By the modified three-field Hu-Washizu principle, this paper establishes a theoretical founda- tion and general convenient formulations to generate convergent stable generalized hybrid/mixed cle- ment (GH/ME) model wh...By the modified three-field Hu-Washizu principle, this paper establishes a theoretical founda- tion and general convenient formulations to generate convergent stable generalized hybrid/mixed cle- ment (GH/ME) model which is invariant with respect to coordinate, insensitive to geometric distortion and suitable for improved stress computation. In the two proposed formulations, the stress equilibrium and orthogonality constraints are imposed through incompatible displacement and internal strain modes respectively. The proposed model by the general formulations in this paper is characterized by including as- sumed stress/strain, assumed stress, variable-node, singular, compatible and incompatible GH/ME models. When using regular meshes or the constant values of the isoparametric Jacobian Det in the assumed strain in- terpolation, the incompatible GH/ME model degenerates to the hybrid/mixed element model. Both general and concrete guidelines for the optimal selection of element shape functions are suggested. By means of the GH/ME theory in this paper, a family of new GH/ME can be and have been easily constructed. The software can also be developed conveniently because all the standard subroutines for the corresponding isoparametric displacement elements can be utilized directly.展开更多
The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing...The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element （MFE） method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence （error estimate） of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.展开更多
Weak formulation of mixed state equations including boundary conditions are presented in a cylindrical coordinate system by introducing Hellinger-Reissner variational principle. Analytical solutions are obtained for l...Weak formulation of mixed state equations including boundary conditions are presented in a cylindrical coordinate system by introducing Hellinger-Reissner variational principle. Analytical solutions are obtained for laminated cylindrical shell by means of state space method. The present study extends and unifies the solution of laminated shells.展开更多
A time semi-discrete Crank-Nicolson （CN） formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed ...A time semi-discrete Crank-Nicolson （CN） formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element （SCNMFVE） formu- lation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial wriables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.展开更多
In this study, we employ mixed finite element （MFE） method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also...In this study, we employ mixed finite element （MFE） method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence, uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.展开更多
[Objective] The paper was to explore the inhibitory effect of mixed biogas slurry-pesticide formulation against Alternaria solani Sorauer. [Method] Different concentrations of Triadimefon, Hekang, Yibao, Propamocarb h...[Objective] The paper was to explore the inhibitory effect of mixed biogas slurry-pesticide formulation against Alternaria solani Sorauer. [Method] Different concentrations of Triadimefon, Hekang, Yibao, Propamocarb hydrochloride and Jinggangmycin were mixed with biogas slurry, and their inhibitory effects were determined by the methods of mycelial inhibition and spore germination. [Result] Mycelial inhibition study showed that mixed formulation of Propamocarb hydrochloride owned the highest inhibition efficiency, and its EC50 value was 3 mg/L. For spore germination, the inhibitory effects of the tested formulations were almost the same as CK, but Hekang and Jinggangmycin had relatively stronger inhibitory effect. The inhibitory effect of mixed formulations with water as solvent was significant. Five kinds of agro-chemicals mixed with biogas slurry had much stronger inhibition effect against the growth of mycelium than that on spore germination. [Conclusion] This study laid foundations for the development of neo-pesticide.展开更多
A mixed vuriational formulation for large deformation analysis of plates is introduced. In this formulation the equilibrium ami compatibility equations are satisfied identically by means of stress functions and displa...A mixed vuriational formulation for large deformation analysis of plates is introduced. In this formulation the equilibrium ami compatibility equations are satisfied identically by means of stress functions and displacement components, respectively, and the constitu,lye equations are satisfied in a least square sense. An example is solved and the results are compared with those available in the literature.Further, the functional is particularized for buckling analysis of plates and a simple example is solved to illustrate the theory.展开更多
In this article, a reduced mixed finite element （MFE） formulation based on proper orthogonal decomposition （POD） for the non-stationary conduction-convection problems is presented. Also the error estimates between...In this article, a reduced mixed finite element （MFE） formulation based on proper orthogonal decomposition （POD） for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.展开更多
In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equatio...In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.展开更多
The multiscale hybrid-mixed(MHM)method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures.The two-dimensional fluid flow in the reservoir and the one-dimensio...The multiscale hybrid-mixed(MHM)method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures.The two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite elements.The coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux.A zero-dimensional pressure(point element)is used to express conservation of mass where fractures intersect.The issuing simulation is then reduced using the MHM method leading to accurate results with a very reduced number of global equations.A general system was developed where fracture geometries and conductivities are specified in an input file and meshes are generated using the public domain mesh generator GMsh.Several test cases illustrate the effectiveness of the proposed approach by comparing the multiscale results with direct simulations.展开更多
On the basis of composition duality principles, augmented three-field macrohybrid mixed variational problems and finite element schemes are analyzed. The compatibility condition adopted here, for compositional dualiza...On the basis of composition duality principles, augmented three-field macrohybrid mixed variational problems and finite element schemes are analyzed. The compatibility condition adopted here, for compositional dualization, is the coupling operator surjectivity, property that expresses in a general operator sense the Ladysenskaja-Babulka-Brezzi inf-sup condition. Variational macro-hybridization is performed under the assumption of decomposable primal and dual spaces relative to nonoverlapping domain decompositions. Then, through compositional dualization macro-hybrid mixed problems are obtained, with internal boundary dual traces as Lagrange multipliers. Also, ＂mass＂ preconditioned aug- mentation of three-field formulations are derived, stabilizing macro-hybrid mixed finite element schemes and rendering possible speed up of rates of convergence. Dual mixed incompressible Darcy flow problems illustrate the theory throughout the paper.展开更多
Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fre...Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fresh water-seawater characterization. For analysis and computational purposes, spatial decompositions based on nonoverlapping multidomains, above and below the sea level, are variationally introduced with internal boundary fluxes dualized as weak transmission constraints. Further, parallel augmented and exactly penalized duality algorithms, and proximation semi-implicit time marching schemes, are established and analyzed.展开更多
In this paper, the general formulation of anew proposed iteration algorithm of mixed BEM/FEM for eigenvalue problems of elastodynamics is described. Approximate fundamental solutions of elastodynamics are adopted in t...In this paper, the general formulation of anew proposed iteration algorithm of mixed BEM/FEM for eigenvalue problems of elastodynamics is described. Approximate fundamental solutions of elastodynamics are adopted in the normal mixed BEM/FEM equations. The accuracy of solutions is progressively improved by the iteration procedure. Not only could the awkwardness of non-algebraic eigenvalue equations be avoided but also the accuracy of numerical solutions is almost independent of the interior meshing. All these give many advantages in numerical calculation. The algorithm is applied to free torsional vibration analysis of bodies of revolution. A few cases are studied. All of the numerical results are very good.展开更多
Reliability optimization plays an important role in design, operation and management of the industrial systems. System reliability can be easily enhanced by improving the reliability of unreliable components and/or by...Reliability optimization plays an important role in design, operation and management of the industrial systems. System reliability can be easily enhanced by improving the reliability of unreliable components and/or by using redundant configuration with subsystems/components in parallel. Redundancy Allocation Problem (RAP) was studied in this research. A mixed integer programming model was proposed to solve the problem, which considers simultaneously two objectives under several resource constraints. The model is only for the hierarchical series-parallel systems in which the elements of any subset of subsystems or components are connected in series or parallel and constitute a larger subsystem or total system. At the end of the study, the performance of the proposed approach was evaluated by a numerical example.展开更多
文摘By the modified three-field Hu-Washizu principle, this paper establishes a theoretical founda- tion and general convenient formulations to generate convergent stable generalized hybrid/mixed cle- ment (GH/ME) model which is invariant with respect to coordinate, insensitive to geometric distortion and suitable for improved stress computation. In the two proposed formulations, the stress equilibrium and orthogonality constraints are imposed through incompatible displacement and internal strain modes respectively. The proposed model by the general formulations in this paper is characterized by including as- sumed stress/strain, assumed stress, variable-node, singular, compatible and incompatible GH/ME models. When using regular meshes or the constant values of the isoparametric Jacobian Det in the assumed strain in- terpolation, the incompatible GH/ME model degenerates to the hybrid/mixed element model. Both general and concrete guidelines for the optimal selection of element shape functions are suggested. By means of the GH/ME theory in this paper, a family of new GH/ME can be and have been easily constructed. The software can also be developed conveniently because all the standard subroutines for the corresponding isoparametric displacement elements can be utilized directly.
基金Project supported by the National Natural Science Foundation of China (Nos.10471100 and 40437017)the Science and Technology Foundation of Beijing Jiaotong University
文摘The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element （MFE） method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence （error estimate） of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.
文摘Weak formulation of mixed state equations including boundary conditions are presented in a cylindrical coordinate system by introducing Hellinger-Reissner variational principle. Analytical solutions are obtained for laminated cylindrical shell by means of state space method. The present study extends and unifies the solution of laminated shells.
基金supported by National Science Foundation of China(11271127)Science Research Project of Guizhou Province Education Department(QJHKYZ[2013]207)
文摘A time semi-discrete Crank-Nicolson （CN） formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element （SCNMFVE） formu- lation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial wriables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.
基金supported by the National Science Foundation of China(11271127)Science Research Project of Guizhou Province Education Department(QJHKYZ[2013]207)
文摘In this study, we employ mixed finite element （MFE） method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence, uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.
基金Supported by Priority Theme of Great Agriculture Project of Zhejiang Science and Technology Office (2010C12001)Social Development Project of Public Technology Research of Zhejiang Science and Technology Office (2011C23065)Students Science and Technology Innovation Activity of Zhejiang Agricultural and Forestry University (201100313)
文摘[Objective] The paper was to explore the inhibitory effect of mixed biogas slurry-pesticide formulation against Alternaria solani Sorauer. [Method] Different concentrations of Triadimefon, Hekang, Yibao, Propamocarb hydrochloride and Jinggangmycin were mixed with biogas slurry, and their inhibitory effects were determined by the methods of mycelial inhibition and spore germination. [Result] Mycelial inhibition study showed that mixed formulation of Propamocarb hydrochloride owned the highest inhibition efficiency, and its EC50 value was 3 mg/L. For spore germination, the inhibitory effects of the tested formulations were almost the same as CK, but Hekang and Jinggangmycin had relatively stronger inhibitory effect. The inhibitory effect of mixed formulations with water as solvent was significant. Five kinds of agro-chemicals mixed with biogas slurry had much stronger inhibition effect against the growth of mycelium than that on spore germination. [Conclusion] This study laid foundations for the development of neo-pesticide.
文摘A mixed vuriational formulation for large deformation analysis of plates is introduced. In this formulation the equilibrium ami compatibility equations are satisfied identically by means of stress functions and displacement components, respectively, and the constitu,lye equations are satisfied in a least square sense. An example is solved and the results are compared with those available in the literature.Further, the functional is particularized for buckling analysis of plates and a simple example is solved to illustrate the theory.
基金supported by the National Science Foundation of China (10871022 11061009+5 种基金 40821092)the National Basic Research Program (2010CB428403 2009CB421407 2010CB951001)Natural Science Foundation of Hebei Province (A2010001663)Chinese Universities Scientific Fund (2009-2-05)
文摘In this article, a reduced mixed finite element （MFE） formulation based on proper orthogonal decomposition （POD） for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.
基金supported by the National Science Foundation of China(11271127 and 11061009)Science Research Program of Guizhou(GJ[2011]2367)the Co-Construction Project of Beijing Municipal Commission of Education
文摘In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.
文摘The multiscale hybrid-mixed(MHM)method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures.The two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite elements.The coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux.A zero-dimensional pressure(point element)is used to express conservation of mass where fractures intersect.The issuing simulation is then reduced using the MHM method leading to accurate results with a very reduced number of global equations.A general system was developed where fracture geometries and conductivities are specified in an input file and meshes are generated using the public domain mesh generator GMsh.Several test cases illustrate the effectiveness of the proposed approach by comparing the multiscale results with direct simulations.
文摘On the basis of composition duality principles, augmented three-field macrohybrid mixed variational problems and finite element schemes are analyzed. The compatibility condition adopted here, for compositional dualization, is the coupling operator surjectivity, property that expresses in a general operator sense the Ladysenskaja-Babulka-Brezzi inf-sup condition. Variational macro-hybridization is performed under the assumption of decomposable primal and dual spaces relative to nonoverlapping domain decompositions. Then, through compositional dualization macro-hybrid mixed problems are obtained, with internal boundary dual traces as Lagrange multipliers. Also, ＂mass＂ preconditioned aug- mentation of three-field formulations are derived, stabilizing macro-hybrid mixed finite element schemes and rendering possible speed up of rates of convergence. Dual mixed incompressible Darcy flow problems illustrate the theory throughout the paper.
文摘Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fresh water-seawater characterization. For analysis and computational purposes, spatial decompositions based on nonoverlapping multidomains, above and below the sea level, are variationally introduced with internal boundary fluxes dualized as weak transmission constraints. Further, parallel augmented and exactly penalized duality algorithms, and proximation semi-implicit time marching schemes, are established and analyzed.
文摘In this paper, the general formulation of anew proposed iteration algorithm of mixed BEM/FEM for eigenvalue problems of elastodynamics is described. Approximate fundamental solutions of elastodynamics are adopted in the normal mixed BEM/FEM equations. The accuracy of solutions is progressively improved by the iteration procedure. Not only could the awkwardness of non-algebraic eigenvalue equations be avoided but also the accuracy of numerical solutions is almost independent of the interior meshing. All these give many advantages in numerical calculation. The algorithm is applied to free torsional vibration analysis of bodies of revolution. A few cases are studied. All of the numerical results are very good.
文摘Reliability optimization plays an important role in design, operation and management of the industrial systems. System reliability can be easily enhanced by improving the reliability of unreliable components and/or by using redundant configuration with subsystems/components in parallel. Redundancy Allocation Problem (RAP) was studied in this research. A mixed integer programming model was proposed to solve the problem, which considers simultaneously two objectives under several resource constraints. The model is only for the hierarchical series-parallel systems in which the elements of any subset of subsystems or components are connected in series or parallel and constitute a larger subsystem or total system. At the end of the study, the performance of the proposed approach was evaluated by a numerical example.
