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If theharmonic index is finite,then each end may be represented by a non-constant positiveharmonic function,and these functions compose a partition of unity.For minimalhypersurfaces with finite total scalar curvature,we can explicitly estimate the harmonicindex.Moreover,the space of bounded harmonic functions are exactly generated bythose functions associated to each end.This gives geometric interpretations of the ends.

若调和指标有限，则每个端均可由一非常值的调和函数代表，它们形成了一个单位分解，对于全纯量曲率有限的极小超曲面，我们明确地估计了调和指标，进一步，有界调和函数正好由代表端的那些调和函数所生成，这就给出了端的几何解释。

In order to solve the repeat modeling in the process of the hull scantling rule check,finite element analysis and production design,the some key technology about the transfer of ship initial scantling model to finite element model is studied.

针对目前船体结构规范计算、有限元分析和生产建模过程中存在的重复建模的问题，研究了船舶初步结构设计模型向有限元模型转换中的几项关键技术，提出了模型转换的方法，开发了模型转换软件，并在16 500t液化气船上进行了局部应用，收到了一定的效果，值得进一步推广应用。

In view of the questions in theoretic analysis and numerical simulation with the finite element method,the separation criterion of chips, the surface contact, the setting of friction coefficient,and the thermal stress coupling are researched. A simulation example is presented by applying the finite element analysis software-ANSYS,and the change of stress and strain in metal cutting process, the forming of shear plane and the influence of the temperature field on metal cutting are analyzed. The tool's strength is also analyzed.

基于理论分析和实际有限元数值模拟计算中遇到的问题，研究、讨论了切屑分离标准、表面接触、摩擦系数的设定、切屑与工件之间的连接以及热应力耦合分析等各项技术，并应用大型有限元分析软件ANSYS，具体分析了金属切削过程中应力和应变的变化、剪切面的形成以及温度场对金属切削的影响，并依此对刀具作强度分析，得到若干结论。

For the first time the endplate bolted connection's finite element model with the original crack is set up by the singular element, the fracture problem study is introduced to the finite element analyzing. The J integral value and stress intensity factor of the crack tip are calculated by the ANSYS Parametric Design Language program, and the developing of original crack is judged from the K Rule and J Integral Rule.

第一次通过构造奇异单元来建立带初始裂纹的节点有限元模型，将断裂问题的研究引入到端板螺栓节点的有限元分析中，并通过ANSYS软件中Parametric Design Language编程来计算裂纹尖端的J积分值、应力强度因子，根据断裂力学中的K准则、J积分准则判断初始裂纹是否会重新启裂。

This paper discusses the yield function, loading unloading criterion and constitutive equation of Lagrangian finite deformation elastic-plasticity theory. Finally, Lagrangian finite elastic plasticity theory is used on constitutive models of elastic-plasticity at infinitesimal strain, and the complete constitutive relation for singular yield surface theory is obtained.

本文讨论了Lagrange型有限变形弹塑性本构理论的屈服函数、加卸载准则、本构方程等，最终将Lagrange型有限变形弹塑性本构理论应用于小变形情况下的奇异屈服面弹塑性模型，得出了完整的Lagrange型有限变形弹塑性本构理论。

Based on the deep analysis of finite element method and process characteristics of tube stagger spinning, through further development of the general FEM software-MSC/MARC, the three dimension plastic-elastic finite element model is founded.

本文在对有限元基本理论和筒形件错距旋压工艺特点进行深入分析的基础上，通过基于MSC／MARC的二次开发，建立了筒形件错距旋压的三维弹塑性有限元模型。

A Material nonlinear finite element analysis for the cast-in-place reinforced concrete hollow slab that occurs from initial loading, cracking, yielding to failing is carried on. The cracking load, ultimate load, the displacement rules and the principal stress distribution rules of the hollow slab under the vertical loads are obtained. A Material nonlinear finite element analysis for the single span hollow flat-plate floor is also carried on. The function of the concealed wide-flat beams is definite by analyzing the principal stress distribution diagram. The calculating results verify the theoretical analysis and give some important conclusions which are great useful to improve the constructing of the new flat-plate floor.

其次对空心板进行了从加荷、开裂、屈服直至破坏的全过程材料非线性有限元计算，得到了空心板在竖向荷载作用下的开裂荷载、极限荷载及位移和应力分布规律；还对单跨无梁楼盖进行了材料非线性有限元计算，通过分析主应力场明确了柱上暗扁梁的作用；有限元计算的结果验证了以上的理论分析并得到了一些重要的结论，对改进现浇空心板无梁楼盖的构造措施有重要的参考价值。

Based on basic theory and finite element software and Hypermesh software MSC.patran to further the establishment of the Former subframe of the finite element model, and in general in MSC.

依据有限元基本理论和Hypermesh软件和MSC.patran软件，进一步建立该副车架的有限元模型，并在通用MSC。

It is important to study the structures of finite groups by combining some subgroups with some properties in the researches on finite groups.

用有限群的子群研究有限群的结构在有限群的研究中有重要的作用。

The present paper presents a short proof of the conjecture that a ring with a finite maximal subring is a finite ring.

摘要给出猜测"包含有限极大子环的环是有限环"的一个简短证明。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。