In this paper,the boundary mapped collocation(BMC)approach is presented for the analysis of heat conduction problems involving heat generation and non-homogeneous thermal conductivity.The proposed methodology is intro...In this paper,the boundary mapped collocation(BMC)approach is presented for the analysis of heat conduction problems involving heat generation and non-homogeneous thermal conductivity.The proposed methodology is introduced to produce the numerical solutions of the temperature field within the framework of the BMC method,a novel boundary meshless method,without resorting to requiring any integral calculation,neither in the domain nor at the boundary.In particular,the arrangement of discrete nodes is restricted to the axis,which brings the spatial dimension down by one.The technique also reduced the traditional complex shape functions to succinct one-dimensional boundary shape functions by using one-dimensional basis functions and weight functions for two-and three-dimensional approximation implementation.In addition,four numerical applications and comparisons with the outcomes of the finite element approach and another meshfree method are used to demonstrate the correctness,convergence,and stability of the BMC method.展开更多
An innovative meshless method is proposed in this paper for the bending problem of arbitrary Kirchhoff plates subjected to external force with various shapes and different boundary conditions.Without using a numerical...An innovative meshless method is proposed in this paper for the bending problem of arbitrary Kirchhoff plates subjected to external force with various shapes and different boundary conditions.Without using a numerical integral,the deflection of the thin plate is approximated by using the boundary mapped collocation approach.Moreover,the computational domain discretization is just dependent on discretized nodes on the axis,while tensor product nodes have been mapped in the domain automatically.Hence,in the boundary mapped collocation implementation,the approximation functions are derived by employing the one-dimensional moving least squares technique for two-dimensional and higher-dimensional problems.Further,the virtual boundary technique is introduced to enforce the boundary conditions in the proposed method.Additionally,four numerical experiments are presented to illustrate the excellent convergence and high precision of the proposed approach.展开更多
In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two ...In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.展开更多
According to a series of important historical maps,i.e.,the Location Map of the South China Sea Islands,the Nansha Islands,Zhongsha Islands,Xisha Islands,Yongxing Island and Shidao Island,and Taiping Island（archived ...According to a series of important historical maps,i.e.,the Location Map of the South China Sea Islands,the Nansha Islands,Zhongsha Islands,Xisha Islands,Yongxing Island and Shidao Island,and Taiping Island（archived by the Territorial Administration Division of the Ministry of Interior of Republic of China in 1946）,and the Administration District Map of the Republic of China published in 1948,the dashed line surrounding the South China Sea Islands represents China＇s sea boundary in the South China Sea at that time.It was both connected with,and an extension of,the land boundary of China.At that time the dashed line was used to represent the waters boundaries while the solid line was used to represent the land boundary—a universal method used in maps that was then recognized internationally.The above observation provides historical and scientific evidence of China＇s sea boundary in the South China Sea that is useful for the international maritime delimitation over the South China Sea area.展开更多
Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic...Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.展开更多
In this paper, we use the deformation method andG-equivariant theory to prove the existence and multiplicity of harmonic maps from an annulus to the unit sphere in? 3 with symmetric boundary value. In particular, we c...In this paper, we use the deformation method andG-equivariant theory to prove the existence and multiplicity of harmonic maps from an annulus to the unit sphere in? 3 with symmetric boundary value. In particular, we can get infinitely many homotopically different harmonic maps if the boundary value isS 1-equivariant and nonconstant.展开更多
基金supported by GuangDong Basic and Applied Basic Research Foundation(No.2021A1515110807)the PhD Starting Foundation of Nanchang Hangkong University(No.EA202411285)+1 种基金the Program for Guangdong Introducing Innovative and Entrepreneurial Teams(No.2019ZT08G315)National Natural Science Foundation of China(No.U19A2098).
文摘In this paper,the boundary mapped collocation(BMC)approach is presented for the analysis of heat conduction problems involving heat generation and non-homogeneous thermal conductivity.The proposed methodology is introduced to produce the numerical solutions of the temperature field within the framework of the BMC method,a novel boundary meshless method,without resorting to requiring any integral calculation,neither in the domain nor at the boundary.In particular,the arrangement of discrete nodes is restricted to the axis,which brings the spatial dimension down by one.The technique also reduced the traditional complex shape functions to succinct one-dimensional boundary shape functions by using one-dimensional basis functions and weight functions for two-and three-dimensional approximation implementation.In addition,four numerical applications and comparisons with the outcomes of the finite element approach and another meshfree method are used to demonstrate the correctness,convergence,and stability of the BMC method.
基金supported by GuangDong Basic and Applied Basic Research Foundation(No.2021A1515110807)the PhD Starting Foundation of Nanchang Hangkong University(No.EA202411285)+1 种基金the Program for Guangdong Introducing Innovative and Entrepreneurial Teams(No.2019ZT08G315)National Natural Science Foundation of China(No.U19A2098).
文摘An innovative meshless method is proposed in this paper for the bending problem of arbitrary Kirchhoff plates subjected to external force with various shapes and different boundary conditions.Without using a numerical integral,the deflection of the thin plate is approximated by using the boundary mapped collocation approach.Moreover,the computational domain discretization is just dependent on discretized nodes on the axis,while tensor product nodes have been mapped in the domain automatically.Hence,in the boundary mapped collocation implementation,the approximation functions are derived by employing the one-dimensional moving least squares technique for two-dimensional and higher-dimensional problems.Further,the virtual boundary technique is introduced to enforce the boundary conditions in the proposed method.Additionally,four numerical experiments are presented to illustrate the excellent convergence and high precision of the proposed approach.
文摘In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.
文摘According to a series of important historical maps,i.e.,the Location Map of the South China Sea Islands,the Nansha Islands,Zhongsha Islands,Xisha Islands,Yongxing Island and Shidao Island,and Taiping Island（archived by the Territorial Administration Division of the Ministry of Interior of Republic of China in 1946）,and the Administration District Map of the Republic of China published in 1948,the dashed line surrounding the South China Sea Islands represents China＇s sea boundary in the South China Sea at that time.It was both connected with,and an extension of,the land boundary of China.At that time the dashed line was used to represent the waters boundaries while the solid line was used to represent the land boundary—a universal method used in maps that was then recognized internationally.The above observation provides historical and scientific evidence of China＇s sea boundary in the South China Sea that is useful for the international maritime delimitation over the South China Sea area.
基金This project is supported by National Natural Science Foundation of China(No.50175031).
文摘Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.
基金This research partially supported by the NNSF,P.R.China
文摘In this paper, we use the deformation method andG-equivariant theory to prove the existence and multiplicity of harmonic maps from an annulus to the unit sphere in? 3 with symmetric boundary value. In particular, we can get infinitely many homotopically different harmonic maps if the boundary value isS 1-equivariant and nonconstant.
