伪可变体系的几何构造分析

Analysis of GeometricaI Construction for Quasi-Variable Systems

伪可变体系几何可变性的研究，对轻型结构的设计分析已变得十分重要。本文先分析能量与平衡之间的普遍关系，进而得出判定体系可变性的能量准则。通过拉格朗日乘子的引入，建立能量泛函，得出判定极值的二次型。然后证明了乘积力法与能量法的一致性，并讨论了宜于计算机分析实现的矩阵表示方法。结果表明，若二次型确定，则体系伪可变；当半确定时，体系部分伪可变部分可变；否则体系含二阶以上的无穷小机构。

The study of geometrical vatiabilty is very important for the calculatin and designingof a structure system.The relationship between energy functional and equilibrium is at firstanalysed in this paper because of geometrical variability corresponding to the equilibrim.Then the potential energy is set up using Lagrangian multiplication factors.And from thesecond variation of the energy,we obtain a quadratic form for judging the variability. Final-ly,a simple expression of matrices is derived.At the same time,we prove that the methodof product-force is associated with energy method.The calculating and analysing resultsshow that if the quadratic form is define(positive or negative),the assembly is quasi-vari-able;if it is semi-define,the system is partial quasi-variable and partial variable;if it is inde-fine,there are some high order mechanisms in the system.