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惯量投影椭球在构造变形分析中的意义初探
投稿时间:2007-05-23  修订日期:2007-12-31  点此下载全文
引用本文:李志勇,曾佐勋,罗文强.2008.惯量投影椭球在构造变形分析中的意义初探[J].地质论评,54(2):243-252,[DOI]:.
.2008.First Approach to the Significance of Inertia Moment Projection Ellipsoid for Structure Deformation Analysis[J].Geological Review,54(2):243-252.
DOI:
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作者单位
李志勇 中国地质大学地球科学学院武汉430074 
曾佐勋 华中构造力学研究中心武汉430074 
罗文强 中国地质大学数学与物理学院武汉430074 
基金项目:本文为国家自然科学基金资助项目(编号 49972068)、湖北省构造地质学精品课程建设项目的成果。
中文摘要: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。
中文关键词:惯量投影椭球  椭圆  任意形状  构造地质  变形
 
First Approach to the Significance of Inertia Moment Projection Ellipsoid for Structure Deformation Analysis
NameInstitution
Abstract: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.
keywords:Inertia Moment Projection Ellipsoid  Ellipse  Arbitrary shape  Structural geology  Deformation
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