摘要
本文以一般变分原理为基础,论述了子结构串连构成的结构分析,阐明了计算结构力学与线性二次型最优控制问题是相通的,存在——对应关系,因此证明了里卡提代数方程有二类迭代解法,分别从上限及下限去迫近于真实解,计算结构力学和最优控制在理论与方法上便得到沟通,可以相互取长补短了。 对于连续坐标或连续时间问题,又可证明它们与椭圆型偏微分方程在条形域中的半解析法是相通的。这几个领域的贯通与渗透,将带来一些新的推动力。
Base on the generalized variational principle, the analysis of substructural chain is considered first, and the one-one correspondence between that structural analysis problem with the linear quadratic optimal control problem is explained. Hence, the algebraic Riccati equation can be solved in two ways, the upper bound and lower bound iterative methods. That the theory and methods of structural analysis problems can be transplanted to the linear quadratic optimal control problems.As to the continuous coordinate and/or continuous-time problems, it can be shown, that the LQ control problem is also correspondent to the semi-analytical method of elliptic partial differential equation. It is hopeful that the unified theory of these disciplines will have some new promotions
