数值函数

Numerical experiments declare that those filled functions have fairish calculated performance.

理论证明分析和数值实验的结果表明，此类填充函数具有较好计算性质。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

According to principle of transport phenomens and reaction engneering the mathematical model of water gas gasifier is established.

介绍了利用基于传递现象和反应工程的理论建立起的水煤气炉数学模型，在计算机上进行了模拟数值计算，得出了操作参数之间的关系，再以气化效率为目标函数，进行寻优得出了水煤气炉优化的循环操作时间，并介绍了在工业生产装置上实际应用的效

Z2Bn z$e0A0 Meshless method is a new numerical computation method that is developed rapidly in recent years. Without element mesh and based on the dispersed nodes to form approximate interpolative function dynamically, meshless method has distinct difference with traditional finite element method. Meshless method conquers the problems caused by mesh generation, mesh aberration and mesh move. With provides a new effective means to engineering problem, meshless method obtain highly recognition in international compute mechanics domain and engineering field.

6L！y6K1Q6h0k0 无网格方法是近年来迅速发展起来的一类新型数值计算方法，它们不借助单元网格而是基于离散结点动态构造近似插值函数，与传统的有限元方法有着显著的区别，克服了网格生成、网格畸变和网格移动引起的问题并为工程问题提供了一种新的有效分析方法，受到了国际计算力学界和工程界的高度重视。

This is due to that the characteristics lenth significantly affects th e maximum lateral electric field and the length of velocity saturation region,bo th of which are very important in modeling the drain current and the substrate c urrent.

在以双曲正切函数描述的 I- V特性基础上，该解析模型的运算量远低于基于数值分析的物理模型，其中提取参数的运用也大大提高了模型的精度，模拟结果与实验数据有很好的一致性。

The numerical results show that our method is effective. For the noncharacteristic Cauchy problem for 2-D and 3-D heat equation, we give the explicit H\"{o}lder type stability estimates by using weighted energy method. Especially,H\"{o}lder type stability estimate for discrete solutions of the heat equation is obtained through a fully discrete method. The numerical results are presented.

对于二维和三维的热传导方程的非特征Cauchy 问题，我们利用权函数方法，给出了一个显式的H\&{o}lder 型的稳定性估计，特别的，对于二维的非特征Cauchy问题，我们利用充分离散的方法，对二维问题的离散形式同样给出了H\&{o}lder 型的稳定性估计，同时，我们也给出了数值例子来说明我们的估计。

With the frequency and mode shape being regarded as functions of damage parameters, the overdetermined algebraic equations with damage parameters as unknowns can then be constructed by differentiating frequency and mode function on the basis of structure mode finite element formula, the damage parameters of which are obtained via Taylor expansion.

本方法从结构模态有限元算式出发，把频率和振型看作损伤参数的函数，经过泰勒展开获得频率、振型对损伤参数的一阶偏导数，然后构造以损伤参数为未知量的超定线代方程组，求解得到全部损伤参数值。

With the frequency and mode shape being regarded as functions of damage parameters, the overdetermined algebraic equations with damage parameters as unknowns can then be constructed by differentiating frequency and mode function on the basis of structure mode finite element formula, the damage parameters of which are obtained via Taylor expansion. The whole damage parameters can be found via solving the algebraic equations.

本方法从结构模态有限元算式出发，把频率和振型看作损伤参数的函数，经过泰勒展开获得频率、振型对损伤参数的一阶偏导数，然后构造以损伤参数为未知量的超定线代方程组，求解得到全部损伤参数值。

Based on Born approximationmethod and the local principles of wave function in inhomogeneous medium and theray theory and the integral equation theory,this dissertation researches the theory andsimulation of the inversion method of large perturbational medium parameters andbreaks through the approximation condition of the small perturbational parametersand the weak scattering in traditional inversion method.

本文在Born近似方法的基础之上，基于非均匀介质中波函数局部理论和射线理论及积分方程等理论方法，对大扰动参数反演方法的理论和数值模拟进行了研究，突破了传统反演方法要求的参数小扰动和弱散射条件。

Based on numerical modeling results of influencing factor, multifactor retrogressive method has been established, according to which a function related to water contamination and recovery extent at each stage of five characteristic points has been established.

结合影响因素数值模拟结果，建立了多因素回归方法，确定了5个特征点的含水和阶段采出程度与多影响因素的函数关系。

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。