惯量投影椭球在构造变形分析中的意义初探

First Approach to the Significance of Inertia Moment Projection Ellipsoid for Structure Deformation Analysis

本文讨论了一种新的数学工具,即惯量投影椭球(和椭圆),在具有任意形状构造变形体的变形描述与应变分析中的意义。论证了在均匀的递进变形过程中,构造标志体惯量投影椭球的变形与其自身的变形保持一致,两者遵循同样的均匀变形方程。在进行构造变形描述和分析时,构造标志体形状与其惯量投影椭球是等效的。惯量投影椭球具有有限应变椭球相同的性质,可以用来描述任意形状构造标志体的变形,并可以替代具有任意形状构造标志体进行变形分析。先前适用于椭圆形标志体变形分析的方法均可应用于具有任意形状的构造标志体。这将为我们对具有任意形状的构造标志体变形的描述和分析提供方便和有用的数学工具。

This paper discusses the significance of a new tool, the Inertia Moment Projection （IMP） ellipsoid （or ellipse in two dimensions）, for the deformation description and strain analysis of structural objects with arbitrary shape. During the progressive uniform deformation, the deformation of the IMP ellipsoid is coincident with that of the structural object. They both follow the same deformation rule. The IMP ellipsoid is equivalent to the arbitrary shape of structural object for the description and analysis of deformation. It has the same characteristics as the finite strain ellipsoid and can substitute for the structural object for strain analysis. So, the former strain analysis methods based on elliptic structural deformation markers can be used for the general structural objects with arbitrary shape. It would be a very useful mathematic tool for the description and analysis of structural deformation.