The determination of initial equilibrium shapes is a common problem in research work and engineering applications related to membrane structures. Using a general structural analysis framework of the finite particle me...The determination of initial equilibrium shapes is a common problem in research work and engineering applications related to membrane structures. Using a general structural analysis framework of the finite particle method （FPM）, this paper presents the first application of the FPM and a recently-developed membrane model to the shape analysis of light weight mem- branes. The FPM is rooted in vector mechanics and physical viewpoints. It discretizes the analyzed domain into a group of parti- cles linked by elements, and the motion of the free particles is directly described by Newton＇s second law while the constrained ones follow the prescribed paths. An efficient physical modeling procedure of handling geometric nonlinearity has been developed to evaluate the particle interaction forces. To achieve the equilibrium shape as fast as possible, an integral-form, explicit time integration scheme has been proposed for solving the equation of motion. The equilibrium shape can be obtained naturally without nonlinear iterative correction and global stiffness matrix integration. Two classical curved surfaces of tension membranes pro- duced under the uniform-stress condition are presented to verify the accuracy and efficiency of the proposed method.展开更多
For a non-relativistic particle that freely moves on a curved surface, the fundamental commutation relations between positions and momenta are insufficient to uniquely determine the operator form of the momenta. With ...For a non-relativistic particle that freely moves on a curved surface, the fundamental commutation relations between positions and momenta are insufficient to uniquely determine the operator form of the momenta. With introduc- tion of more commutation relations between positions and Hamiltonian and those between momenta and Hamiltonian, our recent sequential studies imply that the Cartesian system of coordinates is physically preferable, consistent with Dirae＇s observation. In present paper, we study quantization problem of the motion constrained on the two-dimensional sphere and develop a discriminant that can be used to show how the quantization within the intrinsic geometry is im- proper. Two kinds of parameterization of the spherical surface are explicitly invoked to investigate the quantization problem within the intrinsic geometry.展开更多
基金Project supported by the National Natural Science Foundation of China （Nos. 51025858 and 51178415）
文摘The determination of initial equilibrium shapes is a common problem in research work and engineering applications related to membrane structures. Using a general structural analysis framework of the finite particle method （FPM）, this paper presents the first application of the FPM and a recently-developed membrane model to the shape analysis of light weight mem- branes. The FPM is rooted in vector mechanics and physical viewpoints. It discretizes the analyzed domain into a group of parti- cles linked by elements, and the motion of the free particles is directly described by Newton＇s second law while the constrained ones follow the prescribed paths. An efficient physical modeling procedure of handling geometric nonlinearity has been developed to evaluate the particle interaction forces. To achieve the equilibrium shape as fast as possible, an integral-form, explicit time integration scheme has been proposed for solving the equation of motion. The equilibrium shape can be obtained naturally without nonlinear iterative correction and global stiffness matrix integration. Two classical curved surfaces of tension membranes pro- duced under the uniform-stress condition are presented to verify the accuracy and efficiency of the proposed method.
基金Supported by the National Natural Science Foundation of China under Grant No.11175063
文摘For a non-relativistic particle that freely moves on a curved surface, the fundamental commutation relations between positions and momenta are insufficient to uniquely determine the operator form of the momenta. With introduc- tion of more commutation relations between positions and Hamiltonian and those between momenta and Hamiltonian, our recent sequential studies imply that the Cartesian system of coordinates is physically preferable, consistent with Dirae＇s observation. In present paper, we study quantization problem of the motion constrained on the two-dimensional sphere and develop a discriminant that can be used to show how the quantization within the intrinsic geometry is im- proper. Two kinds of parameterization of the spherical surface are explicitly invoked to investigate the quantization problem within the intrinsic geometry.
