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This paper has presented the formulae of calculating physical base and space metric tensor for complicated system, these formulae are developed by using non-Cartesian tensor analysis and introducing physical base.

本文基于非笛卡儿张量的分析，并引入了物理基，提出了复杂系统的空间度量张量的一系列矩阵公式，据以求出任意曲线坐标系中的数学模型。

The 2PN equations of light ray in the solar-system have been deduced from the metric tensor and Christoffel symbols.

从度规和Christoffel记号出发推导太阳系中的2PN光线方程。

A method for choicing and determining physical base and space metric tensor in an arbitrary curvilinear (orthogonal and non-orthogonal) coordinate system is illustrated by examples.

通过示例说明，在正交或非正交的任意曲线坐标系中选择和确定物理基及空间度量张量的方法，得到了与以往文献吻合的满意结果。

Using the metric tensor ??

利用度量张量？

By the research of metric tensor and Riemann tensor on Riemann manifold, we getthe inherent curvature of configuration space belonging to parallel mechanism.

通过对度量张量和Riemann张量的研究，得出并联机构运动可达子空间的内在"弯曲"性质，指出使用相对坐标系和广义坐标是研究并联机构运动学和动力学问题的必然选择。

Space ; Cartesian coordinates ; non-Cartesian coordinates ; metric tensor ; natural base ; physicalbase ; helical ; parabolic cylindrical

空间；笛卡儿坐标系；非笛卡儿坐标系；度量张量；自然基；物理基；螺旋线；抛物柱面

To establish the constitutive equation of material, the metric tensor for stress , strain and their transformation equations between different configurations are derived, and basic theory of finite deformation as well as elasto-plastic deformation criterion are studied. By analyzing the applicability of different element models, four-node quadrilateral degenerated Mindlin isoparametric element is adopted because of its good versatility, and the element stiffness matrix is derived. The static implicit elasto-plastic finite element equation for complex skin stretch-forming is put forward based on Updated Langrange formulation.

本文首先系统地阐述了有限变形的相关基本理论，针对板料成形建立了应力应变度量张量及其相应的转换关系；介绍了材料的屈服准则、塑性变形强化规律、塑性流动规律以及加、卸载准则，并在此基础上建立了有限变形各向异性弹塑性本构方程；对板料成形的单元模型进行了分析，针对飞机蒙皮零件特点，采用通用性强的四节点四边形退化Mindlin等参壳单元进行成形模拟，并导出其单元刚度矩阵的具体形式；基于以上研究，以逐级更新Langrange描述的持续虚功率原理为基础，建立了率形式的复杂蒙皮拉形过程静态隐式弹塑性有限元方程。

Complicated system ; space metric tensor ; natural base ; physical base ; non-Cartesian tensor ; Cartesian tensor ; helical-Cartesian coordinate system ; parabolic cylindrical coordinate system

复杂系统；空间度量张量；自然基物理基；笛卡儿张量；非笛卡儿；张量；螺旋线——笛卡儿坐标系；抛物柱面坐标系

We need about 200 metric ton s.

我们需要大约200吨。

Out of this, 30% or 5400 metric ton comes from local production by mainly by our farmers.

而在18000吨的30％或5400吨的白米是来自我们当地稻农的生产。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。