If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton＇s second law of mechanics in the Planck＇s scale. This curious velocity dependent term inspires a frictional fe...If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton＇s second law of mechanics in the Planck＇s scale. This curious velocity dependent term inspires a frictional feature of the gravity. In this short letter we address that this new term modifies the effective mass and the Newtonian constant as the time dependent quantities. Thus we must have a running on the value of the effective mass on the particle mass m near the holographic screen and the G. This result has a nigh relation with the Dirac hypothesis about the large numbers hypothesis （L.N.H.）. We propose that the corrected entropie terms via Verlinde idea can be brought as a holographic evidence for the authenticity of the Dirac idea.展开更多
This study presents a structural analysis algorithm called the finite particle method （FPM） for kinematically indeterminate bar assemblies. Different from the traditional analysis method, FPM is based on the combina...This study presents a structural analysis algorithm called the finite particle method （FPM） for kinematically indeterminate bar assemblies. Different from the traditional analysis method, FPM is based on the combination of the vector mechanics and numerical calculations. It models the analyzed domain composed of finite particles. Newton＇s second law is adopted to describe the motions of all particles. A convected material flame and explicit time integration for the solution procedure is also adopted in this method. By using the FPM, there is no need to solve any nonlinear equations, to calculate the stiffness matrix or equilibrium matrix, which is very helpful in the analysis of kinematically indeterminate structures. The basic formulations for the space bar are derived, following its solution procedures for bar assemblies. Three numerical examples are analyzed using the FPM. Results obtained from both the straight pretension cable and the suspension cable assembly show that the FPM can produce a more accurate analysis result. The motion simulation of the four-bar space assembly demonstrates the capability of this method in the analysis ofkinematically indeterminate structures.展开更多
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
Smoothed particle hydrodynamics(SPH)is a mesh-free method which is powerful for large deformation computation of soils.However,the algorithm for the simulation of frictional contact which is common in geotechnical eng...Smoothed particle hydrodynamics(SPH)is a mesh-free method which is powerful for large deformation computation of soils.However,the algorithm for the simulation of frictional contact which is common in geotechnical engineering is still quite immature due to the boundary deficiency.In this study,the cause of boundary deficiency in the SPH simulation for frictional contact is analysed.Then,based on mathematical derivation,the method to correct boundary deficiency related to frictional contact is discussed theoretically,where the frictional contact algorithm is established by dividing the computational domain into several subdomains according to the existing contact boundaries and by using contact forces as bridges of these subdomains to fulfil problem solving,and the value of correction coefficient is obtained by comparing the SPH outcome of the contact particles with that calculated through Newton’s second law of motion.At the same time,from the perspective of numerical computation,an optimized value for the correction coefficient is proposed,and a thorough investigation is performed on the cubic spline kernel function and quintic spline kernel function,whose correction coefficients are found to be 2.0 and[2.0,2.16],respectively.Finally,numerical tests are carried out to verify the proposed method.The outcome of the study is helpful to providing theoretical support for the research of frictional contact simulation within the framework of SPH.展开更多
Discontinuous deformation analysis （DDA） method, proposed firstly by Shi [1] in 1988, is a novel numerical approach to simulate the discontinuous deformation behaviors of blocky rock structures. In DDA, the domain o...Discontinuous deformation analysis （DDA） method, proposed firstly by Shi [1] in 1988, is a novel numerical approach to simulate the discontinuous deformation behaviors of blocky rock structures. In DDA, the domain of interest is represented as an assemblage of discrete blocks and the joints are treated as interfaces between blocks. The governing equations of DDA are derived from Newton’s Second Law of Motion and the Principle of Minimum Potential Energy.展开更多
文摘If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton＇s second law of mechanics in the Planck＇s scale. This curious velocity dependent term inspires a frictional feature of the gravity. In this short letter we address that this new term modifies the effective mass and the Newtonian constant as the time dependent quantities. Thus we must have a running on the value of the effective mass on the particle mass m near the holographic screen and the G. This result has a nigh relation with the Dirac hypothesis about the large numbers hypothesis （L.N.H.）. We propose that the corrected entropie terms via Verlinde idea can be brought as a holographic evidence for the authenticity of the Dirac idea.
基金supported by the National Natural Science Foundation of China (No. 50638050)the National High-Tech R&D (863) Program (No. 2007AA04Z441), China
文摘This study presents a structural analysis algorithm called the finite particle method （FPM） for kinematically indeterminate bar assemblies. Different from the traditional analysis method, FPM is based on the combination of the vector mechanics and numerical calculations. It models the analyzed domain composed of finite particles. Newton＇s second law is adopted to describe the motions of all particles. A convected material flame and explicit time integration for the solution procedure is also adopted in this method. By using the FPM, there is no need to solve any nonlinear equations, to calculate the stiffness matrix or equilibrium matrix, which is very helpful in the analysis of kinematically indeterminate structures. The basic formulations for the space bar are derived, following its solution procedures for bar assemblies. Three numerical examples are analyzed using the FPM. Results obtained from both the straight pretension cable and the suspension cable assembly show that the FPM can produce a more accurate analysis result. The motion simulation of the four-bar space assembly demonstrates the capability of this method in the analysis ofkinematically indeterminate structures.
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 Natural Science Foundation of Jiangsu Province(Grant No.BK20131372)the National Natural Science Founda-tion of China(Grant No.51139001)+1 种基金Special Fund of State Key Laboratory of China(Grant No.20095860120)the Fundamental Research Funds for the Central Universities of China(Grant No.B1020083)
文摘Smoothed particle hydrodynamics(SPH)is a mesh-free method which is powerful for large deformation computation of soils.However,the algorithm for the simulation of frictional contact which is common in geotechnical engineering is still quite immature due to the boundary deficiency.In this study,the cause of boundary deficiency in the SPH simulation for frictional contact is analysed.Then,based on mathematical derivation,the method to correct boundary deficiency related to frictional contact is discussed theoretically,where the frictional contact algorithm is established by dividing the computational domain into several subdomains according to the existing contact boundaries and by using contact forces as bridges of these subdomains to fulfil problem solving,and the value of correction coefficient is obtained by comparing the SPH outcome of the contact particles with that calculated through Newton’s second law of motion.At the same time,from the perspective of numerical computation,an optimized value for the correction coefficient is proposed,and a thorough investigation is performed on the cubic spline kernel function and quintic spline kernel function,whose correction coefficients are found to be 2.0 and[2.0,2.16],respectively.Finally,numerical tests are carried out to verify the proposed method.The outcome of the study is helpful to providing theoretical support for the research of frictional contact simulation within the framework of SPH.
文摘Discontinuous deformation analysis （DDA） method, proposed firstly by Shi [1] in 1988, is a novel numerical approach to simulate the discontinuous deformation behaviors of blocky rock structures. In DDA, the domain of interest is represented as an assemblage of discrete blocks and the joints are treated as interfaces between blocks. The governing equations of DDA are derived from Newton’s Second Law of Motion and the Principle of Minimum Potential Energy.
