四边形

When generating the first layer of elements, the nodes on the interior surface are generated by projecting the nodes on the exterior surface along the normal direction of the exterior surface onto the interior or surface.

将未划分区域的边界继续向内偏置，划分新的单元，和第一层划分时直接将外边界上节点向内投射不同，以后的内边界曲面上的节点和表面四边形单元是直接划分的。

The approach of computational simulation is the finite element method.The whole research is combined by the following three parts. In part one, a program on quadtree method is compiled. It can automatically generate planar structures with all-quadrangular, good quality elements in high speed, and it can create data files on information of elements and nodes, which provide the foundation for finite element analysis. In part two, a program on finite element calculation is compiled by object-oriented method, During the simulation of fracture, the displacement and stress are calculated by the program.

本文的工作可分为三大部分：第一部分编制了四叉树法程序，通过它可对平面结构进行单元离散，快速自动生成质量较好的全四边形单元，并获得离散后的单元信息和节点信息，为有限元计算打下基础；第二部分利用面向对象方法编制了有限元计算程序，在破坏模拟过程中，利用它进行位移、应力分析；第三部分对脆性材料的破坏过程进行了模拟。

By using the method of expanding the aperture function into a finite sum of complex Gaussian functions, approximate closed-form propagation equations of TMn0-Gaussian beams diffracted by hard-edged parallelogram aperture s are derived.

通过将硬边光阑函数展为复高斯函数之和的方法，在直角坐标系下研究了TMn0模高斯光束通过有平行四边形光阑的衍射，得到了近似的解析传输公式。

The works of this period are full of painting language experiments in form, space and material, and we see sparks of what would later form his language matrix, but overall, the Chen Yufei of the '80's was a lonely metaphysicist, focused on using the four-cornered world of painting to extract basic imagery and forms from his daily life and spirit. His pictures had a very strong design feel.

这一时期的作品在造型、空间、材料等绘画语言上有着各种实验，闪现出了他其后的一些基本语言与母题，但总体而言，80年代的陈宇飞属于一个孤独的形而上主义者，专注于用绘画这一四边形的世界从他的日常生活及精神生活中抽离出一些基本的意象和形式，画面有很强的设计感。

The two extremities of this huge parallelogram were occupied, the one by the famous marble table, so long, so broad, and so thick that, say the old territorial records in a style that would whet the appetite of a Gargantua,"Never was such a slab of marble seen in the world"

这座呈平行四边形的宽阔无比的大厅，一端摆着那张名闻遐迩的大理石桌子，那么长，那么宽，那么厚，据古老地籍册所云，世上如此偌大的大理石，真是见所未见，这样一种说法可叫卡岗蒂亚②垂涎欲滴

Applying this rule, we give a kind of definition of discrete Gauss curvature and mean curvature on the discrete parametric curves net.

应用这种加细方法，我们给出了一种针对由离散参数曲线网形成的四边形网格上任意顶点处的离散估计值的定义方法。

Applying this rule, a kind of the definition of the discrete estimated value on the quadrilateral net is given. It includes the definition of discrete Gauss curvature and discrete mean curvature.

应用该方法，给出了一种四边形网格上任意顶点处的离散估计值的定义方法，主要包括离散的Gauss曲率和平均曲率的定义。

Based on geometrical nonlinear finite element theory, a curved quadrilateral isoperimetric element with 8 nodes for initial form analysis of tensile membrane structures is presented.

根据几何非线性有限元理论，提出张力膜结构初始形态分析的8结点曲面四边形等参单元。

Based on the geometrical nonlinear finite element theory, a curved quadrilateral isoperimetric element with 8 nodes for initial form analysis of tensile membrane structures is presented.

本文根据几何非线性有限元理论，提出张力膜结构初始形态分析的8结点曲面四边形等参单元。

With i being the greatest lower bound on the number of latter points in the interior of any TLP with exactly v vertices, i(5)=i(6)=1,i(7)=i(8)=4 , it is proved that i increases without bound as ...

证明了随着TLP顶点数的增加，内格点数无限增加。并得出在允许旋转 180°条件下，有任意内格点数的三角形TLP，任意格点四边形都是TLP。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。