摘要
提出各种工程抗震方法在数学模型上统一为纳维方程的五类反问题,即源项控制反问题、参数控制反问题、区域控制反问题、边界条件控制反问题和初始条件控制反问题;同时,阐述了求解这五类反问题的两种方法:其一,将纳维方程转化为状态形式的波动方程,将反问题转化为最优控制问题进行求解,给出了能量形式的性能指标;其二,采用有限元离散方法将纳维方程转化为振动方程,将反问题转化为最优化问题进行求解,建立优化数学模型。最后以区域控制反问题为例,对拱坝结构的抗震设计进行了计算分析,得到了具有最佳抗震性能的体型形式。
The mathematical models of engineering anti -seismic methods are classified to five inverse problems of Navier' s equations,i.e.,source control in verse problems,parameter control i nverse problems,domain control inverse problems,boundary conditi on control inverse problems and init ial condition control inverse probl ems.In order to solve the five inverse probl ems,1)they are transformed into optimum control problems with the transfor-mation of Navier' s equations into wave state equation s.Energy quality index is proposed.2)Navier' s equations are transformed into vibration equatio ns and mathematical model of optimiz ation is established with FEM.Domain control inverse problems that the sh ape anti -seismic design of arch dam a re given for illustration.The optim um anti -seismic shapes are obtained.
出处
《安徽工业大学学报(自然科学版)》
CAS
2003年第4期311-317,共7页
Journal of Anhui University of Technology(Natural Science)
基金
安徽省教育厅基金项目(2001kj023
2002kj038)
关键词
工程抗震
纳维方程
反问题
最优控制
最优化
能量指标
拱坝
engineering anti -seismic methods
Navier' s equations
inverse problem
optim um control
opti mization
Energy quality index
arch dam