Of concern is the scenario of a heat equation on a domain that contains a thin layer,on which the thermal conductivity is drastically different from that in the bulk.The multi-scales in the spatial variable and the th...Of concern is the scenario of a heat equation on a domain that contains a thin layer,on which the thermal conductivity is drastically different from that in the bulk.The multi-scales in the spatial variable and the thermal conductivity lead to computational difficulties,so we may think of the thin layer as a thickless surface,on which we impose"effective boundary conditions"(EBCs).These boundary conditions not only ease the computational burden,but also reveal the effect of the inclusion.In this paper,by considering the asymptotic behavior of the heat equation with interior inclusion subject to Dirichlet boundary condition,as the thickness of the thin layer shrinks,we derive,on a closed curve inside a two-dimensional domain,EBCs which include a Poisson equation on the curve,and a non-local one.It turns out that the EBCs depend on the magnitude of the thermal conductivity in the thin layer,compared to the reciprocal of its thickness.展开更多
Heavy-duty machine tools are composed of many subsystems with different functions,and their reliability is governed by the reliabilities of these subsystems.It is important to rank the weaknesses of subsystems and ide...Heavy-duty machine tools are composed of many subsystems with different functions,and their reliability is governed by the reliabilities of these subsystems.It is important to rank the weaknesses of subsystems and identify the weakest subsystem to optimize products and improve their reliabilities.However,traditional ranking methods based on failure mode effect and critical analysis(FMECA)does not consider the complex maintenance of products.Herein,a weakness ranking method for the subsystems of heavy-duty machine tools is proposed based on generalized FMECA information.In this method,eight reliability indexes,including maintainability and maintenance cost,are considered in the generalized FMECA information.Subsequently,the cognition best worst method is used to calculate the weight of each screened index,and the weaknesses of the subsystems are ranked using a technique for order preference by similarity to an ideal solution.Finally,based on the failure data collected from certain domestic heavy-duty horizontal lathes,the weakness ranking result of the subsystems is obtained to verify the effectiveness of the proposed method.An improved weakness ranking method that can comprehensively analyze and identify weak subsystems is proposed herein for designing and improving the reliability of complex electromechanical products.展开更多
The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed w...The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects;2) upper-bound solutions;3) accurate solutions and higher convergence rates;4) insensitivity to mesh distortion;5) Jacobian?free;6) volumetric-locking-free;and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on Al-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.展开更多
This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under N...This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet boundary conditions. The partial regularity for the velocity of the fluid is proved for each proper weak solution, that is, for such weak solutions which satisfy some local energy estimates in a similar way to the suitable weak solutions of the Navier-Stokes system. Finally, we study the nature of the set of points in space and time upon which proper weak solutions could be singular.展开更多
基金NSF of China(No.11701180)Fundamental Research Funds for the Central Universities(No.19lgpy232)supported by NSF of China(Nos.11671190,11731005)。
文摘Of concern is the scenario of a heat equation on a domain that contains a thin layer,on which the thermal conductivity is drastically different from that in the bulk.The multi-scales in the spatial variable and the thermal conductivity lead to computational difficulties,so we may think of the thin layer as a thickless surface,on which we impose"effective boundary conditions"(EBCs).These boundary conditions not only ease the computational burden,but also reveal the effect of the inclusion.In this paper,by considering the asymptotic behavior of the heat equation with interior inclusion subject to Dirichlet boundary condition,as the thickness of the thin layer shrinks,we derive,on a closed curve inside a two-dimensional domain,EBCs which include a Poisson equation on the curve,and a non-local one.It turns out that the EBCs depend on the magnitude of the thermal conductivity in the thin layer,compared to the reciprocal of its thickness.
基金Supported by National Nat ural Science Foundation of China(Grant Nos.51675227,51975249)Jilin Province Science and Technology Development Funds(Grant Nos.20180201007GX,20190302017GX)+2 种基金Technology Development and Research of Jilin Province(Grant No.2019C037-01)Changchun Science and Technology Planning Project(Grant No.19SS011)National Science and technology Major Project(Grant No.2014ZX04015031).
文摘Heavy-duty machine tools are composed of many subsystems with different functions,and their reliability is governed by the reliabilities of these subsystems.It is important to rank the weaknesses of subsystems and identify the weakest subsystem to optimize products and improve their reliabilities.However,traditional ranking methods based on failure mode effect and critical analysis(FMECA)does not consider the complex maintenance of products.Herein,a weakness ranking method for the subsystems of heavy-duty machine tools is proposed based on generalized FMECA information.In this method,eight reliability indexes,including maintainability and maintenance cost,are considered in the generalized FMECA information.Subsequently,the cognition best worst method is used to calculate the weight of each screened index,and the weaknesses of the subsystems are ranked using a technique for order preference by similarity to an ideal solution.Finally,based on the failure data collected from certain domestic heavy-duty horizontal lathes,the weakness ranking result of the subsystems is obtained to verify the effectiveness of the proposed method.An improved weakness ranking method that can comprehensively analyze and identify weak subsystems is proposed herein for designing and improving the reliability of complex electromechanical products.
文摘The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects;2) upper-bound solutions;3) accurate solutions and higher convergence rates;4) insensitivity to mesh distortion;5) Jacobian?free;6) volumetric-locking-free;and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on Al-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.
文摘This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet boundary conditions. The partial regularity for the velocity of the fluid is proved for each proper weak solution, that is, for such weak solutions which satisfy some local energy estimates in a similar way to the suitable weak solutions of the Navier-Stokes system. Finally, we study the nature of the set of points in space and time upon which proper weak solutions could be singular.
