几何结构

Moreover, if the optimization problem has certain special feature, the simpler relaxation methods can be provided. For example, considering a generalized geometric programming problem, relevant relaxation linear programming can be obtained using its special structure. Based on the branch and bound method, a linear relaxation algorithm of global optimization is presented for generalized geometric programming, and the convergence of the algorithm is also proven.

此外，当优化问题具有某种特殊性质时，我们能给出更加简便的松弛化方法，如考虑广义几何规划问题，能充分利用其特殊结构，建立了广义几何规划问题的松弛线性规划问题；在分枝定界技术的基础上，提出了一个求广义几何规划全局解的线性松弛算法；证明了算法的收敛性。

Then the shapes and amplitudes of geometrical imperfection can be determined through the decomposition of the correlation matrix.

这种求解拱结构随机几何缺陷的方法同样适用于其它结构中随机分布几何缺陷的分布方式及大小的求解。

The shape-form analysis and load analysis were done by nonlinear FEM. On the basis of surface FEM grid nodes, geometry property research of structure curved surface was progressed, including normal vector, GAUSS curvature, mean curvature and principal direction vector. In this process, the approximate expression of surface didn't need to he known.

采用非线性有限元法进行了膜结构的形态分析和荷载分析，得到了曲面有限元网格；通过离散微分几何方法，研究了薄膜结构曲面的几何性质，包括曲面的法线向量、高斯曲率、平均曲率和主方向矢量，避免了复杂的曲面拟合过程。

Compared with traditional DEM or TIN based methods, this pure vector approach obtains not only the topological structure of drainage system in planar graph, but also the valley distribution polygon range. Depending on geometrical computation and judgment of vector line, polygon, the structured properties in drainage representation is enhanced, avoiding the case of noise disturbance in DEM based method. The core algorithm makes use of the ability of Delaunay triangulation in detecting hierarchical structure of each contour line.

中文摘要：基于Delaunay三角网模型在矢量等高线基础上通过弯曲特征分析，给出了一种地形结构特征提取及谷地树组织的方法，与传统的基于DEM或TIN数据结构提取地形特征的方法相比，该方法不仅得到了谷地系统在平面图上的拓扑结构，还获得了河谷在空间分布上的汇水范围，依托矢量线、多边形的几何关系判断，增强了谷地树组织中的结构化，避免了DEM方法中的噪音干扰，方法的核心是Delaunay三角网在单根等高线弯曲深度表达上的层次结构识别。

The property, called as the geometry intrinsic property of lattice structure, was significant in material/structure design.

分析发现：当原网格结构单胞中各个杆件保持材料性质不变，而面内的几何尺寸扩大相同倍数时，拟膜的弹性本构保持不变，称这种性质为网格结构的几何内禀性。

The shearing failure of structural plane is considered to be corresponding to the maximum of real contact area, a criterion is given to distinguish the shearing failure of structural plane and a new select method of shear strength is brought forward subsequently; Examine the influence of geometrical features and thickness of weak intercalation on the integrative strength of weak structural plane based on the composing of basic strengths, formative mechanism of shearing plane and failure pattern; and present the quantitative relation between the strength and thickness.

4详细研究了依附型滑动面中的硬性结构面和软弱结构面力学特性和破坏模式，对硬性结构面引入摩擦学中的粘着摩擦理论，着重研究结构面在剪切过程中实际接触面的变化规律，提出实际接触面积的最大点即为强度破坏点，并结合实际数据进行了验证；对软弱结构面则从其基本强度的组成、内部剪切面的形成机理和破坏模式入手，研究了结构面的几何特性、夹层厚度和强度关系对软弱结构面综合强度值的影响，并给出了定量关系式。

When the Hamiltonian system is introduced into the research of dynamic buckling in cylindrical shells, the problem uses dual variables in Symplectic space instead of variables in traditional Euclidean space. The symplectic eigenfunction expansion method gives out an exact solution space. So many problems are solved, which can not find the solution in traditional methods.

将哈密顿体系引入结构的动态屈曲研究中，其意义在于将结构的动态屈曲研究从传统的欧几里得几何空间进入到由原变量和对偶变量组成的辛几何空间之中，从而使辛本征函数展开的直接解析法得以实施，这样就可以求解许多以往半逆凑合法无法求解的问题，并且所得到的解空间是完备的。

A new 3D human face model is put forward in this paper after some characters of the human face and the muscle tissues on the face are researched and some actions of the facial expression are analyzed. In this model we divide the whole face into some parts according to its structure. To each part, we apply the principle of elastomer metamorphosing to our face model, so a specific face model can be easily gotten by modifying a common face model.

本文在分析和总结了前人工作的基础上，深入研究了人脸的生理特征、面部肌肉组织结构，分析了人脸面部表情的基本动作，提出了将人脸整体分解为若干个小块的三维人脸几何模型，并根据力学中的弹性体形变原理，将弹性体的形变应用于上述基于面分块的三维人脸几何模型，使特定人脸几何模型的建立变得简单、效率高。

The Practice Evaluation of Quadrilateral Concept for Elementary School Students, a book designed by the researcher of this study, will be a tool in evaluating middle- and high-graders' concept and degree of cognition about quadrilaterals.

采用自编的「国小学生四边形几何概念实作评量」为研究工具，探讨国小中、高年级学生四边形几何概念的认知情形及层次，并藉由模糊取向的认知结构分析了解学生的概念结构。

Since the founding of the symplectic algorithm by famous Chinese scientistFeng Kang and American scientist R.D.Ruth,the resulting theory of structure-preserving algorithm for finite dimensional Hamiltonian system has been wellestablished.

自从我国科学家冯康和美国科学家Ruth创立辛几何算法以来，由此建立的有限维Hamilton系统保结构算法的理论已日益完善，特别是在保辛结构算法即辛几何算法方面。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。