能量变分法在现代结构分析中的应用

Application of energy variational method in the current structure analysis

现代结构的分析方法,基本上可以分为两大类:一类是有限元法,另一类是连续化法。但是这两类分析方法的理论基础均为能量变分原理。对能量变分法在有限元法和连续化法中的应用作了简要的介绍,并对现代结构分析中的势能原理与余能原理以及位移函数与拉格朗日乘子等问题进行了探讨。得出了一些有益的结论,对工程应用有一定参考价值。

The analysis methods of current structures may be divided into two main classes： one is finite element method,the other is equivalent continuum method.But the theory of this two analysis methods are based on the energy variational principle.The application of energy variational method to finite element method and equivalent continuum method was briefly introduced.The problems of potential energy,complementary energy,displacement function and Lagrange multiplier in the current structure analysis were discussed.Some useful conclusions were summarized,which will be valuable for the further practice.