工程抗震方法的统一性研究—反问题、最优控制和最优化

Unity of engineering anti -seismic methods-inverse problem,optimum control and optimization

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.