A new numerical manifold （NMM） method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consis...A new numerical manifold （NMM） method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven- tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin- ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.展开更多
A raised panel method based on NURBS (Non-Uniform Rational B-Splines) forfree-surface flows with forward speed is presented. In this generalized panel method, NURBS areemployed to represent the body geometry, disturbe...A raised panel method based on NURBS (Non-Uniform Rational B-Splines) forfree-surface flows with forward speed is presented. In this generalized panel method, NURBS areemployed to represent the body geometry, disturbed free surface, and to express the unknown sourcestrength distribution, on the body surface and above the free surface. Compared with commonhigher-order panel methods, it has no need of adopting local coordinates. NURBS make the geometryrepresentation of the body shape and the wave pattern more precise. Raised panels above the freesurface produce less numerical dispersion error, need less CPU consumption and are helpful andcombined with collocation-point shifting up-stream, can satisfy the radiation condition numerically.By using continuous and discrete Fourier analysis, numerical errors of this method are discussedand a general expression for the errors of numerical damping and dispersion, including the effectsof the vertical distance of singularities to the free surface, the order of singularity distributionrepresented by B-splines in panels, and collocation-point shifting is derived.展开更多
In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable...In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.展开更多
A desingularized high order panel method based on Non-Uniform Rational B-Spline （NURBS） was developed to deal with three-dimensional potential flow problems. A NURBS surface was used to precisely represent the body ...A desingularized high order panel method based on Non-Uniform Rational B-Spline （NURBS） was developed to deal with three-dimensional potential flow problems. A NURBS surface was used to precisely represent the body geometry. Velocity potential on the body surface was described by the B-spline after the source density distribution on the body surface had been solved. The collocation approach was employed to satisfy the Neurnann boundary condition and Gaussian quadrature points were chosen as both the collocation points and the source points. The singularity was removed by a combined method, so the process of the numerical computation was non-singular. In order to verify the method proposed, the unbounded flow problems of sphere and ellipsoid, the wave-making problem of a submerged ellipsoid were chosen as computational examples. It is shown that the numerical results are in good agreement with analytical solutions and other numerical results in all cases, and sufficient accuracy of numerical solution can be reached with a small number of panels.展开更多
In this paper, we apply the particle method to solve the numerical solution of a family of non-li-near Evolutionary Partial Differential Equations. It is called b-equation because of its bi-Hamiltonian structure. We i...In this paper, we apply the particle method to solve the numerical solution of a family of non-li-near Evolutionary Partial Differential Equations. It is called b-equation because of its bi-Hamiltonian structure. We introduce the particle method as an approximation of these equations in Lagrangian representation for simulating collisions between wave fronts. Several numerical examples will be set to illustrate the feasibility of the particle method.展开更多
This paper deals with the efficiency of the search, with a method of organization and storage of the information that allows better results than the research trees or binary trees. No one ever dared to present better ...This paper deals with the efficiency of the search, with a method of organization and storage of the information that allows better results than the research trees or binary trees. No one ever dared to present better results than 0(log n) complexity, and when they wish to improve, they use balanced trees, but they continue to use principles that do not impact the pre-semantic information treatment. The Heru search method has as main characteristic the total or partial substitution of the use of the binary trees, enabling the elimination of the approximate results and informing the user the desired information instead of occurrences by sampling outside the desired information. The breakdown of the 0(log n) paradigm and the refinement of the searches are achieved with the use of a set of unpublished mathematical formulas and concepts called Infinite Series with Multiple Ratios.展开更多
Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions...Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.展开更多
基金supported by the Fund of National Engineering and Research Center for Highways in Mountain Area(No.gsgzj-2012-05)the Fundamental Research Funds for the Central Universities of China(No.CDJXS12240003)the Scientific Research Foundation of State Key Laboratory of Coal Mine Disaster Dynamics and Control(No.2011DA105287-MS201213)
文摘A new numerical manifold （NMM） method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven- tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin- ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.
文摘A raised panel method based on NURBS (Non-Uniform Rational B-Splines) forfree-surface flows with forward speed is presented. In this generalized panel method, NURBS areemployed to represent the body geometry, disturbed free surface, and to express the unknown sourcestrength distribution, on the body surface and above the free surface. Compared with commonhigher-order panel methods, it has no need of adopting local coordinates. NURBS make the geometryrepresentation of the body shape and the wave pattern more precise. Raised panels above the freesurface produce less numerical dispersion error, need less CPU consumption and are helpful andcombined with collocation-point shifting up-stream, can satisfy the radiation condition numerically.By using continuous and discrete Fourier analysis, numerical errors of this method are discussedand a general expression for the errors of numerical damping and dispersion, including the effectsof the vertical distance of singularities to the free surface, the order of singularity distributionrepresented by B-splines in panels, and collocation-point shifting is derived.
文摘In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.
基金supported by the National Natural SciencFoundation of China (Grant No. 10572094)the NaturScience Foundation of Shanghai (Grant No. 06ZR14050)
文摘A desingularized high order panel method based on Non-Uniform Rational B-Spline （NURBS） was developed to deal with three-dimensional potential flow problems. A NURBS surface was used to precisely represent the body geometry. Velocity potential on the body surface was described by the B-spline after the source density distribution on the body surface had been solved. The collocation approach was employed to satisfy the Neurnann boundary condition and Gaussian quadrature points were chosen as both the collocation points and the source points. The singularity was removed by a combined method, so the process of the numerical computation was non-singular. In order to verify the method proposed, the unbounded flow problems of sphere and ellipsoid, the wave-making problem of a submerged ellipsoid were chosen as computational examples. It is shown that the numerical results are in good agreement with analytical solutions and other numerical results in all cases, and sufficient accuracy of numerical solution can be reached with a small number of panels.
文摘In this paper, we apply the particle method to solve the numerical solution of a family of non-li-near Evolutionary Partial Differential Equations. It is called b-equation because of its bi-Hamiltonian structure. We introduce the particle method as an approximation of these equations in Lagrangian representation for simulating collisions between wave fronts. Several numerical examples will be set to illustrate the feasibility of the particle method.
文摘This paper deals with the efficiency of the search, with a method of organization and storage of the information that allows better results than the research trees or binary trees. No one ever dared to present better results than 0(log n) complexity, and when they wish to improve, they use balanced trees, but they continue to use principles that do not impact the pre-semantic information treatment. The Heru search method has as main characteristic the total or partial substitution of the use of the binary trees, enabling the elimination of the approximate results and informing the user the desired information instead of occurrences by sampling outside the desired information. The breakdown of the 0(log n) paradigm and the refinement of the searches are achieved with the use of a set of unpublished mathematical formulas and concepts called Infinite Series with Multiple Ratios.
基金supported by the National Natural Science Foundation of China(11001037,11102037 and 11290143)the Fundamental Research Funds for the Central Universities
文摘Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.
