弹性板平面问题的半解析法分析

Semi-analytical Solution Analysis of Elastic Plate

文章探讨的半解析法突破了有限条半解析法只能处理简单边界条件的局限性,将求解域剖分为若干条形单元,在条形单元上采用等参变换技术,通过在边界曲线上布置若干结点来适应复杂边界条件。用最小势能原理得到控制微分方程组,采用状态空间法将微分方程化为状态方程。利用格林函数法及其自然边界条件转化方程获得解答。

The semi-analytical method to be discussed in the paper breakthroughs the semi-analytical finite strip method that may only deal with the plates with simply boundary conditions. Solution domains divided into many strip elements to be adopted is, o-parametric transfer. Arranging lots of nodes in the boundary curve is to adapt compound boundary conditions. Utilizing principle of potential energy to obtain governing differential equations, to turn differential equations into state equations by means of state space method. The solution of equations are obtained by means of both Green function method and natural boundary conditions.