有限元法

Objective: To present a good procedure to generate a three-dimensional finite element model of a mandible with dental implant inserted for biomechanics researches.

有限元分析研究的基础是建立适宜的有限元模型，理想的试验模型是准确计算和分析的基础，是有限元法使用的关键。

This method overcome the problems of many supposition conditions in theory and difficulty in searching critical slip surface in 3D limiting equilibrium analysis; It uses the 3D FEM\'s stress field directly, differs from the practical value of 3D FEM strength reduction method used hypothesized load, and differs from the characteristic of the FEM with limiting equilibrium theory still to need to divide the columniation, and suppose the critical slip surface in advance.

该方法克服了三维极限平衡分析方法在理论上引入较多假设条件，且搜索临界滑裂面困难的问题；它直接采用三维有限元应力场，不同于三维有限元强度折减法基于虚拟荷载上得出的实用价值；同时异于沿用极限平衡理论的有限元法仍需要进行条柱划分，并事先假设滑裂面形状及位置的缺点。

Sobolev equation is widely used in many areas, such as hydromechanics, thermodynamics and so on.

中文摘要： Sobolev方程是在流体力学，热力学等领域应用广泛的一类方程，其有限元数值方法研究已有很多工作，如[5]中提出了位移有限元法，[9]中建立了特征混合元方法，[7]提出了H1-Galerkin混合有限元方法，[10]中提出了最小二乘混合元方法。

Firstly, the article expatiates the concept of fuzzy reliability and the relation between random and fuzzy. It presents a list of random-finite element formula that is suitable for the reliability analysis for mechanical rigid frame system. Secondly, it presents two arrangements' reliability analysis methods that fit for component and fabric system. Finally, according to the characteristic of engineering mechanical, the article first brings forward half random-half fuzzy"stress-intensity intermeddle model"for mechanical intensity analysis, and according to Gerber equation for weariness intensity calculation, the article presents fuzzy number's calculating principle and the fuzzy reliability analysis method for engineering structure weariness intensity.

首先阐述了模糊可靠性概念、随机性与模糊性的关系；在导出摄动随机有限元法随机变量的变分原理、随机有限元控制方程和递归方程组基础上，给出了适合于工程机械刚架系统可靠性分析的随机有限元列式；给出了构件和结构体系两个层次的可靠性分析方法；根据工程机械的特点，首次提出机械强度分析的半随机半模糊"应力-强度干涉模型"，并依据疲劳强度计算的Gerber方程，给出了模糊强度的模糊数运算法则及工程结构疲劳强度模糊可靠性分析计算方法，该方法具有简便实用的特点和普遍意义。

Many methods, including difference methods,collocation methods and standard finite element methods for singular parabolic equations have been proposed and analyzed ,and some good results have been obtained.

但利用非标准有限元方法，对奇异微分方程进行研究的文章迄今很少见到。时空有限元法将时间和空间两个变量统一起来，在时间和空间两个方向上同时发挥有限元的优势，实现时间和空间两个方向的高精度。

Based on the theory of finite element method and modal analysis, the model of a piano soundboard is established in the ANSYS, then the models' natural frequency, mode shape are calculated. What is more, the influence of tree species on the piano soundboard's fundamental frequency is discussed.

基于有限元法和模态分析的基本理论，利用有限元分析软件ANSYS建立了钢琴音板的有限元模型，然后对钢琴音板进行模态分析，得到了它们的固有频率、模态振型等参数，分析了树种对于钢琴音板基频的影响。

In this paper, the space-time finite element theory and its application technologies are studied and discussed. Furthermore the space-time finite element method is used to analyze the transient characteristics of electromagnetism equipments. The work is important to develop the numerical method for the transient electromagnetic field. The detailed work is as follow.In the basis theory of finite element method used in the transient engineering problem, the functional theory and the finite element theory are applied to studied the existence condition of a generalized variation principle, which is the basis of the space-time finite element method.

本文在完善时空有限元法的基础理论和应用技术并将该方法应用于解决电磁装置的瞬态过程分析等相关方面进行了深入的研究与探讨，该工作对于发展瞬变电磁场问题的数值计算方法具有重要的意义，为此进行了如下几方面的工作：在工程瞬变问题的有限元方法的基础理论方面，本文应用泛函理论和有限元理论，系统讨论了一般工程瞬变问题的变分定理的存在条件及对应的变分定理。

In this paper, the research object is the XM18 spherical generator, in order to improve the dynamic behavior of the machine tool, the following aspects have been studied in this thesis: Firstly, based on the elasticity theory and finite element analysis theory, the finite element models of the lathe bed, dovetail, dovetail shelf, headstock, fanlike plank and millhead shelf, which were the main parts of the spherical generator, were built up using ANSYS9.0. And based on the modal analysis theory and FEM technology, the free modal and the constrained modal analysis of the main parts were studied. Accordance to the analytical results, put forword methods to optimize the key parts.

本课题以XM18球面铣磨机为研究对象，为了提高其动态特性，本文主要从以下几个方面进行研究：首先，根据弹性力学理论和有限元分析的基本理论，利用ANSYS9.0软件建立了铣磨机的主要零部件床身、燕尾、燕尾座、主轴箱、扇形板和磨头座的有限元模型，利用有限元法对主要零部件进行了自由模态和约束模态分析，并根据分析结果对关键部件提出了改进方案。

The present study also shows its possible and promising extension to threedimensional FEMOL and to two- and three-dimensional FEM.

而且在得出超收敛的应力和位移后，可进一步进行有限元法和有限元线法的误差估计和自适应求解。

This paper reviews and summarizes the progress in this field as follows: the mathematical model and the difficulty of the analytical solutions is introduced; discusses the latest progress of the numerical solutions is discussed; the finite difference method, the Godunov method, the Boltzmann method, and the KFVS method of one-dimensional dam-break problem are introduced; the TVD method, the discontinuous finite element method, the finite volume method and characteristic method of two-dimensional dam-break problem are discussed; the applicability, the advantage and the disadvantage of each method are analyzed; and the progress in the numerical calculations of flow of fluid with free surface are presented.

回顾和总结了国内外对溃坝水流演进问题的研究进展：介绍了溃坝水流的数学模型及解析解法存在的困难，进而讨论了数值解法的最新进展；论述了求解溃坝水流一维问题的有限差分法、近似黎曼解的Godunov格式法、Boltzmann法、KFVS法和二维问题的TVD格式法、间断有限元法、有限体积法、特征线法，并分析了各种方法的适用范围和优缺点，及讨论了限制函数的使用；介绍了利用自由水面追踪方法计算溃坝水流的研究进展，并根据目前存在的不足和实际工程的需要，提出了进一步研究的方向和发展趋势。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。