层合板的一类数学模型及其有限元分析

ONE KIND OF MATHEMATICAL MODEL OF LAMINA TED PLATE AND FINITE ELEMENT ANALYSIS

本文基于弹性理论的混合变分原理,异出了包含横向剪切变形效应的层状复合材料板的混合形式的宏观数模型,其中,挠度W仅只出现一阶偏导数,从而易于构造相容的有限元模式;并且采用隔离存贮和分段、分片的求解技巧,克服了求解对称非正定有限元方程组的困难,从而使该数学模型易于求解。

In this paper, a new macroscopic mathe matical model of lamin ated plate on the basis of mixed principle was derived. In this model, the shear deformation was considered and the highest order partial derivative appearing in the functional was of order one, therefore the compatible element can easily be constructed.To solve symmetric but nonpositive definite linear equations, we presented an elimination method whic is called segregative store and segment by segment method. By sing this method, the mathematical model can easily be solved.