W-30 wt%Cu and TiC-50 wt%Ag were successfully synthesized by a novel simplified pretreatment followed by electroless plating. The 0 wt% TiC, 0.5 wt% TiC, and 0.5 wt%TiC-0.5 wt%Ag composite powders were added to W-30 w...W-30 wt%Cu and TiC-50 wt%Ag were successfully synthesized by a novel simplified pretreatment followed by electroless plating. The 0 wt% TiC, 0.5 wt% TiC, and 0.5 wt%TiC-0.5 wt%Ag composite powders were added to W-30 wt%Cu composite powders by blending, and then reduced. The reduced W-30 Cu, W-30 Cu/0.5 TiC, and W-30 Cu-0.5 Ag/0.5 TiC composite powders were then compacted and sintered at 1 300 ℃ in protective hydrogen for 60 min. The phase and morphology of the composite powders and materials were analyzed using X-ray diffraction and field emission scanning electron microscopy. The relative density, electrical conductivity, and hardness of the sintered samples were examined. Results showed that W-30 Cu and TiC-Ag composite powders with uniform structure were obtained using simplified pretreatment followed by electroless plating. The addition of TiC particles can significantly increase the compressive strength and hardness of the W-30 Cu composite material but decrease the electrical conductivity. Next, 0.5 wt% Ag was added to prepare W-30 Cu-0.5 Ag/TiC composites with excellent electrical conductivity. The electrical conductivity of these composites(61.2%) is higher than that in the national standard(the imaginary line denotes electrical conductivity of GB IACS 42%) of 45.7%.展开更多
A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accura...A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.展开更多
Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolatio...Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.展开更多
Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms.One estimator is shown to be reliable and efficient,which ...Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms.One estimator is shown to be reliable and efficient,which yields global upper and lower bounds for the error in piecewise W1,p seminorm.The other one is proved to give a global upper bound of the error in Lp-norm.By taking the two estimators as refinement indicators,adaptive algorithms are suggested,which are experimentally shown to attain optimal convergence orders.展开更多
This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint proble...This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.展开更多
This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both com...This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element enriched with the intersected term on each element to approximate the displacement, whereas the second one uses the enriched modified nonconforming rotated Q1 element to approximate both the rotation and the displacement. Both elements employ a more complicated shear force space to overcome the shear force locking, which will be described in detail in the introduction. We prove that both methods converge at optimal rates uniformly in the plate thickness t and the mesh distortion parameter in both the H1-and the L2-norms, and consequently they are locking free.展开更多
基金Funded by the National Magnetic Confinement Fusion Program(No.2014GB121001)
文摘W-30 wt%Cu and TiC-50 wt%Ag were successfully synthesized by a novel simplified pretreatment followed by electroless plating. The 0 wt% TiC, 0.5 wt% TiC, and 0.5 wt%TiC-0.5 wt%Ag composite powders were added to W-30 wt%Cu composite powders by blending, and then reduced. The reduced W-30 Cu, W-30 Cu/0.5 TiC, and W-30 Cu-0.5 Ag/0.5 TiC composite powders were then compacted and sintered at 1 300 ℃ in protective hydrogen for 60 min. The phase and morphology of the composite powders and materials were analyzed using X-ray diffraction and field emission scanning electron microscopy. The relative density, electrical conductivity, and hardness of the sintered samples were examined. Results showed that W-30 Cu and TiC-Ag composite powders with uniform structure were obtained using simplified pretreatment followed by electroless plating. The addition of TiC particles can significantly increase the compressive strength and hardness of the W-30 Cu composite material but decrease the electrical conductivity. Next, 0.5 wt% Ag was added to prepare W-30 Cu-0.5 Ag/TiC composites with excellent electrical conductivity. The electrical conductivity of these composites(61.2%) is higher than that in the national standard(the imaginary line denotes electrical conductivity of GB IACS 42%) of 45.7%.
基金supported by National Natural Science Foundation of China (Grant Nos. 10871022, 10771065,and 60573158)Natural Science Foundation of Hebei Province (Grant No. A2007001027)
文摘A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.
基金the National Nutural Science Foundation of China(Grant Nos.10771198,10590353)
文摘Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.
基金the National Natural Science Foundation of China(Grant No.10771150)the National Basic Research Program of China(Grant No.2005CB321701)the Program for New Century Excellent Talents in University(Grant No.NCET-07-0584)
文摘Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms.One estimator is shown to be reliable and efficient,which yields global upper and lower bounds for the error in piecewise W1,p seminorm.The other one is proved to give a global upper bound of the error in Lp-norm.By taking the two estimators as refinement indicators,adaptive algorithms are suggested,which are experimentally shown to attain optimal convergence orders.
基金supported by National Natural Science Foundation of China (Grant No.10761003) the Governor's Special Foundation of Guizhou Province for Outstanding Scientific Education Personnel (Grant No.[2005]155)
文摘This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
基金the National Natural Science Foundation of China (Grant No. 10601003)National Excellent Doctoral Dissertation of China (Grant No. 200718)
文摘This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element enriched with the intersected term on each element to approximate the displacement, whereas the second one uses the enriched modified nonconforming rotated Q1 element to approximate both the rotation and the displacement. Both elements employ a more complicated shear force space to overcome the shear force locking, which will be described in detail in the introduction. We prove that both methods converge at optimal rates uniformly in the plate thickness t and the mesh distortion parameter in both the H1-and the L2-norms, and consequently they are locking free.
