A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines...A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.展开更多
Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,compara...Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,comparatively fewer works have been devoted to study the effect of adsorption boundary layer(ABL)in throats based on the digital rock method.By considering an ABL,we investigate its effects on fluid flow.We build digital rock model based on computed tomography technology.Then,microscopic pore structures are extracted with watershed segmentation and pore geometries are meshed through Delaunay triangulation approach.Finally,using the meshed digital simulation model and finite element method,we investigate the effects of viscosity and thickness of ABL on microscale flow.Our results demonstrate that viscosity and thickness of ABL are major factors that significantly hinder fluid flow in throats.展开更多
This paper describes a software tool, called LEVSOFT, suitable for the electric field simulations of corona electrodes by the Finite Element Method （FEM）. Special attention was paid to the user friendly construction...This paper describes a software tool, called LEVSOFT, suitable for the electric field simulations of corona electrodes by the Finite Element Method （FEM）. Special attention was paid to the user friendly construction of geometries with corners and sharp points, and to the fast generation of highly refined triangular meshes and field maps. The execution of selfadaptive meshes was also implemented. These customized features make the code attractive for the simulation of needle-type corona electrodes. Some case examples involving needle type electrodes are presented.展开更多
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their...This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.展开更多
With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and re...With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.展开更多
In order to study the laws of the extrusion pressure changing with the extrusion parameters in the process of hydrostatic extrusion for the tungsten alloys, the large deformation elasto plastic theory and the sof...In order to study the laws of the extrusion pressure changing with the extrusion parameters in the process of hydrostatic extrusion for the tungsten alloys, the large deformation elasto plastic theory and the software of ANSYS 5 5 are used to carry out the numerical simulation research. The laws of the extrusion pressure changing with the extrusion parameters, such as the die angle, extrusion ratio, and friction coefficient, are obtained. The simulation results are in good agreement with the experimental ones, and the simulated results are believable.展开更多
Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-materia...Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-material interfaces is demonstrated. Discontinuous Galerkin finite element method is used to solve Euleri- an equations. And the fifth-order weighted essentially non-oscillatory （WENO） scheme is used to solve the level set equation for capturing multi-material interfaces. The ghost fluid method is used to deal with the interfacial boundary condition. Results are obtained for two bubble interacting with a moving shock. The contours of the constant density and the pressure at different time are given. In the computational domain, three different cases are considered, i.e. two helium bubbles, a helium bubble followed by an R22 bubble in the direction of the moving shock, and an R22 bubble followed by a helium bubble. Computational results indicate that multi-mate- rial interfaces can be properly captured by the level set method. Therefore, for problems involving the flow of three different materials with two different interfaces, each interface separating two different materials can be similarly handled.展开更多
This paper attempts to investigate the use of approximate 2D numerical simulation techniques for the evaluation of lignite pillar geomechanical response, formed via the room and pillar mining method.Performance and ap...This paper attempts to investigate the use of approximate 2D numerical simulation techniques for the evaluation of lignite pillar geomechanical response, formed via the room and pillar mining method.Performance and applicability of the developing methodology are assessed through benchmarking with a more direct and accurate 3D numerical model. This analysis utilizes an underground lignite mine which is being developed in soft rock environment. Through the decisions made for the optimum room and pillar layout, the design process highlights the strong points and the weaknesses of 2D finite element analysis, and provides useful recommendations for future reference. The interpretations of results demonstrate that 2D approximation techniques come near quite well to the actual 3D problem.However, external load approximation technique seems to fit even better with the respective outcomes from the 3D analyses.展开更多
The neutron shielding component of ITER （International Thermonuclear Experimental Reactor） vacuum vessel is a kind of structure resembling a wall in appearance. A FE （finite element） model is set up by using ANSYS...The neutron shielding component of ITER （International Thermonuclear Experimental Reactor） vacuum vessel is a kind of structure resembling a wall in appearance. A FE （finite element） model is set up by using ANSYS code in terms of its structural features. Static analysis, thermal expansion analysis and dynamic analysis are performed. The static results show that the stress and displacement distribution are allowable, but the high stress appears in the junction between the upper and lower parts. The modal analysis indicates that the biggest deformation exists in the port area. Through modal superposition, the single-point response has been found with the lower rank frequency of the acceleration seismic response spectrum. But the deformation and the stress values are within the permissible limit. The analysis results would benefit the work in the next step and provide some reference for the implementation of the engineering plan in the future.展开更多
The gradual increase in shipping and drilling activities in the Arctic regions has resulted in the increased importance of studying the structural safety of polar ships in various ice conditions.Rafted ice refers to a...The gradual increase in shipping and drilling activities in the Arctic regions has resulted in the increased importance of studying the structural safety of polar ships in various ice conditions.Rafted ice refers to a type of accumulated and overlapped sea ice;it is driven by external forces,such as wind and waves,and may exert high loads on ships and threaten their structural safety.Therefore,the properties of rafted ice and the construction of numerical models should be studied before exploring the interaction and collision between ships and rafted ice.Based on the nonlinear finite-element method,this paper introduces the cohesive element model for the simulation of rafted ice.The interaction between ships and rafted ice is studied,and the ice force of the hull is obtained.Numerical simulation results are compared with model test findings,and the effectiveness of the cohesive element method in the construction of the model of rafted ice materials is verified.On this basis,a multilayer rafted ice model is constructed,and its interaction with the ship is studied.The research unveils that rafted ice parts impede crack generation and slow down crack propagation to a certain extent.展开更多
基金supported by the National Natural Science Foundation of China(11871312,12131014)the Natural Science Foundation of Shandong Province,China(ZR2023MA086)。
文摘A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.
基金National Natural Science Foundation of China(No.51674280,51774308,51704033,51722406,51950410591)Shandong Provincial Natural Science Foundation(ZR2019JQ21,JQ201808)+3 种基金the Fundamental Research Funds for the Central Universities(No.20CX02113A)National Science and Technology Major Project(2016ZX05014-000407)Program for Changjiang Scholars and Innovative Research Team in University(IRT_16R69)PetroChina Innovation Foundation(No.2018D-5007-0210)。
文摘Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,comparatively fewer works have been devoted to study the effect of adsorption boundary layer(ABL)in throats based on the digital rock method.By considering an ABL,we investigate its effects on fluid flow.We build digital rock model based on computed tomography technology.Then,microscopic pore structures are extracted with watershed segmentation and pore geometries are meshed through Delaunay triangulation approach.Finally,using the meshed digital simulation model and finite element method,we investigate the effects of viscosity and thickness of ABL on microscale flow.Our results demonstrate that viscosity and thickness of ABL are major factors that significantly hinder fluid flow in throats.
基金FAPESP (Fundacào de Amparo à Pesquisa do Estado de Sào Paulo)(Grant No.98/07789-7)
文摘This paper describes a software tool, called LEVSOFT, suitable for the electric field simulations of corona electrodes by the Finite Element Method （FEM）. Special attention was paid to the user friendly construction of geometries with corners and sharp points, and to the fast generation of highly refined triangular meshes and field maps. The execution of selfadaptive meshes was also implemented. These customized features make the code attractive for the simulation of needle-type corona electrodes. Some case examples involving needle type electrodes are presented.
文摘This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.
文摘With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.
文摘In order to study the laws of the extrusion pressure changing with the extrusion parameters in the process of hydrostatic extrusion for the tungsten alloys, the large deformation elasto plastic theory and the software of ANSYS 5 5 are used to carry out the numerical simulation research. The laws of the extrusion pressure changing with the extrusion parameters, such as the die angle, extrusion ratio, and friction coefficient, are obtained. The simulation results are in good agreement with the experimental ones, and the simulated results are believable.
基金Supported by the National Natural Science Foundation of China(10476011)~~
文摘Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-material interfaces is demonstrated. Discontinuous Galerkin finite element method is used to solve Euleri- an equations. And the fifth-order weighted essentially non-oscillatory （WENO） scheme is used to solve the level set equation for capturing multi-material interfaces. The ghost fluid method is used to deal with the interfacial boundary condition. Results are obtained for two bubble interacting with a moving shock. The contours of the constant density and the pressure at different time are given. In the computational domain, three different cases are considered, i.e. two helium bubbles, a helium bubble followed by an R22 bubble in the direction of the moving shock, and an R22 bubble followed by a helium bubble. Computational results indicate that multi-mate- rial interfaces can be properly captured by the level set method. Therefore, for problems involving the flow of three different materials with two different interfaces, each interface separating two different materials can be similarly handled.
文摘This paper attempts to investigate the use of approximate 2D numerical simulation techniques for the evaluation of lignite pillar geomechanical response, formed via the room and pillar mining method.Performance and applicability of the developing methodology are assessed through benchmarking with a more direct and accurate 3D numerical model. This analysis utilizes an underground lignite mine which is being developed in soft rock environment. Through the decisions made for the optimum room and pillar layout, the design process highlights the strong points and the weaknesses of 2D finite element analysis, and provides useful recommendations for future reference. The interpretations of results demonstrate that 2D approximation techniques come near quite well to the actual 3D problem.However, external load approximation technique seems to fit even better with the respective outcomes from the 3D analyses.
基金the National 973 program of China(No.2004CB720704)
文摘The neutron shielding component of ITER （International Thermonuclear Experimental Reactor） vacuum vessel is a kind of structure resembling a wall in appearance. A FE （finite element） model is set up by using ANSYS code in terms of its structural features. Static analysis, thermal expansion analysis and dynamic analysis are performed. The static results show that the stress and displacement distribution are allowable, but the high stress appears in the junction between the upper and lower parts. The modal analysis indicates that the biggest deformation exists in the port area. Through modal superposition, the single-point response has been found with the lower rank frequency of the acceleration seismic response spectrum. But the deformation and the stress values are within the permissible limit. The analysis results would benefit the work in the next step and provide some reference for the implementation of the engineering plan in the future.
基金The National Natural Science Foundation of China(Grant Nos.52192693,52192690,51979051,51979056 and U20A20327)the National Key Research and Development Program of China(Grant No.2021YFC2803400)。
文摘The gradual increase in shipping and drilling activities in the Arctic regions has resulted in the increased importance of studying the structural safety of polar ships in various ice conditions.Rafted ice refers to a type of accumulated and overlapped sea ice;it is driven by external forces,such as wind and waves,and may exert high loads on ships and threaten their structural safety.Therefore,the properties of rafted ice and the construction of numerical models should be studied before exploring the interaction and collision between ships and rafted ice.Based on the nonlinear finite-element method,this paper introduces the cohesive element model for the simulation of rafted ice.The interaction between ships and rafted ice is studied,and the ice force of the hull is obtained.Numerical simulation results are compared with model test findings,and the effectiveness of the cohesive element method in the construction of the model of rafted ice materials is verified.On this basis,a multilayer rafted ice model is constructed,and its interaction with the ship is studied.The research unveils that rafted ice parts impede crack generation and slow down crack propagation to a certain extent.
