计算单元

The coordinate transformation and numerical integration was executed on the discretized tetrahedral elements based on which the 3-D MT vector-finite element method was implemented. A whole computation framework for 3-D vector-finite element method with unstructured mesh was given. Based on this some typical models were tested which has demonstrated that our algorithm could distinctively avoid problems caused by the fake solution and both the accuracy and efficiency were enhanced which made our algorithm has a bright future for further application.3. According to theory of Sobolev vector space and the discretization of Helmholtz space, the error estimate which was suitable for 3-D MT vector-finite element modeling was deduced by which the procedure of adaptive technique was guaranteed.4. Based on the fully unstructured tetrahedralization and optical strategy, the 3-D magnetotelluric h-adaptive vector-finite element method was presented through combining the error estimate. With this work, the accuracy and creditableness for 3-D MT complicatedly modeling was guaranteed.5. The 3-D magnetotelluric h-adaptive vector-finite element algorithm with unstructured mesh was implemented.

针对非结构化的四面体单元，采用坐标变换和数值积分方法，实现了MT三维矢量有限单元分析，建立起基于非结构化网格的三维MT矢量有限元计算流程，并对典型模型和国际标准电磁模型进行了数值模拟，结果对比和分析表明，基于非结构化网格的三维MT矢量有限元不仅消除了节点型有限元的伪解，而且具有很高的计算精度和速度，有广阔的应用前景。3、根据Sobolev函数的向量空间和Hemlholtz空间的分解，推导出基于残差的三维大地电磁矢量有限元后验误差估计公式，为三维大地电磁自适应矢量有限元数值模拟的实现奠定了基础。4、在完全非结构化四面体单元剖分及优化基础上，结合三维大地电磁矢量有限元后验误差估计公式，提出了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算策略，保证了对复杂大地电磁模型数值计算的精度和可靠性。5、实现了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算流程，对典型模型和国际标准电磁模型进行了数值模拟。

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。

Firstly, the 3D solid model of the analyzed object is built directly in the FEM software ANSYS 8.0 without using other CAD software. The influence of the side sizes of solid elements on computing results and the influence of coupling ways between different parts on the modal parameters are researched by simply modeling. And a new connecting method about joints in ANSYS is proposed and applied to finite element modeling of the test-bed for spindle system. Furthermore, several different computing techniques for modal parameters extraction are compared in solving the finite element model of spindle system test-bed. Many modal solutions are also done to achieve the relationships between the whole or part stiffness value and computed modal parameters. The laws about joint rigid parameters" influences on modal parameters are discussed by means of altering their values for conjoint parts. And by changing local rigid parameter values, the different location selections" influence on computed modal parameters is also studied.

本文通过使用ANSYS 8.0软件直接建立研究对象的实体结构模型，而没有借助其他的CAD软件；通过构建简单的模型研究实体单元边长大小对计算结果的影响，部件之间不同的联结方式对模态参数的影响，探讨在ANSYS中实现结合部的方法，提出一种新的联结方法，并建立主轴系统试验台的有限元模型；对建立的主轴系统试验台有限元模型求解，比较几种不同模态提取方法；通过改变结合部联结单元的刚度参数进行的计算，寻找联结刚度对模态参数变化的影响规律；改变局部联结单元的刚度参数，研究刚度值位置差异对计算模态参数的影响。

First mostly contraposing hull deck structure it goes along FEA analysis, discuss the different influence degree of calculational results between the different simplifications of the mathematical model, thereinto mostly analyse five different simplifications of the deck model; Second contraposing hold section and hull deck structure it goes along FEA analysis together, discuss the different influence degree of calculational results between the different elements style, gridding number and gridding density, thereinto mostly analyse the difference between adopting 8 node shell element and 4 node shell element, nondense gridding and thick gridding, and numerous gridding number and few gridding number, In the end mostly contraposing hold section structure it goes along FEA analysis, discuss the different influence degree of calculational results between the different boundary conditions, thereinto mostly analyse the difference between adopting CCS boundary conditions and LR boundary conditions.

首先主要针对船体甲板结构进行分析研究，讨论结构简化不同对有限元计算结果的影响程度，其中主要研究分析了五种不同甲板结构简化模型；紧接着针对舱段与甲板结构一起进行分析研究，讨论单元类型，网格数量与密度的不同对有限元计算结果的影响程度，其中主要研究分析了分别采用8节点板壳单元与4节点板壳单元的不同，以及分别采用疏的网格与密的网格，多的网格数量与少的网格数量的计算结果的差异。最后主要针对舱段模型进行分析研究，讨论不同的边界条件对有限元计算结果的影响程度，其中主要研究分析了分别采用CCS舱段边界条件与LR舱段边界条件进行有限元计算而带来的结果上的差异。本文第二部分为港工建筑物中的大直径薄壁圆筒结构的有限元比较分析。在研究大圆筒的有限元比较分析中，主要讨论用不同的网格密度与数量来划分网格引起的差异。其中用了网格密，数量多与网格疏，数量少两种模型进行大圆筒结构的有限元分析对比

In chapter 4,on the basis of chapter 3,a new formulation of hybrid/mixedsingular plate element based on Reissner's plate theory is set up,and 4-node arbitraryquadrilateral hybrid/mixed singular bending plate element formulas including theeffects of transverse shear deformation is derived,then by the use of this method,alarge quantity of numerical computations are carried out,at the same time,the resultsare compared with theoretical solutions and the results obtained by other singularfinite element methods.

第四章 在第三章的基础之上，建立基于Reissner型板理论之上的杂交/混合奇异板单元列式，推导出了考虑剪切效应的四节点任意四边形杂交/混合奇异弯曲板单元公式，并进行了大量的数值计算，同时与理论解析解和其它有限元解进行了比较，计算结果表明：本文提出的杂交/混合奇异板单元方法是可以用于计算含裂纹平板弯曲应力强度因子的一种高效、可靠、简便易行的方法。

The advantages of this new method are:(1) The field conductivity distribution function is fitter the actual condition than tradition methods:(2) On the condition of triangle elements cut of field, making the calculation speed increase in large degree than tradition methods.

与单元电导率重建算法相比，节点电导率重建算法的优点有：(1)使场域电导率分布函数更符合实际情况，克服了传统算法中对电导率作离散化处理的缺陷；(2)当场域采用三角形单元剖分方式时，在场域的剖分密度保持不变的情况下，可以大大提高重建计算的速度；(3)在场域采用三角形单元剖分方式时，场域的剖分密度可以比以前加大一倍，在不降低重建计算速度的前提下，可以改善重建计算的精度；(4)由于重建的是所有节点的电导率，避免了先前单元电导率重建图像中"阶梯"状边缘和"锯齿"状边缘的出现，明显地改善了图像的视觉效果。

The results of numerical analysis show that the elastic modular and the poisson ratio have no effect on two-dimensional bearing capacity, but can affect the ultimate bearing capacity of three-dimensional foundations and control the convergence and precision of finite element calculation; the earth pressure coefficient controls the geostatic stress of foundation, sequentially affects the ultimate bearing capacity of foundations and the convergence of numerical calculation. When calculating the ultimate bearing capacity of undrained saturated foundation, the complete formulation exists shear locking, and reduce formulation exists hourglassing, so the hybrid formulation is suitable to imitate the geomaterial. When the soil obeys nonrelevent flow rule, the yielding function is different from potential function, and the elastic-plastic matrix of soil is asymmetric, so the unsymmetry numerical solver and appropriate finite element mesh is required.

研究结果表明，土体弹性模量和泊松比对二维基础极限承载力没有影响，但是影响着三维矩形基础的极限承载力，控制着ABAQUS数值算法的计算精度与收敛速度；地基土压力系数控制着地基土体中的地应力平衡，从而影响着二维条形基础和三维矩形基础的极限承载力和地基破坏包络面；对于不排水饱和软黏土地基，常规的完全积分单元会造成剪力自锁现象，而减缩积分单元则存在过于柔化的现象，故采用杂交单元来模拟较合适；当土体服从非关联流动法则时，屈服函数与塑性势函数之间存在差异，从而导致土体弹塑性矩阵呈现非对称性，在有限元计算中必须采用非对称数值解法，并且合理地划分单元才能对极限承载力进行准确求解。

It effectively solves the problem of contact mechanics between burden granules. The dynamic data structure that is a linked list is built to save and delete the varying data in simulation calculation process. Therefore, the distinct element method simulation model of charging bell-less top blast furnace is established in view of the distinct element method model of blast furnace burden granular.

本文首先对离散单元法的基本原理和数值计算方法进行了系统研究，针对高炉炉料颗粒介质特点，对离散单元法进行了相应改进，建立了高炉炉料颗粒运动的离散单元法基本数学模型，推导出了相应的高炉炉料颗粒离散单元法数值计算基本参数的计算公式，例如阻尼、刚度、时步等，并确定了合理的数值模拟参数值。

The effect of joint deformation to truss displacement: 4 kinds of steel tube truss compute models are established making use of shell elements, truss elements, beam elements and combination of beam elements and truss elements.

采用板壳单元、桁架单元、梁单元以及弦杆为梁单元和腹杆为桁架单元的混合模型等四种计算模型分别建立了一个钢管桁架的有限元模型，计算并整理了各模型下桁架腹杆的轴力及各节点的位移。

The inner force of the line element for underground structure have been calculated using the traditional finite element mesh and high-order manifold method to guarantee the numerical precision of the line element and overcome the disadvantages due to the geometry error between the actual position and computational position of the beam and truss element in common use.

用传统的有限元网格和流形方法的高阶覆盖位移函数来进行地下结构的杆、梁单元计算，保证了线单元模拟的数值精度，同时又克服了常用的杆、梁线单元计算位置与实际位置不相符合从而带来计算误差和结构设计不便等缺点，提供了一种解决结构数值计算的较好的途径。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。