求大挠度板高级变分近似解的一种算法

An Algorithm for Finding High-Class Variational Approximate Solution of Large Deflection Plates

采用变分法求解薄板大挠度问题的高级近似解时将导致多元三次代数方程组.为了求解这样的非线性代数方程组,本文给出了一元化三次方程迭代解法.这个方法首先对每个方程进行"一元化"处理,然后用一元三次方程根的公式计算近似解,再通过迭代过程求出任意精度的解.文中对受均布荷载作用的周边固定圆板的大挠度问题进行了具体讨论,计算了它的三级变分近似解.数值结果表明,该法是简便可行的.

The problem of solving large deflection plate by the variational method is changed into that of solving systems of cubic algebraic equations with multi-unknown quantities. In order to solve such nonlinear algebraic equations , this paper preposes an iterative method of the cubic equtions with one unkown. In this method , each equation is treated as a cubic algebraic equation with one unkown to which the solution may be found by using the formula of its roots and then the solution of arbitrary accuracy is obtained by the iterative process. In this paper , the three-class variational approximate solution of large deflection bending of a circular plate subjected to uniformly distributed load has been obtained with the present method . The numerical results illustrate that the present method is simple and feasible.