By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is propose...By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.展开更多
In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow e...In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.展开更多
Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For th...Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.展开更多
In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear conve...In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion problems.In the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are considered.In the time discretization,the convection term is treated explicitly and the diffusion term implicitly.By the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size h.Opti-mal error estimate is also obtained by the aid of a special global projection.Numerical experiments are given to verify the stability and accuracy of the proposed schemes.展开更多
We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forwa...We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.展开更多
Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green func...Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.展开更多
With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for th...With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given.展开更多
In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problem...In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution, of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient 5, and it may be convergent independent of δ under some conditions. The numerical results demonstrating the theoretical results are presented in this article.展开更多
In this paper, we use differential game theory to study the three-dimensional two-aircraft air-to-air combat problem. We give the ways to determine the Capture Ranges (CR) and the Dangerous Ranges (DR) for these two a...In this paper, we use differential game theory to study the three-dimensional two-aircraft air-to-air combat problem. We give the ways to determine the Capture Ranges (CR) and the Dangerous Ranges (DR) for these two aircraft according to the target entry directions, barrier and isochronic lines respectively. The simulations are given by referring to two sets of real aircraft parameters. After discussing the simulation results, we have obtained some conclusions that match the real air-to-air combat situation quite well.展开更多
The paper discusses the application of three-dimensional textbook in English teaching. The three-dimensional textbook plays an incomparable function than the traditional textbook and thus has an extensive application ...The paper discusses the application of three-dimensional textbook in English teaching. The three-dimensional textbook plays an incomparable function than the traditional textbook and thus has an extensive application in the college English education. It demonstrates the application through the usage of the three-dimensional textbook in the real teaching and shows that excessive usage of sound and pictures or drawings may distract the attention of students. It raises several suggestions at the end.展开更多
This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method （FEM） by recursive application of the one-dimensional （1D） element energy pro...This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method （FEM） by recursive application of the one-dimensional （1D） element energy projection （EEP） technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element （FE） model is reached. This conceptual dimension-by- dimension （D-by-D） discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional （2D） and three-dimensional （3D） problems can be obtained over the domain. Numerical examples of 3D Poisson＇s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.展开更多
The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped i...The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.展开更多
Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock s...Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.展开更多
A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle ...A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.展开更多
It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY iss...It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all.展开更多
Petroleum science has made remarkable progress in organic geochcmistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the kno...Petroleum science has made remarkable progress in organic geochcmistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model can be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems. This thesis, from actual conditions such as the effect of fluid compressibility and the three-dimensional characteristic of large-scale science-engineering computation, we put forward a kind of characteristic finite element alternating-direction schemes and obtain optimal order estimates in L^2 norm for the error in the approximate assumption.展开更多
In this paper. an analytic method is. presented. for the research of nonlinear Three-dimensional problems of composite laminated plates. The perturbation method and the variational principle are used to satisfy the ba...In this paper. an analytic method is. presented. for the research of nonlinear Three-dimensional problems of composite laminated plates. The perturbation method and the variational principle are used to satisfy the basic differential equations and the boundary conditions of the three-dimensional theory of elasticity. The nonlinear three-dimensional problems are studied .for composite anisotropic circular laminas and laminates subjected to transverse loading. The perturbation series solutions of high accuracy are obtained. A large number of results show that transverse normal stress and transverse shear stresses are very important in the nonlinear three-dimensional analysis of laminated plates.展开更多
By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local ...By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local thermal and force loadings.The material plane of isotropy is assumed to be parallel to the limiting surface of the halfspace.By reducing the original thermoelasticity equations to the governing ones for individual stress-tensor components,the effect of material anisotropy in the stress field is analyzed with regard to the feasibility requirement,i.e.,the finiteness of the stress field at a distance from the disturbed area.As a result,the solution is constructed in the form of explicit analytical dependencies on the force and thermal loadings for various kinds of transversely isotropic materials and agrees with the basic principles of the continua mechanics.The solution can be efficiently used as a benchmark one for the direct computation of temperature and thermal stresses in transversely isotropic semi-infinite domains,as well as for the verification of solutions constructed by different means.展开更多
This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary condi...This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.展开更多
An operator-splitting algorithm for the three-dimensional convection-diffusion equa- tion is presented.The flow region is discretized into tetrahedronal elements which are fixed in time. The transport equation is spli...An operator-splitting algorithm for the three-dimensional convection-diffusion equa- tion is presented.The flow region is discretized into tetrahedronal elements which are fixed in time. The transport equation is split into two successive initial value problems:a pure convection problem and a pure diffusion problem.For the pure convection problem,solutions are found by the method of characteristiCS.The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point.A cubic polynomial is used to interpolate the concentration and its derivatives within each element.For the diffusion problem,an explicit finite element algorithm is employed.Numerical examples are given which agree well with the analytical solutions.展开更多
基金supported by the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LY20A010021,LY19A010002,LY20G030025)the Natural Science Founda-tion of Ningbo City,China(Grant Nos.2021J147,2021J235).
文摘By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA019)the National Natural Science Foundation of China(11871312)。
文摘In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.
基金supported by the National Natural Science Foundation of China(Nos.11362018,11261045,and 11261401)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116401110002)
文摘Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.
基金the NSFC grant 11871428the Nature Science Research Program for Colleges and Universities of Jiangsu Province grant 20KJB110011Qiang Zhang:Research supported by the NSFC grant 11671199。
文摘In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion problems.In the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are considered.In the time discretization,the convection term is treated explicitly and the diffusion term implicitly.By the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size h.Opti-mal error estimate is also obtained by the aid of a special global projection.Numerical experiments are given to verify the stability and accuracy of the proposed schemes.
基金Supported by the National Natural Science Foundation of China under Grant No 11774374the Natural Science Foundation of Shandong Province of China under Grant No ZR2016AL10
文摘We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.
基金Project supported by the National Natural Science Foundation of China (No. 50776097)
文摘Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.
基金Natural Science Foundation of Gansu Province of China
文摘With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given.
基金the Special Funds for Major State Basic Research Projects （No.G2000067102） National Natural Science Foundation of China （No.60474027）.
文摘In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution, of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient 5, and it may be convergent independent of δ under some conditions. The numerical results demonstrating the theoretical results are presented in this article.
基金research was supported by Aviation Science Fund.
文摘In this paper, we use differential game theory to study the three-dimensional two-aircraft air-to-air combat problem. We give the ways to determine the Capture Ranges (CR) and the Dangerous Ranges (DR) for these two aircraft according to the target entry directions, barrier and isochronic lines respectively. The simulations are given by referring to two sets of real aircraft parameters. After discussing the simulation results, we have obtained some conclusions that match the real air-to-air combat situation quite well.
文摘The paper discusses the application of three-dimensional textbook in English teaching. The three-dimensional textbook plays an incomparable function than the traditional textbook and thus has an extensive application in the college English education. It demonstrates the application through the usage of the three-dimensional textbook in the real teaching and shows that excessive usage of sound and pictures or drawings may distract the attention of students. It raises several suggestions at the end.
基金supported by the National Natural Science Foundation of China(Nos.51378293 and 51078199)
文摘This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method （FEM） by recursive application of the one-dimensional （1D） element energy projection （EEP） technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element （FE） model is reached. This conceptual dimension-by- dimension （D-by-D） discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional （2D） and three-dimensional （3D） problems can be obtained over the domain. Numerical examples of 3D Poisson＇s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.
文摘The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.
基金This work was supported in part by National Nature Science Foundation of China(11371141 and 11871218)by Science and Technology Commission of Shanghai Municipality(18dz2271000).
文摘Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.
文摘A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.
基金the National Natural Science Foundation of China(No.10590353)theNatural Science Foundation of Shaanxi Province of China(No.2005A16)
文摘It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all.
基金Project supported by the National Science Foundation,the National Scaling Programthe Doctoral Foundation of the National Education Commission
文摘Petroleum science has made remarkable progress in organic geochcmistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model can be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems. This thesis, from actual conditions such as the effect of fluid compressibility and the three-dimensional characteristic of large-scale science-engineering computation, we put forward a kind of characteristic finite element alternating-direction schemes and obtain optimal order estimates in L^2 norm for the error in the approximate assumption.
文摘In this paper. an analytic method is. presented. for the research of nonlinear Three-dimensional problems of composite laminated plates. The perturbation method and the variational principle are used to satisfy the basic differential equations and the boundary conditions of the three-dimensional theory of elasticity. The nonlinear three-dimensional problems are studied .for composite anisotropic circular laminas and laminates subjected to transverse loading. The perturbation series solutions of high accuracy are obtained. A large number of results show that transverse normal stress and transverse shear stresses are very important in the nonlinear three-dimensional analysis of laminated plates.
基金supported by Joint Fund of Advanced Aerospace Manufacturing Technology Research(No. U1937601)the partial financial support of this research by the budget program of Ukraine“Support for the Development of Priority Research Areas”(No.CPCEC 6451230)。
文摘By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local thermal and force loadings.The material plane of isotropy is assumed to be parallel to the limiting surface of the halfspace.By reducing the original thermoelasticity equations to the governing ones for individual stress-tensor components,the effect of material anisotropy in the stress field is analyzed with regard to the feasibility requirement,i.e.,the finiteness of the stress field at a distance from the disturbed area.As a result,the solution is constructed in the form of explicit analytical dependencies on the force and thermal loadings for various kinds of transversely isotropic materials and agrees with the basic principles of the continua mechanics.The solution can be efficiently used as a benchmark one for the direct computation of temperature and thermal stresses in transversely isotropic semi-infinite domains,as well as for the verification of solutions constructed by different means.
文摘This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.
文摘An operator-splitting algorithm for the three-dimensional convection-diffusion equa- tion is presented.The flow region is discretized into tetrahedronal elements which are fixed in time. The transport equation is split into two successive initial value problems:a pure convection problem and a pure diffusion problem.For the pure convection problem,solutions are found by the method of characteristiCS.The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point.A cubic polynomial is used to interpolate the concentration and its derivatives within each element.For the diffusion problem,an explicit finite element algorithm is employed.Numerical examples are given which agree well with the analytical solutions.
