In computer aided geometric design(CAGD),the Bernstein-Bézier system for polynomial space including the triangular domain is an important tool for modeling free form shapes.The Bernstein-like bases for other spac...In computer aided geometric design(CAGD),the Bernstein-Bézier system for polynomial space including the triangular domain is an important tool for modeling free form shapes.The Bernstein-like bases for other spaces(trigonometric polynomial,hyperbolic polynomial,or blended space) has also been studied.However,none of them was extended to the triangular domain.In this paper,we extend the linear trigonometric polynomial basis to the triangular domain and obtain a new Bernstein-like basis,which is linearly independent and satisfies positivity,partition of unity,symmetry,and boundary represen-tation.We prove some properties of the corresponding surfaces,including differentiation,subdivision,convex hull,and so forth.Some applications are shown.展开更多
The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices...The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.展开更多
Based on the nonlocal theory and Mindlin plate theory,the governing equations(i.e.,a system of partial differential equations(PDEs)for bending problem)of magnetoelectroelastic(MEE)nanoplates resting on the Pasternak e...Based on the nonlocal theory and Mindlin plate theory,the governing equations(i.e.,a system of partial differential equations(PDEs)for bending problem)of magnetoelectroelastic(MEE)nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle.The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions(MPS)to solve the governing equations numerically.It is confirmed that for the present bending model,the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points.The effects of different boundary conditions,applied loads,and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method.Some important conclusions are drawn,which should be helpful for the design and applications of electromagnetic nanoplate structures.展开更多
Split Trailing Suction Hopper Dredgers (TSHD) are special type of working ships, whose hulls open to discharge cargo to certain unloading positions while being at sea. Although they have variable hull geometry, their ...Split Trailing Suction Hopper Dredgers (TSHD) are special type of working ships, whose hulls open to discharge cargo to certain unloading positions while being at sea. Although they have variable hull geometry, their hydrostatic and stability characteristics are usually calculated for unchanged initial hull geometry loading conditions only, and such calculations are supported by classification society stability regulations for that ship type. Nevertheless, in this study, we show that hydrostatic particulars for intermediate loading conditions of variable ship geometry can be calculated by using analytical solutions of basic hydrostatic integrals for arbitrary list angles, obtained for polynomial radial basis function description of ship geometry. The calculations will be performed for symmetric hopper opening during cargo discharge procedure, thus covering all Split TSHD regular unloading conditions, without examination of ship hull opening failure modes. Thus, all ship hydrostatic properties will be pre-calculated analytically and prepared for further stability calculations, as opposed to the usual numerical calculations for initial geometry and even keel only, as currently used in naval architecture design.展开更多
基金supported by the National Natural Science Foundation of China (Nos.60773179,60933008,and 60970079)the National Basic Research Program (973) of China (No.2004CB318000)the China Hungary Joint Project (No.CHN21/2006)
文摘In computer aided geometric design(CAGD),the Bernstein-Bézier system for polynomial space including the triangular domain is an important tool for modeling free form shapes.The Bernstein-like bases for other spaces(trigonometric polynomial,hyperbolic polynomial,or blended space) has also been studied.However,none of them was extended to the triangular domain.In this paper,we extend the linear trigonometric polynomial basis to the triangular domain and obtain a new Bernstein-like basis,which is linearly independent and satisfies positivity,partition of unity,symmetry,and boundary represen-tation.We prove some properties of the corresponding surfaces,including differentiation,subdivision,convex hull,and so forth.Some applications are shown.
基金Project supported by Hong Kong Baptist University RC’s Start-up Grant for New Academics,the Hong Kong Research Grant Council(Nos.PolyU 15302114,15300715,15301716,and 15300717)the National Natural Science Foundation of China(No.11372124)
文摘The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.
基金Project supported by the National Natural Science Foundation of China(Nos.11872257 and 11572358)the German Research Foundation(No.ZH 15/14-1)。
文摘Based on the nonlocal theory and Mindlin plate theory,the governing equations(i.e.,a system of partial differential equations(PDEs)for bending problem)of magnetoelectroelastic(MEE)nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle.The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions(MPS)to solve the governing equations numerically.It is confirmed that for the present bending model,the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points.The effects of different boundary conditions,applied loads,and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method.Some important conclusions are drawn,which should be helpful for the design and applications of electromagnetic nanoplate structures.
文摘Split Trailing Suction Hopper Dredgers (TSHD) are special type of working ships, whose hulls open to discharge cargo to certain unloading positions while being at sea. Although they have variable hull geometry, their hydrostatic and stability characteristics are usually calculated for unchanged initial hull geometry loading conditions only, and such calculations are supported by classification society stability regulations for that ship type. Nevertheless, in this study, we show that hydrostatic particulars for intermediate loading conditions of variable ship geometry can be calculated by using analytical solutions of basic hydrostatic integrals for arbitrary list angles, obtained for polynomial radial basis function description of ship geometry. The calculations will be performed for symmetric hopper opening during cargo discharge procedure, thus covering all Split TSHD regular unloading conditions, without examination of ship hull opening failure modes. Thus, all ship hydrostatic properties will be pre-calculated analytically and prepared for further stability calculations, as opposed to the usual numerical calculations for initial geometry and even keel only, as currently used in naval architecture design.
