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mathematics cover
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     MATHEMATICS AND DIALECTICS
     数学与辩证法
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     Application of Mathematics
     数学的应用
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     COVER STORY
     封面的故事
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     Cover Browse
     封面浏览
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     Discover in Beauty Mathematics
     在数学中发掘数学美
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This paper probes into the techniques of forming of covering system of numerical manifold method. Firstly, the method of automatically forming for the mathematics covers and physics covers as well as its grid was studied; and then the way of automatically forming for number of two series of covers was also researched.

系统地探讨了流形元覆盖系统的形成方法 ,基于三角形有限元网格 ,探讨了流形元数学覆盖和物理覆盖及其流形元分析网格的形成技术 ,研究了流形元两套覆盖编号的自动形成方法。

The mesh generation of the numerical manifold method for the rock block system is studied.It is one kind of methods for the discontinuous deformation analysis in the rock engineering.It is success to discuss the process of a finite element mesh transforms to a cover system for the numerical manifold method.Solutions to the mathematics cover,the physic cover,and the numbering of manifold elements are proposed in the paper.All those are based on the plane triangle mesh.Meanwhile,a computer program...

The mesh generation of the numerical manifold method for the rock block system is studied.It is one kind of methods for the discontinuous deformation analysis in the rock engineering.It is success to discuss the process of a finite element mesh transforms to a cover system for the numerical manifold method.Solutions to the mathematics cover,the physic cover,and the numbering of manifold elements are proposed in the paper.All those are based on the plane triangle mesh.Meanwhile,a computer program is developed for the study.An example shows that the computing result is correct

根据数值流形方法的基本理论 ,系统地研究了数值流形元覆盖系统形成的方法。基于平面三角形有限元网格 ,探讨了岩石块体系统数值流形方法分析之数学覆盖和物理覆盖及其流形元分析网格的形成技术 ,研究了覆盖系统两套覆盖编号的自动形成方法。据此研制成计算机分析软件并应用于计算实例 ,取得良好效果。该文所取得的研究成果为数值流形方法应用于大型岩土工程分析与计算奠定了坚实的基础 ,具有广泛的工程应用前景

The development of mathematics covers three stages: elementary mathematics, advanced mathematics, and modern mathematics. As the studied objects, number and shape have very different implication in the three different stages. The number in the stage of elementary mathematics is a constant, while shape is an isolate and simple geometric form; the number in the stage of advanced mathematics is variable, while shape is curve and curved surface; and the objects of modern mathematic...

The development of mathematics covers three stages: elementary mathematics, advanced mathematics, and modern mathematics. As the studied objects, number and shape have very different implication in the three different stages. The number in the stage of elementary mathematics is a constant, while shape is an isolate and simple geometric form; the number in the stage of advanced mathematics is variable, while shape is curve and curved surface; and the objects of modern mathematic studies are general assemble, all kinds of space and manifold, so that it's very difficult to distinguish the categories of number and shape. Modern mathematics is ofaxiomatization, structurization, unification, abstractness, adaptability, nonlinear, uncertainty and so on.

数学的发展经历了初等数学、高等数学、现代数学三个阶段,作为数学研究对象的数和形,在这三个阶段的含义是很不同的。初等数学阶段的数是常量,形是孤立的、简单的几何形体;高等数学阶段的数是变量,形是曲线和曲面;现代数学研究的对象是一般的集合、各种空间和流形,很难区分数和形的范畴了,现代数学具有公理化、结构化、统一化、泛函性、抽象性、应用性、非线性、不确定性等特点。

 
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