A flexible and adaptable design method for the tooth crown is presented based on the direct manipulation of free-form deformation （FFD）. The correct shape of the tooth crown can be obtained by adding, modifying, and...A flexible and adaptable design method for the tooth crown is presented based on the direct manipulation of free-form deformation （FFD）. The correct shape of the tooth crown can be obtained by adding, modifying, and deleting constraint points or load points based on stretching and compressing operation. Finally, an example is given to illustrate the method to be efficient.展开更多
Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very i...Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very important to investigate the instability of thermocapillary convection in liquid bridges with deformable free-surface under microgravity. In this works, the Volume of Fluid(VOF) method is employed to track the free-surface movement. The results are presented as the behavior of flow structure and temperature distribution of the molten zone. The impact of Marangoni number(Ma) is also investigated on free-surface deformation as well as the instability of thermocapillary convection. The free-surface exhibits a noticeable axisymmetric(but it is non-centrosymmetric) and elliptical shape along the circumferential direction. This specific surface shape presents a typical narrow ‘neck-shaped' structure with convex at two ends of the zone and concave at the mid-plane along the axial direction. At both θ = 0° and θ = 90°, the deformation ratio ξ increases rapidly with Ma at first, and then increases slowly. Moreover, the hydrothermal wave number m and the instability of thermocapillary convection increase with Ma.展开更多
Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are...Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form.展开更多
This paper demonstrates the plane stress state and the stress free thermo-elastic deformation of FGM thick plate under thermal loading.First,the Sneddon-Lockett theorem on the plane stress state in an isotropic infini...This paper demonstrates the plane stress state and the stress free thermo-elastic deformation of FGM thick plate under thermal loading.First,the Sneddon-Lockett theorem on the plane stress state in an isotropic infinite thick plate is generalized for a case of FGM problem in which all thermo-mechanical properties are optional functions of depth co-ordinate.The proof is based on application of the Iljushin thermo-elastic potential to displacement type system of equations that reduces it to the plane stress state problem.Then an existence of the purely thermal deformation is proved in two ways:first,it is shown that the unique solution fulfils conditions of simultaneous constant temperature and linear gradation of thermal expansion coefficient,second,proof is based directly on stress type system of equations which straightforwardly reduces to compatibility equations for purely thermal deformation if only stress field is homogeneous in domain and at boundary.Finally,couple examples of application to an engineering problem are presented.展开更多
In hydraulic engineering,free-surface aeration is a natural phenomenon occurring in smooth channel flows.In self-aerated flows,a key aspect that has not yet been well understood is the formation mechanism of free-surf...In hydraulic engineering,free-surface aeration is a natural phenomenon occurring in smooth channel flows.In self-aerated flows,a key aspect that has not yet been well understood is the formation mechanism of free-surface air entrainment.In this research,the process of free-surface entrapped deformation is analyzed theoretically and the critical radius of curvature for air entrainment is obtained,affected by flow mean velocity and depth.When the severity of local free-surface deformation exceeds the critical condition,the entrapped free surface encounters closure in the unstable deformation movement process,resulting in air entrainment.This inference agrees well with observed experimental results that are obtained from the processes of surface entrapped deformation and air entrainment captured by a high-speed camera-based data acquisition system.This agreement indicates that self-aeration occurs in low-velocity open-channel flows.It is also confirmed that free-surface turbulent deformation provides a mechanism for air entrainment.展开更多
文摘A flexible and adaptable design method for the tooth crown is presented based on the direct manipulation of free-form deformation （FFD）. The correct shape of the tooth crown can be obtained by adding, modifying, and deleting constraint points or load points based on stretching and compressing operation. Finally, an example is given to illustrate the method to be efficient.
基金supported by National Natural Science Foundation of China(Grant Number 51276089)
文摘Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very important to investigate the instability of thermocapillary convection in liquid bridges with deformable free-surface under microgravity. In this works, the Volume of Fluid(VOF) method is employed to track the free-surface movement. The results are presented as the behavior of flow structure and temperature distribution of the molten zone. The impact of Marangoni number(Ma) is also investigated on free-surface deformation as well as the instability of thermocapillary convection. The free-surface exhibits a noticeable axisymmetric(but it is non-centrosymmetric) and elliptical shape along the circumferential direction. This specific surface shape presents a typical narrow ‘neck-shaped' structure with convex at two ends of the zone and concave at the mid-plane along the axial direction. At both θ = 0° and θ = 90°, the deformation ratio ξ increases rapidly with Ma at first, and then increases slowly. Moreover, the hydrothermal wave number m and the instability of thermocapillary convection increase with Ma.
基金supported by National Natural Science Foundation of China (Grant Nos.10801006,10971110,10771005)
文摘Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form.
文摘This paper demonstrates the plane stress state and the stress free thermo-elastic deformation of FGM thick plate under thermal loading.First,the Sneddon-Lockett theorem on the plane stress state in an isotropic infinite thick plate is generalized for a case of FGM problem in which all thermo-mechanical properties are optional functions of depth co-ordinate.The proof is based on application of the Iljushin thermo-elastic potential to displacement type system of equations that reduces it to the plane stress state problem.Then an existence of the purely thermal deformation is proved in two ways:first,it is shown that the unique solution fulfils conditions of simultaneous constant temperature and linear gradation of thermal expansion coefficient,second,proof is based directly on stress type system of equations which straightforwardly reduces to compatibility equations for purely thermal deformation if only stress field is homogeneous in domain and at boundary.Finally,couple examples of application to an engineering problem are presented.
基金supported by the National Natural Science Foundation of China (Grant No. 51379138)the National Basic Research Program of China (“973” Project) (Grant No. 2013CB035905)
文摘In hydraulic engineering,free-surface aeration is a natural phenomenon occurring in smooth channel flows.In self-aerated flows,a key aspect that has not yet been well understood is the formation mechanism of free-surface air entrainment.In this research,the process of free-surface entrapped deformation is analyzed theoretically and the critical radius of curvature for air entrainment is obtained,affected by flow mean velocity and depth.When the severity of local free-surface deformation exceeds the critical condition,the entrapped free surface encounters closure in the unstable deformation movement process,resulting in air entrainment.This inference agrees well with observed experimental results that are obtained from the processes of surface entrapped deformation and air entrainment captured by a high-speed camera-based data acquisition system.This agreement indicates that self-aeration occurs in low-velocity open-channel flows.It is also confirmed that free-surface turbulent deformation provides a mechanism for air entrainment.
