广义变分原理在有限元半分析法中的应用

本文是在文献1]中所指出的广义变分原理在合理处理有限元法的边限条件的应用价值还没有受到足够的重视这一思想启发下,应用广义变分原理,选用样条函数与正弦(或余弦)函数乘积型的级数形式再加上多项式,作为板壳的逼近函数,以薄板弯曲问题为例较好地解决了有限元半分析法中出现的耦联问题.由于其未知数个数比有限元法、有限条法均少很多,而精度更高,故为用微机解决一类工程问题,提供了一个有效的方法.

The Application of Generalized Variational Principle in Finite Element-Semianalytical Method

The method developed in this paper is inspired by the viewpoint in reference 1] that sufficient attention has not been paid to the value of the generalized varialional principle in dealing with the boundary conditions in the finite element method. This, method applies the generalized varialional principle and chooses the series constituted by spline junction multiplied by sinusoidal junction and added by polynomial as the approximate deflection of plates and shells. By taking the deflection problem of thin plate, it shows that this method can solve the coupling problem in the finite element-semianalytical method. Compared with the finite elementt method and finite stripe method, this method has much fewer unknown variables and higher precision. Hence, it proposes an effective way to solve this kind of engineering problems by minicomputer.