This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods develo...This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov’s criterion, Neǐgauz and Lidskiǐ’s criterion. Secondly, we present stability criteria on Hill’s equations with sign-changing potential in which Brog’s criterion and Krein’s criterion are included.展开更多
Some necessary and sufficient conditions for absolute stability of several classes of direct control system were given, and two simplified forms of the control systems obtained twice were discussed. The results improv...Some necessary and sufficient conditions for absolute stability of several classes of direct control system were given, and two simplified forms of the control systems obtained twice were discussed. The results improve those of previous works.展开更多
Since different underground engineering contains different geological conditions,structure and excavation methods,their disturbing degree on the ground also differs,but ground surface settlement caused by excavation h...Since different underground engineering contains different geological conditions,structure and excavation methods,their disturbing degree on the ground also differs,but ground surface settlement caused by excavation has one common point that they will form a ground surface settlement curve.Based on data statistical analysis,the article puts forward the relationship between point of inflection in digging tunnels with shallowburied method and the span of tunnel excavation against typical geological conditions in Changchun so as to predict the impact of tunnel excavation and improve reasonable ground surface settlement control standard.Research result will be useful for study on ground surface control standard in digging tunnels with shallow-buried method and setting settlement standard.展开更多
为分析高地温水工隧洞衬砌结构温度应力特性,基于拉普拉斯变换推导出衬砌结构瞬态温度场的解析解,并借助弹性抗力法推导出衬砌结构的弹性温度应力分量。依托新疆布伦口水电站监测数据对衬砌结构瞬态温度场及应力场进行计算分析,并采用...为分析高地温水工隧洞衬砌结构温度应力特性,基于拉普拉斯变换推导出衬砌结构瞬态温度场的解析解,并借助弹性抗力法推导出衬砌结构的弹性温度应力分量。依托新疆布伦口水电站监测数据对衬砌结构瞬态温度场及应力场进行计算分析,并采用抗拉强度准则和裂缝尖端强度因子对衬砌结构破坏进行分析,提出合理的温控防裂措施。结果表明:1)衬砌温度场前期整体温度迅速上升,在第7天左右达到最大值,其中衬砌内壁温度可达到37℃,外壁温度可达到56℃。2)衬砌结构外墙环向应力可达到2.2 MPa,体现为拉应力状态;径向应力可达到2.7 MPa,呈现为压应力状态。3)衬砌结构强度的破坏主要受温度及结构本身稳定性2方面影响,可通过采用低热水泥、控制混凝土的入模温度以及严格监控施工过程来提高衬砌的稳定性。其中,采用低热水泥可降低衬砌结构的温升值,混凝土的最终水化热每降低50 k J/kg,衬砌结构内外壁的温差可降低1.85℃左右;适当提高入模温度可缩短水化热的放热周期及降低衬砌内外壁温差。展开更多
基金supported by NSFC(11401089,11671071)the Scientific Technological Project of Jilin Province’s Education Department in Thirteenth Five-Year(JJKH20170535KJ)+1 种基金supported by NSFC(11571065)the National Basic Research Program of China(2013CB834102)
文摘This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov’s criterion, Neǐgauz and Lidskiǐ’s criterion. Secondly, we present stability criteria on Hill’s equations with sign-changing potential in which Brog’s criterion and Krein’s criterion are included.
文摘Some necessary and sufficient conditions for absolute stability of several classes of direct control system were given, and two simplified forms of the control systems obtained twice were discussed. The results improve those of previous works.
文摘Since different underground engineering contains different geological conditions,structure and excavation methods,their disturbing degree on the ground also differs,but ground surface settlement caused by excavation has one common point that they will form a ground surface settlement curve.Based on data statistical analysis,the article puts forward the relationship between point of inflection in digging tunnels with shallowburied method and the span of tunnel excavation against typical geological conditions in Changchun so as to predict the impact of tunnel excavation and improve reasonable ground surface settlement control standard.Research result will be useful for study on ground surface control standard in digging tunnels with shallow-buried method and setting settlement standard.
文摘为分析高地温水工隧洞衬砌结构温度应力特性,基于拉普拉斯变换推导出衬砌结构瞬态温度场的解析解,并借助弹性抗力法推导出衬砌结构的弹性温度应力分量。依托新疆布伦口水电站监测数据对衬砌结构瞬态温度场及应力场进行计算分析,并采用抗拉强度准则和裂缝尖端强度因子对衬砌结构破坏进行分析,提出合理的温控防裂措施。结果表明:1)衬砌温度场前期整体温度迅速上升,在第7天左右达到最大值,其中衬砌内壁温度可达到37℃,外壁温度可达到56℃。2)衬砌结构外墙环向应力可达到2.2 MPa,体现为拉应力状态;径向应力可达到2.7 MPa,呈现为压应力状态。3)衬砌结构强度的破坏主要受温度及结构本身稳定性2方面影响,可通过采用低热水泥、控制混凝土的入模温度以及严格监控施工过程来提高衬砌的稳定性。其中,采用低热水泥可降低衬砌结构的温升值,混凝土的最终水化热每降低50 k J/kg,衬砌结构内外壁的温差可降低1.85℃左右;适当提高入模温度可缩短水化热的放热周期及降低衬砌内外壁温差。
