GDQ method is a kind of high order accurate numerical methods developed several years ago, which have been successfully used to simulate the solution of smooth engineering problems such as structure mechanics and inco...GDQ method is a kind of high order accurate numerical methods developed several years ago, which have been successfully used to simulate the solution of smooth engineering problems such as structure mechanics and incompressible fluid dynamics. In this paper, extending the traditional GDQ method, we develop a new kind of discontinuous GDQ methods to solve compressible flow problems of which solutions may be discontinuous. In order to capture the local features of fluid flows, firstly, the computational domain is divided into many small pieces of subdomains. Then, in each small subdomain, the GDQ method is implementedand some kinds of numerical flux limitation conditions will be required to keep the correct flow direction. At the boundary interface between subdomains, we also use some kind of flux conditions according to the flow direction. The numerical method obtained by the above steps has the advantages of high order accuracy and easy to treat boundary conditions. It can simulate perfectly nonlinear waves such as shock, rarefaction wave and contact discontinuity. Finally, the numerical experiments on one dimensional Burgers equation and Euler equations are given.The numerical results verify the validation of the method.展开更多
Nanobeams have promising applications in areas such as sensors,actuators,and resonators in nanoelectromechanical systems(NEMS).Considering the effects of gyration inertia,surface layer mass,surface residual stress,and...Nanobeams have promising applications in areas such as sensors,actuators,and resonators in nanoelectromechanical systems(NEMS).Considering the effects of gyration inertia,surface layer mass,surface residual stress,and surface Young's modulus,this study develops the vibration equations of the Timoshenko nanobeam.The generalized differential quadrature(GDQ)method and molecular dynamics(MD)simulation are used to study the surface effect on vibration.For a rectangular cross section,surface residual stress and surface Young's modulus are all affected by the height of the cross section rather than by the length-height ratio.If surface layer mass is considered,then the first three natural frequencies all decrease relative to their counterparts in the case in which surface layer mass is ignored.Results show that the effect of gyration inertia on resonance frequency is negligible.Longitudinal vibration does not easily occur relative to the bending and rotation vibrations of nanobeams.In addition,the results obtained by the GDQ method fit those obtained by MD simulation for beams with length-height ratios of 4-8.This study provides insights into the mechanism of the vibration of short and deep nanobeams and sheds light on the quantitative design of the elements in NEMSs.展开更多
This paper presents the stability of two-dimensional functionally graded(2D-FG)cylindrical shells subjected to combined external pressure and axial compression loads,based on classical shell theory.The material proper...This paper presents the stability of two-dimensional functionally graded(2D-FG)cylindrical shells subjected to combined external pressure and axial compression loads,based on classical shell theory.The material properties of functionally graded cylindrical shell are graded in two directional(radial and axial)and determined by the rule of mixture.The Euler’s equation is employed to derive the stability equations,which are solved by GDQ method to obtain the critical mechanical buckling loads of the 2D-FG cylindrical shells.The effects of shell geometry,the mechanical properties distribution in radial and axial direction on the critical buckling load are studied and compared with a cylindrical shell made of 1D-FGM.The numerical results reveal that the 2D-FGM has a significant effect on the critical buckling load.展开更多
文摘GDQ method is a kind of high order accurate numerical methods developed several years ago, which have been successfully used to simulate the solution of smooth engineering problems such as structure mechanics and incompressible fluid dynamics. In this paper, extending the traditional GDQ method, we develop a new kind of discontinuous GDQ methods to solve compressible flow problems of which solutions may be discontinuous. In order to capture the local features of fluid flows, firstly, the computational domain is divided into many small pieces of subdomains. Then, in each small subdomain, the GDQ method is implementedand some kinds of numerical flux limitation conditions will be required to keep the correct flow direction. At the boundary interface between subdomains, we also use some kind of flux conditions according to the flow direction. The numerical method obtained by the above steps has the advantages of high order accuracy and easy to treat boundary conditions. It can simulate perfectly nonlinear waves such as shock, rarefaction wave and contact discontinuity. Finally, the numerical experiments on one dimensional Burgers equation and Euler equations are given.The numerical results verify the validation of the method.
基金This study was supported by the National Natural Science Foundation of China(Grand Number 11672334).
文摘Nanobeams have promising applications in areas such as sensors,actuators,and resonators in nanoelectromechanical systems(NEMS).Considering the effects of gyration inertia,surface layer mass,surface residual stress,and surface Young's modulus,this study develops the vibration equations of the Timoshenko nanobeam.The generalized differential quadrature(GDQ)method and molecular dynamics(MD)simulation are used to study the surface effect on vibration.For a rectangular cross section,surface residual stress and surface Young's modulus are all affected by the height of the cross section rather than by the length-height ratio.If surface layer mass is considered,then the first three natural frequencies all decrease relative to their counterparts in the case in which surface layer mass is ignored.Results show that the effect of gyration inertia on resonance frequency is negligible.Longitudinal vibration does not easily occur relative to the bending and rotation vibrations of nanobeams.In addition,the results obtained by the GDQ method fit those obtained by MD simulation for beams with length-height ratios of 4-8.This study provides insights into the mechanism of the vibration of short and deep nanobeams and sheds light on the quantitative design of the elements in NEMSs.
文摘This paper presents the stability of two-dimensional functionally graded(2D-FG)cylindrical shells subjected to combined external pressure and axial compression loads,based on classical shell theory.The material properties of functionally graded cylindrical shell are graded in two directional(radial and axial)and determined by the rule of mixture.The Euler’s equation is employed to derive the stability equations,which are solved by GDQ method to obtain the critical mechanical buckling loads of the 2D-FG cylindrical shells.The effects of shell geometry,the mechanical properties distribution in radial and axial direction on the critical buckling load are studied and compared with a cylindrical shell made of 1D-FGM.The numerical results reveal that the 2D-FGM has a significant effect on the critical buckling load.
