四边形的

In the second chapter, elementary theories and ideas of one step forming inverse approach were described and warped modification method, implemented by Cook, was introduced into one step forming simulation and based on idea of surface spreading; new quadrilateral element modification arithmetic was put forward. By spreading warped quadrilateral onto plane in local coordinate system, a plane quadrilateral element whose shape and area were equal to original warped quadrilateral element was gotten and internal force vectors of four nodes and stiffness matrix of elements were improved to increase precision of simulations on this plane element.

第二章从一步成形逆有限元法的基本理论和思想出发，将Cook基于弹性理论的四边形单元的翘曲修正算法引入基于塑性的一步成形，并且基于曲面展开的思想，本文提出一种新的四节点单元翘曲修正方案，通过把翘曲的单元展开的方法在局部参考系中得到一个与实际翘曲单元的形状与面积非常接近的平面单元，在该平面单元中进行单元刚度及内力向量的计算，进一步改善模拟结果的精度。

The results are listed as follows:(1) In peneplain with plenty water-resource, hexagonal spatial structure of urban system can be formed. Due to differential competed function of central places, the hexagonal system is distorted. The result is that the area covered is decr eased and the girth is unchanged——but every border is usually unequal;(2) A pattern of pentagonal system evolves from hexagonal system controlled by a river;(3) A pattern of quadrilateral develops from hexagonal system under two parallel rivers;(4) The equal distance distribution of central places in narrow geographic space has its special reasons. The results are very important for understanding urban's formation and development and urban plan in Huang-Huai-Hai plain.

本文通过自然地理因素中水文、地形这两个重要要素对城镇体系空间结构形成的影响，分析了华北平原区在不同要素影响下的城镇体系空间结构样式：①在水源充足的准"均质"河北冲积平原上，基本满足六边形形成条件，但由于周边中心地发展竞争力不同，故使得正六边形发生畸变——覆盖面积减小而周长却保持不变；②构建了在一条河流影响下的六边形网络结构朝五边形网络演变的模型；③构建了在平行状河流作用下六边形网络向四边形网络演替的模式；④指出了在水源充足的狭长地理空间，城镇体系空间结构发育成等间距的现象与原因。

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。

Based on the variational principle of virtual voltage and virtual displacement derived in this thesis and the classical theory of linear laminated plates, and by using the constitutive equations of elastic piezoelectric materials, and the DKQ quadrilateral plate bending element, the finite element modeling for the fabric reinforced laminated plates with nonlinear voltage-electric strain relationship of piezoelectric actuators has been established for the first time in this thesis. And the expressions for the electric loadings with obvious mechanical meaning and convenient for computation are established, which can be used to the deformation analysis of laminated plates with piezoelectric actuators under specified voltages.

以本文直接导出的压电结构的虚电势—虚位移变分原理为基础，依据经典线性层合板理论和压电弹性体的本构方程，采用基于离散法线假设的DKQ四结点任意四边形薄板弯曲单元，首次建立了考虑非线性电压—电应变关系的含压电致动器的纤维增强型层合板的有限元分析模型，并推导建立了力学意义明确、便于计算的电荷载表达式，可用于指定电压条件下纤维增强型叠层合成板的变形分析。

The calculated results show: the ground state structures of PtNi5, Pt2Ni4 and Pt3Ni3 clusters are quadrangular bi-pyramid, and Pt4Ni2 and Pt5Ni clusters are triangular bi-pyramid with hat and triangular pyramid with quadrilateral, respectively. From the point of view of thermodynamics, PtnNim clusters are stable because of the negative enthalpy of formation; the positive NICS of PtNi5 clusters show anti-aromaticity, The negative NICS of Pt2Ni4 and Pt5Ni clusters show aromaticity. The number of the IR absorption peak of Pt3Ni3 is the most. The IR and raman absorption peak of PtNi5 , IR of Pt2Ni4, Raman of Pt3Ni3 and Pt4Ni2 have only one. The absorption peak of Pt5Ni appears in the bigger frequencies only, and is zero almost in the small frequencies.

研究结果表明：PtNi5、、Pt2Ni4、Pt3Ni3团簇的基态结构都为四角双锥结构，Pt4Ni2 和Pt5Ni团簇的基态结构分别是戴帽三角双锥和三角锥戴四边形结构；PtnNim团簇的生成焓都为负值，表明团簇在热力学上是稳定的；由NICS值可得，PtNi5团簇具有反芳香性，Pt2Ni4和Pt5Ni团簇具有芳香性；从光谱分析来看，Pt3Ni3团簇的IR较强吸收峰的个数最多，PtNi5团簇的IR和Raman、Pt2Ni4团簇的IR、Pt3Ni3和Pt4Ni2团簇的Raman只有一个强吸收峰值，Pt5Ni团簇的峰值只出现在频率较大的位置，频率小的位置几乎为零。

The results of XRD indicated that the addition of lanthanum in skutterudite could enhance the formation of skutterudite during the synthesis process. The content of skutterudite increases with the increase of the filling fraction in 〓. The lattice parameter of filled skutterudite increases with the increase of lanthanum filling fraction. It is caused by the deformation of Sb〓 ring arising from the "rattling"of the filling atoms in the voids in skutterudite.

对不同填充率方钴矿La〓Fe〓CoSb〓材料的XRD研究发现，镧元素的引入可以促进方钴矿相的合成，相同条件下合成的方钴矿的纯度随镧填充率的增大而提高，材料的晶胞参数随镧填充率的提高而增大，这是填充原子在方钴矿晶体的的孔隙内震颤和晶胞内Sb〓四边形发生扭曲变形所致。

The foundation of arch dam usually is layer rock base, and the depths of the layer are small, it is common that several layer rock base contact with one layer element grid. According to the geometry relation and the property of shape function, a new element kind that includes 24 nodes has been proposed to dissect the dam and foundation effectively, whose shape function are independent. In fact the element can be looked as a hexahedron divided into five small hexahedrons. It can be simulate all kind of the condition of the base and the dam.

拱坝的地基一般是层状岩石地基，有的层厚度很小，这样就有多个岩层和坝体某层单元接触，本文根据岩基与坝体接触的几何关系，利用形函数的性质，提出24节点六面体层单元，这种单元实际上是将一个厚的六面体单元分成5个更薄的六面体单元而形成的，其形函数采用可以拆分的形式表达，因此可以方便地解决坝体单元的一、二、三、四个面与错动带接触的情况，可以模拟一、二、三、四个棱边与错动带接触的情况，还可以退化为12节点的四边形面单元，以及五面体层单元。

Questions in this content area are based on the properties and relations of plane figures, including angles and relations among perpendicular and parallel lines; properties of circles, triangles, rectangles, parallelograms, and trapezoids; transformation; the concept of proof and proof techniques; volume; and applications of geometry to three dimensions.

平面几何（23％）。这方面的考试内容是基于平面图形的性质及关系，包括角度，垂直线和平行线之间的关系；圆，三角形，矩形，平行四边形和梯形的特性；图形的转化；几何证明的概念和证明的技巧；体积以及几何在三维的应用。

Research found, generally speaking, students' concept image is not fully covered about quadrilaterals. That is to say, some graph is excluded wrongly. For example:students took oblique square is rhombi, not square. This phenomenon probably caused by they see the typical shape all the time, which will impact the development of the higher level reasoning. Say, students might not be able to understand the inclusion relationship between square and rhombi.

研究发现，学生在四边形几何图形的概念心像上普遍有包含性不足的情况，也就是有些图例被错误地排除（如：以为斜摆的正方形是菱形，但不是正方形），此一现象应与学生接触的通常是典型图例所致，且会影响更高层次的几何推理之发展，例如无法理解正方形与菱形的包含关系。

Finally, after these nodes are connected according to the certain rule, the quadrilateral grid of tooth profile plane model is generated.

先按照齿廓的形状，在齿廓平面模型的不同部分生成一定疏密间隔的控制线，然后在控制线上生成一定疏密间隔的节点，最后根据一定的规则连接这些节点，即可自动生成齿廓平面模型的四边形网格。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。