条形域平面弹性问题与哈密尔顿体系

Plane elasticity Problem in strip domain and Hamiltonian system

利用结构力学与最优控制相模拟的理论，将弹性力学势能变分原理导向部分一般 变分原理，并将哈密尔顿体系的理论引入到弹性力学与椭圆型偏微分方程之中，导出 一套横向哈密尔顿算子矩阵的本征函数向量展开解法。这种方法可广泛地用于柱形域 的课题。具体通过条形域平面弹性问题的推导与求解，表现出这套方法的特点。

Based on the analogy of structural mechanics and optimal contro1, and a1so based on carrying the minimum potential energy variational principle in elastici- ty to the generalized one, the theory of Hami1tonian system can be introduced into theory of e1asticity and e11iptic PDE. The transverse eigensolutions of the Hamiltonian operator matrix and its expansion solution method can be deduced. Such method can be wide1y app1ied for prismatic domain prob1ems.The method is given in detail through the so1ution of the p1ane elastic prob1em in a strip domain.