces, there are a number of difficulties with the traditional zonal methods. To circumvent these difficulties, a new simplified method was pro- posed, which employed imaginary planes, referred to as the imaginary plane model. With the new model, crown wall reduction process was simplified. Therefore, every model zone could be treated as a closed square cavity. It could also solve the problem of radiative blocking in industrial furnaces more effectively. Besides, the new imaginary plane based model may lead to a problem that the denominator was zero. This problem was solved by transforming the ex- pressions of reflex heat flux in the model. The model was capable of dealing with the systems that included black sur- faces. The model was validated by considering the heat transfer in a reheating furnace where the temperature fields in the furnace chamber （including the steel, wall and gas） were obtained. A detailed comparison was made between the simulation and the black box experiment. The results show that the new model developed was valid and accurate.展开更多
In this paper, based on the step reduction method[1] and exact analytic method[2] anew method-exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational ...In this paper, based on the step reduction method[1] and exact analytic method[2] anew method-exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a quadrilateral noncompatible element with 8 degrees of freedom is derived for the solution of plane problem. Since Jacobi's transformation is not applied, the present element may degenerate into a triangle element. It is convenient to use the element in engineering. In this paper, the convergence is proved. Numerical examples are given at the endof this paper, which indicate satisfactory results of stress and displacements can be obtained and have higher numerical precision in nodes.展开更多
The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for...The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for the eigenvalue matrix system that can be directly solved for the angular frequencies and field profiles when bianisotropy is included. To demonstrate the computation process and expected state diagrams and field profiles, numerical computation examples are provided for a bianisotropic Bragg Array with central defect. It is shown that the location of the magnetoelectric tensor elements has a significant effect on the eigenstates of an equivalent isotropic (anisotropic) structure. One form of the magnetoelectric tensor (diagonal elements only) leads to the observation of merging states and the formation of exceptional points. The numerical approach presented can be implemented as an add-on to the familiar plane wave numerical technique.展开更多
Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious...Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.展开更多
In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem...In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.展开更多
The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the ...The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.展开更多
In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calcula...In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calculate these terms and the modelled equations. Discrepancies between model calculations and measurements are quite often attributed to incorrect modelling, while the suitability and accuracy of the numerical methods used are seldom scrutinized. Instead, alternate near-wall and Reynolds-stress models are proposed to remedy the incorrect turbulent flow calculations. On the other hand, if care is not taken in the numerical treatment of the Reynolds-stress gradient terms, physically unrealistic results and solution instability could occur. Previous studies by the author and his collaborators on the effects of numerical methods have shown that some of the more commonly used numerical methods could enhance numerical stability in the solution procedure but would introduce considerable inaccuracy to the results. The flow cases chosen to demonstrate these inaccuracies are a backstep flow and flow in a square duct, where flow complexities are present. The current investigation attempts to show that the above-mentioned effects of numerical methods could also occur in the calculation of a developing plane channel flow, where flow complexities are absent. In addition, this study shows that the results thus obtained lead to a predicted skin friction coefficient that is influenced more by the numerical method used than by the turbulence model invoked. Together, these results show that numerical treatment of the Reynolds-stress gradients in the equations play an important role, even for a developing plane channel flow.展开更多
基金sponsored by the National Defense Science and Technology Innovation Fund Projects of Chinese Academy of Science(No.CXJJ-14-M06)
文摘Recently, stratospheric airships prefer to employ a vectored tail rotor or differential main propellers for the yaw control, rather than the control surfaces like common low-altitude airship. The load capacity of vectored mechanism and propellers are always limited by the weight and strength, which bring challenges for the attitude controller. In this paper, the yaw channel of airship dynamics is firstly rewritten as a simplified two-order dynamics equation and the dynamic charac- teristics is analyzed with a phase plane method. Analysis shows that when ignoring damping, the yaw control channel is available to the minimum principle of Pontryagin for optimal control, which can obtain a Bang-Bang controller. But under this controller, the control output could he bouncing around the theoretical switch curve due to the presence of disturbance and damping, which makes adverse effects for the servo structure. Considering the structure requirements of actuators, a phase plane method controller is employed, with a dead zone surrounded by several phase switch curve. Thus, the controller outputs are limited to finite values. Finally, through the numerical simulation and actual flight experiment, the method is proved to be effective.
文摘The steady calculation based on the mixing-plane method is still the most widely-used three-dimensional flow analysis tool for multistage turbomachines. For modern turbomachines,the trend of design is to reach higher aerodynamic loading but with still further compact size. In such a case, the traditional mixing-plane method has to be revised to give a more physically meaningful prediction. In this paper, a novel mixing-plane method was proposed, and three representative test cases including a transonic compressor, a highly-loaded centrifugal compressor and a highpressure axial turbine were performed for validation purpose. This novel mixing-plane method can satisfy the flux conservation perfectly. Reverse flow across the mixing-plane interface can be resolved naturally, thus making this method numerically robust. Artificial reflection at the mixing-plane interface is almost eliminated, and then its detrimental impact on the flow field is minimized. Generally, this mixing-plane method is suitable to simulate steady flows in highly-loaded multistage turbomachines.
文摘The prediction of the fracture plane orientation in fatigue is a scientific topic and remains relevant for every type of material. However, in this work, we compared the orientation of the fracture plane obtained experimentally through tests on specimens under multiaxial loading with that calculated by the variance method. In the statistical approach criteria, several methods have been developed but we have presented only one method, namely the variance method using the equivalent stress. She assumes that the fracture plane orientation is the one on which the variance of the equivalent stress is maximum. Three types of equivalent stress are defined for this method [1]: normal stress, shear stress and combined normal and shear stress. The results obtained were compared with experimental results for multiaxial cyclic stress states, and it emerges that the variance method for the case of combined loading is conservative as it gives a better prediction of the fracture plane.
文摘The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.
基金Project supported by the National Key R&D Program of China(No.2018YFB0204300)the National Natural Science Foundation of China(Nos.61872376 and 61806216)。
文摘Although concern has been recently expressed with regard to the solution to the non-convex problem, convex optimization is still important in machine learning, especially when the situation requires an interpretable model. Solution to the convex problem is a global minimum, and the final model can be explained mathematically. Typically, the convex problem is re-casted as a regularized risk minimization problem to prevent overfitting. The cutting plane method (CPM) is one of the best solvers for the convex problem, irrespective of whether the objective function is differentiable or not. However, CPM and its variants fail to adequately address large-scale data-intensive cases because these algorithms access the entire dataset in each iteration, which substantially increases the computational burden and memory cost. To alleviate this problem, we propose a novel algorithm named the mini-batch cutting plane method (MBCPM), which iterates with estimated cutting planes calculated on a small batch of sampled data and is capable of handling large-scale problems. Furthermore, the proposed MBCPM adopts a "sink" operation that detects and adjusts noisy estimations to guarantee convergence. Numerical experiments on extensive real-world datasets demonstrate the effectiveness of MBCPM, which is superior to the bundle methods for regularized risk minimization as well as popular stochastic gradient descent methods in terms of convergence speed.
文摘The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point with cutting plane （IP/CP） method is proposed to solve the mixed-integer optimization problem of the electrical power generation expansion planning. The IP/CP method could improve the overall efficiency of the solution and reduce the computational time. Proposed method is combined with the Bender＇s decomposition technique in order to decompose the generation expansion problem into a master investment problem and a slave operational problem. The numerical example is presented to compare with the effectiveness of the proposed algorithm.
文摘In this paper, the basic principles and mathematical process of the Second-order Imaginary Plane Method (IPM) for modeling the radiative heat transfer are analysed and proved in detail. Through the numerical computation for the real process of the radiative heat transfer using the Second-order IPM,the previous IPM (the first-order), the Analytic Method and the Zone Method, it was shown that the calculation accuracy of the Secondr-order IPM is much higher than that of the first-order IPM, and its demand to computer capacity and time consuming is much lower than that of the Zone Method or the Analytic Method. It is verilied that the method is more effective and has a higher accuracy for modeling radiative heat transfer in engineering.
基金the National Natural Science Foundation of China(50478014)the National 973 Program(2007CB714200)the Beijing Natural Science Foundation(8061003).
文摘A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.
文摘VARTM (Vacuum Assisted Resin Transfer Molding) is a popular method for manufacturing large-scaled, single-sided mold composite structures, such as wind turbine blades and yachts. Simulation to find the proper infusion scenario before manufacturing is essential to avoid dry spots as well as incomplete saturation and various fiber weaves with different permeability affect numerical simulation tremendously. This study focused on deriving the in-plane permeability prediction method for FRP (Fiber Reinforced Plastics) laminates in the VARTM process by experimental measurements and numerical analysis. The method provided an efficient way to determine the permeability of laminates without conducting lots of experiments in the future. In-plane permeability imported into the software, RTM-Worx, to simulate resin flowing pattern before the infusion experiments of a 3D ship hull with two different infusion scenarios. The close agreement between experiments and simulations proved the correctness and applicability of the prediction method for the in-plane permeability.
文摘In this papert a cutting planelnethod is presented for solving the linear BLPP.An optimality criterion for the linear BLPP is derived from two related linear programsconstructed by using the complementarity conditions for the second level problem. Twotypes of cutting planes are developed in order to deal with different situations and to obtaina maximal efficiency. The method makes use of the special cuts and the implicit vertexenumeration idea to avoid some drawbacks in some existing cuttillg plane methods. Thealgorithm can be proved to be finitely convergent.
文摘In this paper, we are concerned with a positive solution of the non-homogeneous A-Laplacian equation in an open bounded connected domain. We use moving planes method to prove that the domain is a ball and the solution is radially symmetric.
基金Item Sponsored by National High Technology Research and Development Program(863Program)of China(2011AA060104)
文摘When solving the complex radiative heat transfer problems in reheating furnaces, there are a number of difficulties with the traditional zonal methods. To circumvent these difficulties, a new simplified method was pro- posed, which employed imaginary planes, referred to as the imaginary plane model. With the new model, crown wall reduction process was simplified. Therefore, every model zone could be treated as a closed square cavity. It could also solve the problem of radiative blocking in industrial furnaces more effectively. Besides, the new imaginary plane based model may lead to a problem that the denominator was zero. This problem was solved by transforming the ex- pressions of reflex heat flux in the model. The model was capable of dealing with the systems that included black sur- faces. The model was validated by considering the heat transfer in a reheating furnace where the temperature fields in the furnace chamber （including the steel, wall and gas） were obtained. A detailed comparison was made between the simulation and the black box experiment. The results show that the new model developed was valid and accurate.
文摘In this paper, based on the step reduction method[1] and exact analytic method[2] anew method-exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a quadrilateral noncompatible element with 8 degrees of freedom is derived for the solution of plane problem. Since Jacobi's transformation is not applied, the present element may degenerate into a triangle element. It is convenient to use the element in engineering. In this paper, the convergence is proved. Numerical examples are given at the endof this paper, which indicate satisfactory results of stress and displacements can be obtained and have higher numerical precision in nodes.
文摘The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for the eigenvalue matrix system that can be directly solved for the angular frequencies and field profiles when bianisotropy is included. To demonstrate the computation process and expected state diagrams and field profiles, numerical computation examples are provided for a bianisotropic Bragg Array with central defect. It is shown that the location of the magnetoelectric tensor elements has a significant effect on the eigenstates of an equivalent isotropic (anisotropic) structure. One form of the magnetoelectric tensor (diagonal elements only) leads to the observation of merging states and the formation of exceptional points. The numerical approach presented can be implemented as an add-on to the familiar plane wave numerical technique.
文摘Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.
文摘In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11304074,61475042,and 11274088)the Natural Science Foundation of Hebei Province,China(Grant Nos.A2015202320 and GCC2014048)the Key Subject Construction Project of Hebei Province University,China
文摘The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.
文摘In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calculate these terms and the modelled equations. Discrepancies between model calculations and measurements are quite often attributed to incorrect modelling, while the suitability and accuracy of the numerical methods used are seldom scrutinized. Instead, alternate near-wall and Reynolds-stress models are proposed to remedy the incorrect turbulent flow calculations. On the other hand, if care is not taken in the numerical treatment of the Reynolds-stress gradient terms, physically unrealistic results and solution instability could occur. Previous studies by the author and his collaborators on the effects of numerical methods have shown that some of the more commonly used numerical methods could enhance numerical stability in the solution procedure but would introduce considerable inaccuracy to the results. The flow cases chosen to demonstrate these inaccuracies are a backstep flow and flow in a square duct, where flow complexities are present. The current investigation attempts to show that the above-mentioned effects of numerical methods could also occur in the calculation of a developing plane channel flow, where flow complexities are absent. In addition, this study shows that the results thus obtained lead to a predicted skin friction coefficient that is influenced more by the numerical method used than by the turbulence model invoked. Together, these results show that numerical treatment of the Reynolds-stress gradients in the equations play an important role, even for a developing plane channel flow.
