结构拓扑变化理论中主Z值单调性定理与计算特征值的新方法

MONOTONOUSNESS THEOREM OF PRINCIPAL Z-DEFORMATIONS IN THE THEORY OF STRUCTURAL TOPOLOGICAL VARIATIONS AND A NEW METHOD FOR CALCULATING EIGENVALUES

该文是文[1]～[3]的继续，主要讨论两个内容，其一是论证静力体系的结构拓外变化理论中的主Z值具有一定的定值域，这一重要性质保障着用拓扑变化法进行分析的可靠性，称之为主Z值的定值域定理；其二是引入一个新概念，质量基元，从而把动力体系也纳入拓扑变化理论，且证明动力体系中的主Z值对于模数变化呈单调性，称为主Z值的单调性定理．作为它的应用，该文提出一套计算特征值的新方法，称为Z变形法．新方法的主要特点和优点在于：其精度不受相邻特征值之比值的影响，且其计算过程不需求解任何方程组，有广泛实用价值．

This paper is the continuation of the author's previous works[1~3] and prirnarily discusses two topics. The one is the demonstration of the fact that the principal Z-deformations defined in the theory of structural topological variations for static systems have certain limited range, being stated as the range theorem of principal Z-deformations. This important property will ensure the reliability of the structural topological variation method for analysis. The other is the intreduction of a new concept, the mass-subelement, via which dynamical systems can be also treated by the theory of structural topological variations; and it will be proven that the principal Z-deformations in dynamical systems are monotonously increasing almost everywhere with respect to the stiffness meduli of Tnass-subelements, being stated as the monotonousness theorem of principal Z-deformations. As an applicatoon of this theorem, a new method for calculating eigenvalues will be put forth, being stated as the Z-deformation method. The distinguishing feature and advantage 0f the new methed is that the accuracy of the method is not affected by the ratio of any two adjacent eingenvalues and the procedure of it does not need to solve any simultaneous equations; it has a great potential of practical applications.