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Optimization solution algorithm is the most important in topology optimization.Algorithms fit for discrete structure and continuum structure are all investigated. Thecharacteristic and different using limit of both optimization criteria method andmathematics programming method are all analyzed in this paper. OC algorithm and theseries MMA algorithm based on SIMP approach are deducedand used for the topology optimization problem of continuum structure.

优化求解算法是拓扑优化问题求解的核心和关键，本文系统分析了适用于离散结构和连续体结构优化的优化求解算法，重点讨论了 OC 算法和 MP 算法，分析比较了不同算法的特点和适用范围，推导了基于 SIMP 理论的优化准则法和 MMA 系列算法，并将MMA 系列算法应用于连续体结构拓扑优化问题的求解。

In spite of the granular nature, soil has traditionally been modeled as a continuum. This continuum mechanics cannot get the precise solution while soil\'s nonlinear, discontinuous, large deformation, and strain localization behavior are considered. The discrete element method is based on discontinuum theory, and is pioneered by Cundall.

土是由多相介质组成的离散颗粒集合体，尽管研究者早已在土的散粒状属性上达成共识，但关于土体力学性质的研究还经常沿用连续介质力学方法，这种基于连续体小变形假设的方法在求解实际土体非线性、非连续、大变形、应变局部化问题时往往无法得到精确解答。

Continuum Mechanics is one of the basic courses of the modern mechanics. The fundamental equations of Continuum Mechanics are essentially divided into two types.

它主要侧重于其相关的基本概念和原理以及应用，因而在科学技术方面起着重要的作用。

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下："此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。"

Western attitudes toward economic planning can be found along a continuum. The two poles of that continuum are 1 libertarianism and 2 micromanagement.

西方对经济计划的态度是各种各样的，两种极端的观点是：1自由主义否认任何计划，2微观管理主张具体到细节的计划。

On the basis of wavelength distribution of the continuum emission,we suggested that atom Al resonantly absorbing continuum radiation was absorbs energy by atom solid,which consists o...

我们认为：Al原子吸收能量的主要机制是原子实吸收连续辐射光子，原子实吸收光子的方式是与价电子构成极性振子对连续辐射共振吸收。

Tow canopy models are developed according to uniform partial cover and non-uniform partial cover: continuum canopy model and non-continuum canopy model.

根据植被均匀非完全覆盖和非均匀非完全覆盖情况建立了相应的两种冠层模式：连续冠层模式和非连续冠层模式。

The total radiative loss include the sum of every possible transition between two levels under the atomical models of hydrogen (4 level + 1 continuum), ionized calcium (5 level + 1 continuum), and magnesium (3 level) beside the contributions from nagtive hydrogen of f-f and f-b tranditions.

并将辐射损失速率与非热电子束轰击和软x线作用下的产能率作了比较，结果表明：耀斑不同时刻的色球辐射损失变化可达一个量级以上；耀斑脉冲相前后电子束加热相当有效；耀斑强度极大时，电子束轰击和软x线加热都有作用；耀斑主相时，软x线加热更能有效地平衡辐射损失。

According to the distribution of time resolved relative intensity of continuum emission of the plasma induced by laser ablating Al in Ar,we have briefly discussed the mechanism of the continuum radiation of the plasma induced by laser ablating Aluminum.

根据连续辐射强度的时间分布，简要讨论了激光诱导等离子体连续辐射的产生机理。根据连续辐射强度的波长分布，提出了原子对激光诱导等离子体连续辐射共振吸收理论。

Through the Laplace and Z transformations, it represents the varying features of electromechanical disturbance in a uniform chain network using the family of Bessel functions; the growing or attenuating laws are the same as that of electromechanical wave in a continuum model along the corresponding transmission media. Furthermore, the time of electromechanical disturbance arriving at any bus in the discrete model is also the same as that of electromechanical wave arriving at the corresponding bus in the continuum model.

通过Laplace和Z联合变换，用Bessel函数表示出机电扰动在均匀离散系统中的变化特征，得出扰动的增衰规律与连续体模型中机电波的增衰规律完全相同，而且离散系统中扰动传播到每一条母线所需要的时间与连续体模型中机电波传播到相应母线所需时间也完全相等。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。