In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical syst...In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.展开更多
The proliferation of Hoek-Brown nonlinear failure criterion and upper bound theorem makes it possible to evaluate the stability of circular tunnels with an original curved collapsing mechanism. The arch effect of shal...The proliferation of Hoek-Brown nonlinear failure criterion and upper bound theorem makes it possible to evaluate the stability of circular tunnels with an original curved collapsing mechanism. The arch effect of shallow circle tunnel is not taken into consideration so that the mechanical characteristics can be easily described. Based on the mechanism, the upper bound solution of supporting pressure of tunnels under the condition of surface settlements and overloads on the ground surface is derived. The objective function is formed from virtual work equations under the variational principle, and solutions are presented by the optimum theory. Comparisons with previous works are made. The numerical results of the present method show great agreement with those of existing ones. With regard to the surface settlement and overloads, the influence of different rock parameters on the collapsing shape is analyzed.展开更多
An A1-5.8Mg-0.4Mn-0.35（Sc＋Zr） （mass fraction, %） alloy sheet was prepared using water chilling copper mould ingot metallurgy processing which was protected by active flux. The influence of stabilizing annealing o...An A1-5.8Mg-0.4Mn-0.35（Sc＋Zr） （mass fraction, %） alloy sheet was prepared using water chilling copper mould ingot metallurgy processing which was protected by active flux. The influence of stabilizing annealing on mechanical properties and microstructure of the cold rolling sheet was studied. The results show that the strength and hardness of the alloy decrease, while the elongation increases with increasing the stabilizing annealing temperature. With the increase of stabilizing annealing time, the strength and hardness of the alloy drop slightly but its ductility exhibits no change. Partial recovery and recrystallization orderly occur with the increase of annealing temperature during stabilizing treatment. Only different degrees of recovery occur in the alloys annealed below 400 ℃ for 1 h. Partial recrystallization occurs after annealed at 450 ℃ for 1 h. By annealing at 300 ℃ for 1 h, the alloy can obtain the optimum application values of δb, δ0.2 and δ, which are 436 MPa, 327 MPa and 16.7%, respectively.展开更多
Rational composite design is highly important for the development of high-performance composite polymer electrolytes(CPEs)for solid-state lithium(Li)metal batteries.In this work,Li closo-borohydride,Li_(2)B_(12)H_(12)...Rational composite design is highly important for the development of high-performance composite polymer electrolytes(CPEs)for solid-state lithium(Li)metal batteries.In this work,Li closo-borohydride,Li_(2)B_(12)H_(12),is introduced to poly(vinylidene fluoride)-Li-bis-(trifluoromethanesulfonyl)imide(PVDF-LiTFSI)with a bound N-methyl pyrrolidone plasticizer to form a novel CPE.This CPE shows superb Li^(+)conduction properties,as evidenced by its conductivity of 1.43×10^(-4) S cm^(-1) and Li^(+)transference number of 0.34 at 25℃.Density functional theory calculations reveal that Li_(2)B_(12)H_(12),which features electron-deficient multicenter bonds,can facilitate the dissociation of LiTFSI and enhance the immobilization of TFSI to improve the Li^(+)conduction properties of the CPE.Moreover,the fabricated CPE exhibits excellent electrochemical,thermal,and mechanical stability.The addition of Li_(2)B_(12)H_(12) can help form a protective layer at the anode/electrolyte interface,thereby preventing unwanted reactions.The above benefits of the fabricated CPE contribute to the high compatibility of the electrode.Symmetric Li cells can be stably cycled at 0.2mA cm^(-2) for over 1200 h,and Li||LiFePO_(4) cells can deliver a reversible specific capacity of 140mAh g^(-1) after 200 cycles at 1C at 25℃ with a capacity retention of 98%.展开更多
基金Natural Science Foundation of High Education of Jiangsu Province of China，"Qing Lan" Project Foundation of Jiangsu Province
文摘In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.
基金Project(2013CB036004)supported by the National Basic Research Program of ChinaProjects(51178468,51378510)supported by the National Natural Science Foundation of China
文摘The proliferation of Hoek-Brown nonlinear failure criterion and upper bound theorem makes it possible to evaluate the stability of circular tunnels with an original curved collapsing mechanism. The arch effect of shallow circle tunnel is not taken into consideration so that the mechanical characteristics can be easily described. Based on the mechanism, the upper bound solution of supporting pressure of tunnels under the condition of surface settlements and overloads on the ground surface is derived. The objective function is formed from virtual work equations under the variational principle, and solutions are presented by the optimum theory. Comparisons with previous works are made. The numerical results of the present method show great agreement with those of existing ones. With regard to the surface settlement and overloads, the influence of different rock parameters on the collapsing shape is analyzed.
基金Project(2006AA03Z523)supported by the National High Technology Research and Development Program of China
文摘An A1-5.8Mg-0.4Mn-0.35（Sc＋Zr） （mass fraction, %） alloy sheet was prepared using water chilling copper mould ingot metallurgy processing which was protected by active flux. The influence of stabilizing annealing on mechanical properties and microstructure of the cold rolling sheet was studied. The results show that the strength and hardness of the alloy decrease, while the elongation increases with increasing the stabilizing annealing temperature. With the increase of stabilizing annealing time, the strength and hardness of the alloy drop slightly but its ductility exhibits no change. Partial recovery and recrystallization orderly occur with the increase of annealing temperature during stabilizing treatment. Only different degrees of recovery occur in the alloys annealed below 400 ℃ for 1 h. Partial recrystallization occurs after annealed at 450 ℃ for 1 h. By annealing at 300 ℃ for 1 h, the alloy can obtain the optimum application values of δb, δ0.2 and δ, which are 436 MPa, 327 MPa and 16.7%, respectively.
基金supported by the National Natural Science Foundation of China(51971146 and 51971147)the Major Program for the Scientific Research Innovation Plan of Shanghai Education Commission(2019-01-07-00-07-E00015)+3 种基金Shanghai Outstanding Academic Leaders PlanGuangxi Key Laboratory of Information Materials(Guilin University of Electronic Technology,201017-K)Shanghai Rising-Star Program(20QA1407100)the General Program of Natural Science Foundation of Shanghai(20ZR1438400).
文摘Rational composite design is highly important for the development of high-performance composite polymer electrolytes(CPEs)for solid-state lithium(Li)metal batteries.In this work,Li closo-borohydride,Li_(2)B_(12)H_(12),is introduced to poly(vinylidene fluoride)-Li-bis-(trifluoromethanesulfonyl)imide(PVDF-LiTFSI)with a bound N-methyl pyrrolidone plasticizer to form a novel CPE.This CPE shows superb Li^(+)conduction properties,as evidenced by its conductivity of 1.43×10^(-4) S cm^(-1) and Li^(+)transference number of 0.34 at 25℃.Density functional theory calculations reveal that Li_(2)B_(12)H_(12),which features electron-deficient multicenter bonds,can facilitate the dissociation of LiTFSI and enhance the immobilization of TFSI to improve the Li^(+)conduction properties of the CPE.Moreover,the fabricated CPE exhibits excellent electrochemical,thermal,and mechanical stability.The addition of Li_(2)B_(12)H_(12) can help form a protective layer at the anode/electrolyte interface,thereby preventing unwanted reactions.The above benefits of the fabricated CPE contribute to the high compatibility of the electrode.Symmetric Li cells can be stably cycled at 0.2mA cm^(-2) for over 1200 h,and Li||LiFePO_(4) cells can deliver a reversible specific capacity of 140mAh g^(-1) after 200 cycles at 1C at 25℃ with a capacity retention of 98%.
