Ceramic tapes, containing Al2O3-25 wt pct TiB2(B) and Al2O3-25 wt pct nano-TiC (c), have been obtained by tape casting process. Numerous tapes (about 60～80 tapes) were prepared by stacking in turn the composition (B)...Ceramic tapes, containing Al2O3-25 wt pct TiB2(B) and Al2O3-25 wt pct nano-TiC (c), have been obtained by tape casting process. Numerous tapes (about 60～80 tapes) were prepared by stacking in turn the composition (B) and (C), laminating under 10 MPa pressure, eliminating the solvent and burning out the polymer additives. The final green bodies were hot pressed at 1750℃ and 30 MPa. The composite has a bending strength of 568 MPa and a fracture toughness of 5.8 M Pa·m1/2. SEM analysis exhibits that Al2O3 particle growth was inhibited by TiC particles in C. but TiB2 particles could not hinder Al2O3 growth in B. The curves of GTA indicates that all organic additives could be removed completely above 600℃展开更多
In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it i...In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.展开更多
A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity.More precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fu...A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity.More precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fuid pressure is approximated by using the node conforming finite elements.The well-posedness of the fully discrete scheme is established,and a corresponding priori error estimate with optimal order in the energy norm is also derived.Numerical experiments are provided to validate the theoretical results.展开更多
In this paper, we study a weakly over-penalized interior penalty method for non-self- adjoint and indefinite problems. An optimal a priori error estimate in the energy norm is derived. In addition, we introduce a resi...In this paper, we study a weakly over-penalized interior penalty method for non-self- adjoint and indefinite problems. An optimal a priori error estimate in the energy norm is derived. In addition, we introduce a residual-based a posteriori error estimator, which is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to validate our theoretical analysis.展开更多
Cu matrix composites reinforced by TiB_(2)/TiN ceramic reinforcements(Cu/TBN composites)were prepared by hot pressing method.Prior to the hot pressing,Cu/TiB_(2)/TiN composite powders(CTBN powders),which were used as ...Cu matrix composites reinforced by TiB_(2)/TiN ceramic reinforcements(Cu/TBN composites)were prepared by hot pressing method.Prior to the hot pressing,Cu/TiB_(2)/TiN composite powders(CTBN powders),which were used as the starting materials of Cu/TBN composites,were fabricated by self-propagating high-temperature synthesis method.The CTBN particles were found to be in a special core–shell structure with a Cu–Ti alloy core and a TiB_(2)/TiN ceramic shell.The test results presented obvious improvements in mechanical properties.The highest ultimate tensile strength reached up to 297 MPa,77 MPa higher than that of Cu.And the highest hardness reached up to 70.7 HRF,15.7 HRF higher than that of Cu.A comparative study indicated that the core–shell structured particles could bring about more obvious strengthening eff ect than the traditional irregularly shaped particles,which was due to the improved Cu/ceramics interfacial bonding,the linkage strengthening effect of both TiB_(2) and TiN,and higher load bearing ability of the core–shell structured reinforcements.展开更多
In this paper,we derive a residual based a posteriori error estimator for a modified weak Galerkin formulation of second order elliptic problems.We prove that the error estimator used for interior penalty discontinuou...In this paper,we derive a residual based a posteriori error estimator for a modified weak Galerkin formulation of second order elliptic problems.We prove that the error estimator used for interior penalty discontinuous Galerkin methods still gives both upper and lower bounds for the modified weak Galerkin method,though they have essentially different bilinear forms.More precisely,we prove its reliability and efficiency for the actual error measured in the standard DG norm.We further provide an improved a priori error estimate under minimal regularity assumptions on the exact solution.Numerical results are presented to verify the theoretical analysis.展开更多
In this paper,we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem.An optimal a priori error estimate in the energy norm is proved.In addition,a residual-based a poster...In this paper,we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem.An optimal a priori error estimate in the energy norm is proved.In addition,a residual-based a posteriori error estimator is obtained.The estimator is proved to be both reliable and efficient in the energy norm.Some numerical testes are presented to demonstrate the effectiveness of our method.展开更多
文摘Ceramic tapes, containing Al2O3-25 wt pct TiB2(B) and Al2O3-25 wt pct nano-TiC (c), have been obtained by tape casting process. Numerous tapes (about 60～80 tapes) were prepared by stacking in turn the composition (B) and (C), laminating under 10 MPa pressure, eliminating the solvent and burning out the polymer additives. The final green bodies were hot pressed at 1750℃ and 30 MPa. The composite has a bending strength of 568 MPa and a fracture toughness of 5.8 M Pa·m1/2. SEM analysis exhibits that Al2O3 particle growth was inhibited by TiC particles in C. but TiB2 particles could not hinder Al2O3 growth in B. The curves of GTA indicates that all organic additives could be removed completely above 600℃
文摘In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020A1515011032)The work of M.Cai is supported in part by the NIH-BUILD(Grant No.UL1GM118973)+2 种基金by the NIH-RCMI(Grant No.U54MD013376)the National Science Foundation awards(Grant Nos.1700328,1831950)The work of L.Zhong is supported by the National Natural Science Foundation of China(Grant No.12071160)。
文摘A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity.More precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fuid pressure is approximated by using the node conforming finite elements.The well-posedness of the fully discrete scheme is established,and a corresponding priori error estimate with optimal order in the energy norm is also derived.Numerical experiments are provided to validate the theoretical results.
基金We thank the anonymous referees for their valuable comments and suggestions which lead to an improved presentation of this paper. This work was supported by NSFC under the grant 11371199, 11226334 and 11301275, the Jiangsu Provincial 2011 Program （Collaborative Innovation Center of Climate Change）, the Program of Natural Science Research of Jiangsu Higher Education Institutions of China （Grant No. 12KJB110013）, Natural Science Foundation of Guangdong Province of China （Grant No. S2012040007993） and Educational Commission of Guangdong Province of China （Grant No. 2012LYM0122）.
文摘In this paper, we study a weakly over-penalized interior penalty method for non-self- adjoint and indefinite problems. An optimal a priori error estimate in the energy norm is derived. In addition, we introduce a residual-based a posteriori error estimator, which is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to validate our theoretical analysis.
基金financially supported by the National Key R&D Program of China(No.2018YFF01013605)the National Natural Science Foundation of China(No.51501215)+2 种基金the Youth Innovation Promotion Association CAS(No.2019254)the Science Foundation for Youth Scholar of State Key Laboratory of High Performance Ceramics and Superfine Microstructures(No.SKL201701)the State Key Laboratory of New Ceramic and Fine Processing Tsinghua University(No.KF201806)。
文摘Cu matrix composites reinforced by TiB_(2)/TiN ceramic reinforcements(Cu/TBN composites)were prepared by hot pressing method.Prior to the hot pressing,Cu/TiB_(2)/TiN composite powders(CTBN powders),which were used as the starting materials of Cu/TBN composites,were fabricated by self-propagating high-temperature synthesis method.The CTBN particles were found to be in a special core–shell structure with a Cu–Ti alloy core and a TiB_(2)/TiN ceramic shell.The test results presented obvious improvements in mechanical properties.The highest ultimate tensile strength reached up to 297 MPa,77 MPa higher than that of Cu.And the highest hardness reached up to 70.7 HRF,15.7 HRF higher than that of Cu.A comparative study indicated that the core–shell structured particles could bring about more obvious strengthening eff ect than the traditional irregularly shaped particles,which was due to the improved Cu/ceramics interfacial bonding,the linkage strengthening effect of both TiB_(2) and TiN,and higher load bearing ability of the core–shell structured reinforcements.
基金The first author was supported by Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2018A030307024 and 2020A1515011032)by National Natural Science Foundation of China(Grant No.11526097)+2 种基金The second author was supported by National Natural Science Foundation of China(Grant Nos.11871272 and 11871281)The third author was supported by National Natural Science Foundation of China(Grant No.11701197)The fourth author was supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2018A0303100016).
文摘In this paper,we derive a residual based a posteriori error estimator for a modified weak Galerkin formulation of second order elliptic problems.We prove that the error estimator used for interior penalty discontinuous Galerkin methods still gives both upper and lower bounds for the modified weak Galerkin method,though they have essentially different bilinear forms.More precisely,we prove its reliability and efficiency for the actual error measured in the standard DG norm.We further provide an improved a priori error estimate under minimal regularity assumptions on the exact solution.Numerical results are presented to verify the theoretical analysis.
文摘In this paper,we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem.An optimal a priori error estimate in the energy norm is proved.In addition,a residual-based a posteriori error estimator is obtained.The estimator is proved to be both reliable and efficient in the energy norm.Some numerical testes are presented to demonstrate the effectiveness of our method.
