有限元法

The high-frequency response characters of a simple-supported beam is obtained by NASTRAN.The result is strongly influenced by the mesh size.The comparison based on FEM,SEA and the closed form solution reveals the effectiveness of SEA in the prediction of high-frequency response.

利用NASTRAN软件得到一简支梁从低频到高频的频响特性，研究了不同有限元网格划分对结构高频特性的影响，并通过SEA法、有法元法以及解析解的对比揭示了SEA法在高频响应预示中的有效性。

Based on the basic theoryof non linear finite element, the author of the paper set up the double non linearfinite element equation based on the updated Lagrangefor mutations forthe 8-node degenerate shell element and considering the nonlinear of geometryand the nonlinear of materials.

本文根据非线性有限元的基本理论，采用基于修正的拉格朗日法描述的八节点超参数壳体单元，考虑几何非线性和材料非线性，推导建立了双重非线性有限元方程，结合混合强化本构关系，编制了非线性有限元计算程序。

E. new extrapolation value s of finite element solutions on the first two level grids are used to provide the good initial value s on the third level grids and then an exacter finite element solution can be obtained by several CG-iterations.

摘要提出一种求解大规模有限元方程组的新外推多网格法，即用前两层网格上有限元的新外推值提供第3层细网格上的好初值，然后用几次CG-迭代能得到较准确的有限元解。

In chapter 2, a finite element model for the composite sandwich plates is developed, based on the Zig-Zag deformation assumption and the first order shear deformation theory, and the finite element buckling analysis governing equations for the plates under mechanical, thermal and/or thermal-mechanical mixed loads are deduced respectively. By Von-Karman nonlinear deformation relations and Total Lagrange formulation, an incremental governing equation for postbuckling analysis is established and a corresponding effective computational scheme is presented..

第二章首先建立了基于Zig-Zag截面变形假定和Mindlin一阶剪切理论的夹层板有限元分析模型，分别推导了夹层板机械力、热载和热—机械力耦合屈曲分析的有限元列式和相应的屈曲前以及屈曲临界状态的平衡方程，基于Von-Karman大挠度理论，采用增量形式的全局lagrangian法推导了复合材料夹层板增量形式的几何非线性有限元离散平衡方程，给出了一种有效的非线性平衡方程的迭代求解格式。

Based on the inverse mapping with linear deformation, the geometric mapping was used to carry out the second element transformation in order to avoid the abnormality of the stiffness matrix and to improve the stability and the convergence of the numerical calculations.

在现有线性变形逆向映射法的基础上，采用几何映射法计算变换单元，避免单元刚度矩阵出现畸形，提高钣金展开有限元逆算法的稳定性和收敛速度，对几何映射法与投影法所计算的变换单元进行了对比，数值计算结果表明用几何映射法计算的初始估算展开料形状更接近于最终的钣金件展开形状。

Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.

其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。

The primary studying works and characteristics:1 To summarize reinforcing theory of cement mixing pile composite foundation2 To analyze the primary mechanics characters and changing rules of cement mixing pile, based on analysis of test data both indoor and outdoor.3 To discuss siding frictional resistance, ending resistance, ultimate bearing capacity of simple mixing pile and effectiveness factor of grouped piles, loading ratio of soil between piles under cushion cap of grouped piles and stress ratio of pile and soil and so on, and use many computation method and experimentation method to ensure bearing capacity of mixing piles composite foundation.4 To point out and analyze eight sides flaws and problems of the bearing capacity calculation method of mixing pile compositefoundation which ensured by national and normative method/ formula.5 To apply test results of loading tests and a few settlement observation data, use gray theory to predicate ultimate bearing capacity of deep mixing piles, actual example demonstrate engaging between theoretical predicted value and actual value.6 To apply groovy layerwise summation method to discuss entity piles method, double foundation method, equivalent layerwise summation method and consolidation theoretical method and so on, especially by combination of engineering example, use FEM to calculate or discuss the settlement and changing rules of composite foundation.7 To discuss problems of critical length of composite foundation by combination of engineering example and numerical analysis method, and analyze the contrast of critical length between simple pile load and most area load of composite foundation, not only critical length of composite foundation is relative to modulus ratio between piles and soil, but also upside load distribution area of composite foundation.

主要的研究工作与特色为：(1)总结了水泥搅拌桩复合地基的加固原理；(2)在对室内外试验资料进行统计分析的基础上，系统分析了搅拌桩水泥土的主要力学特性及其变化规律；(3)探讨了搅拌单桩的侧摩阻力、端阻力、极限承载力及群桩效率系数、群桩承台下桩间土荷载分担比及桩土应力比等，提出用多种计算方法并结合试验方法来综合确定搅拌桩复合地基的承载力；(4)明确指出和分析了按国家有关规范的方法确定搅拌桩复合地基承载力所存在的八个方面的缺陷与问题；(5)利用过去没有加载至破坏阶段的载荷试验成果和较少的沉降观测数据，尝试了用灰色理论预测深层搅拌桩的极限承载力，实例表明理论预测值与实测值吻合较好；(6)在常规分层总和法的基础上，探讨了复合地基沉降计算的实体墩基法、双层地基法、等效作用分层总和法、固结理论法等，特别是结合工程实例，用有限元数值计算等方法计算和讨论了搅拌桩复合地基的沉降及其变化规律；(7)结合工程实例，用数值分析方法探讨了复合地基临界桩长的问题，指出和分析了单桩荷载下的临界桩长与复合地基大面积荷载下的临界桩长存在很大的差别，复合地基的临界桩长不仅与桩土模量比有关，而且与复合地基上部荷载分布面积有关。

This article analyses the application conditions of freezing method, current research status and the problems in this field. It points that it's necessary to study deep freezing temperature field deeply and discusses the factors which influence the freezing wall such as soil's nature, moisture content, geological conditions, etc. It introduces the theory, process of freezing method, the distribution of temperature field of freezing method and key thermotics parameters influencing freezing temperature field. It simplifies the deep freezing temperature field model. Through ANSYS, this article founds the deep freezing temperature field model, and simulates the field on vary heat conductivities. It analyzes the results of ANSYS simulation, gains the theoretical value of thermometric holes which is needed by back-analysis. Using the simulation temperature and actual value, it gets the equivalent heat conductivity. Then it solves the deep freezing temperature field by the equivalent value, simulates the freezing wall development process and temperature change curve. Against the actual project, the results are favorable.

文中分析了冻结法施工的应用条件，目前对冻结法施工的研究现状和在此领域内存在的问题，指出了对深土冻结温度场进行深入研究分析的必要性；对影响冻结壁形成发展的因素如冻土土性、含水量、地质条件及施工方法等因素进行了论述；对冻结法施工的原理、过程，冻结法温度场的分布情况，影响冻结温度场分布的主要热学参数进行了综述；对深土冻土温度场模型进行了合理的简化，通过ANSYS大型有限元分析软件，建立了深土冻结温度场的模型，对不同导热系数情况下的深土冻结温度场进行了模拟；对ANSYS的模拟结果进行了定性的分析，通过对ANSYS结果的后处理取得了反分析时需要用到的测温孔理论温度值；经过对测温孔模拟温度值和实测温度值的分析，得到了冻结温度场的等效导热系数；使用等效导热系数对深土冻结温度场进行了求解，模拟了冻结壁发展情况和温度场中的温度变化曲线，用所得结果对比工程实际情况，取得了较好的效果。

In this dissertation, first, based on theory of cutting tooth about the gleason spiral bevel gear, the equation of meshing in the process of cutting tooth, the surface equation of generating gear as well as the general tooth surface equation of the double circular arc spiral bevel gear, using GB12759-1991 type of double circular arc gear as a basic gear profile, a three-dimension solid model of double circular arc spiral bevel gear which has the good adaptability was carried out by used of Unigraphics software;Second, by researching of the algorithm about contact and collision as well as various contact types based upon Contacting Finite Element Method, a foundation was laid for selecting the contact type in analyzing contact stress of double circular arc spiral bevel gearing;Finally, through the connection port of PARASOLID between UG software and ANSYS/LS-DYNA software, the three-dimension solid model of double circular arc spiral bevel gearing obtained above in UG was imported into ANSYS/LS-DYNA, a finite element analyzing about contact stress of double circular arc spiral bevel gearing was carried out by applying new loading method.

本文首先基于格利森弧齿锥齿轮加工原理及切齿啮合过程中的啮合方程、产形轮齿面方程以及双圆弧弧齿锥齿轮的齿面方程，选用GB12759-1991型双圆弧齿轮基本齿廓为基准齿形，利用Unigraphics软件的建模功能，绘制了有较好适应性的双圆弧弧齿锥齿轮传动三维实体模型。其次，描述了应用有限单元法进行实体接触与碰撞问题算法的公式，研究了有限元分析中的各种接触类型以及双圆弧弧齿锥齿轮接触应力分析中所选择接触类型的依据。最后，通过UG软件和ANSYS/LS-DYNA之间的PARASOLID接口工具包，将UG软件中得到的啮合齿轮模型导入ANSYS/LS-DYNA有限元分析软件，给出一种新的加载方法，进行了双圆弧弧齿锥齿轮传动的接触应力的有限元分析。

Aim at the false-solutions(the meaning is the solutions do not satisfy the divergence theorem) of FEM, impose the magnetic divergence conditions

针对有限元数值解中存在的伪解问题(即求出的解不满足相应的散度条件)，推导出了强加散度条件的磁场有限元系数矩阵的表达式，本文混合法中的有限元系数矩阵即是在此基础上形成的。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。