The existence of approximate inertial manifold Using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation ...The existence of approximate inertial manifold Using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation has a good localization property of the numerical solution distinguishably.展开更多
The vibration problem of a fluid conveying cylindrical shell consisted of newly developed multi-scale hybrid nanocomposites is solved in the present manuscript within the framework of an analytical solution.The consis...The vibration problem of a fluid conveying cylindrical shell consisted of newly developed multi-scale hybrid nanocomposites is solved in the present manuscript within the framework of an analytical solution.The consistent material is considered to be made from an initial matrix strengthened via both macro-and nano-scale reinforcements.The influence of nanofillers’agglomeration,generated due to the high surface to volume ratio in nanostructures,is included by implementing Eshelby-Mori-Tanaka homogenization scheme.Afterwards,the equivalent material properties of the carbon nanotube reinforced(CNTR)nanocomposite are coupled with those of CFs within the framework of a modified rule of mixture.On the other hand,the influences of viscous flow are covered by extending the Navier-Stokes equation for cylinders.A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the dynamic form of principle of virtual work.Next,the achieved governing equations will be solved by Galerkin’s method to reach the natural frequency of the structure for both simply supported and clamped boundary conditions.Presenting a set of illustrations,effects of each parameter on the dimensionless frequency of nanocomposite shells will be shown graphically.展开更多
This paper deals with the design and analysis of adaptive wavelet method for the Stokes problem. First, the limitation of Richardson iteration is explained and the multiplied matrix M0 in the paper of Bramble and Pasc...This paper deals with the design and analysis of adaptive wavelet method for the Stokes problem. First, the limitation of Richardson iteration is explained and the multiplied matrix M0 in the paper of Bramble and Pasciak is proved to be the simplest possible in an appropiate sense. Similar to the divergence operator, an exact application of its dual is shown; Second, based on these above observations, an adaptive wavelet algorithm for the Stokes problem is designed. Error analysis and computational complexity are given; Finally, since our algorithm is mainly to deal with an elliptic and positive definite operator equation, the last section is devoted to the Galerkin solution of an elliptic and positive definite equation. It turns out that the upper bound for error estimation may be improved.展开更多
文摘The existence of approximate inertial manifold Using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation has a good localization property of the numerical solution distinguishably.
文摘The vibration problem of a fluid conveying cylindrical shell consisted of newly developed multi-scale hybrid nanocomposites is solved in the present manuscript within the framework of an analytical solution.The consistent material is considered to be made from an initial matrix strengthened via both macro-and nano-scale reinforcements.The influence of nanofillers’agglomeration,generated due to the high surface to volume ratio in nanostructures,is included by implementing Eshelby-Mori-Tanaka homogenization scheme.Afterwards,the equivalent material properties of the carbon nanotube reinforced(CNTR)nanocomposite are coupled with those of CFs within the framework of a modified rule of mixture.On the other hand,the influences of viscous flow are covered by extending the Navier-Stokes equation for cylinders.A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the dynamic form of principle of virtual work.Next,the achieved governing equations will be solved by Galerkin’s method to reach the natural frequency of the structure for both simply supported and clamped boundary conditions.Presenting a set of illustrations,effects of each parameter on the dimensionless frequency of nanocomposite shells will be shown graphically.
基金Supported by the Natural Science Foundation of Beijing(No.1082003).
文摘This paper deals with the design and analysis of adaptive wavelet method for the Stokes problem. First, the limitation of Richardson iteration is explained and the multiplied matrix M0 in the paper of Bramble and Pasciak is proved to be the simplest possible in an appropiate sense. Similar to the divergence operator, an exact application of its dual is shown; Second, based on these above observations, an adaptive wavelet algorithm for the Stokes problem is designed. Error analysis and computational complexity are given; Finally, since our algorithm is mainly to deal with an elliptic and positive definite operator equation, the last section is devoted to the Galerkin solution of an elliptic and positive definite equation. It turns out that the upper bound for error estimation may be improved.
