不变形的

G. Lekhnitskii and the Hankel integral transformation are used, And thereby a solution of the Stress field and displacement field of an embedded penny-shaped crack lying in a transverely isotropic plane under the action of the uniform tension stress at the far end perpendicular to the crack surface is obtained.

本文利用对于横观各向同性体轴对称变形时应力函数解法的基本方程，并应用Hankel积分变换，求解了位于横观各向同性平面内的埋藏圆片裂纹在垂直于裂纹面远处均匀拉应力作用下的应力场和位移场，获得了与各向同性材料相同的应力强度因子，不同于各向同性材料的应力场和应变能释放率裂。

By anchoring an imaginary spring between each data point and deformable curve or surface, the fairing model is established. Then FEM is used to solve the deformation problem of the model caused by imaginary springs and a bicubic B-spline surface patch is taken as one element. Lastly the B-spline active surface model is applied to surface reconstruction from layer data and the problem resulted from fitting for uneven cross-sectional curves can be solved.

通过在数据点与模型之间连接虚拟弹簧，建立光顺模型，并以双三次B样条曲面片作为单元，运用有限元法对模型在虚拟弹簧作用下的变形问题进行求解，得到光顺后的B样条曲面；并在此基础上，提出了一种新的基于断层数据的表面重建方法，可很好地解决不均匀截面族的曲面生成问题。

It is indicated that the damping of the alloy is induced by phase interface slipping or grain boundary viscous sliding, the infinitesimal plastic deformation which is caused by the difference of elastic modules and heat expansion coefficients between phases of the alloy.

结果表明： ZA27-4%Si合金阻尼随频率增大而减小，随温度升高而增大，阻尼不随应变振幅的变化而变化； ZA27-4%Si合金室温阻尼为5.83×10-3，与ZA27合金阻尼相当； ZA27-4%Si合金的阻尼是由合金内部的晶界和相界面滑动、位错振动以及各相的热膨胀系数和弹性模量间差造成的微塑性变形共同造成的。

This thesis consists of five chapters. At first, We introduce the study history as well as present situation on KKM theory. Secondly, We discuss the invariability of transfer open valued multimap under the restriction of upper and lower semicontinuity on generalized convex spaces. Then, We obtain new KKM type theorems from the classical KKM theorem by applying upper and lower semicontinuity. We also obtain intersection theorems by applying the KKM type theorems for a multimap from a topological space to another topological space. Further, We obtain Ky-Fan type coincidence theorem by applying known variational results on the KKM type theorems. Finally, We give an application to new theorems.

本文共分五章，首先回顾了KKM理论的研究历史和现状，其次讨论了在一般化凸空间上转移开值映射在上、下半连续映射下的不变性，然后在上、下半连续映射下，以古典的KKM定理为基础得到新的KKM型定理，并利用从一个拓扑空间到另一个拓扑空间的集值映射及KKM型定理得到相交定理，进一步利用已知的KKM型定理的变形结论得到Ky-Fan型重叠定理，最后给出新定理的一个应用。

The control principle of electrostatic shaping was introduced according to the balance between electrostatic force and resulting force formed by membrane deformation and the complex shaping process of SMEC. Then, taking the trisection circularity electrode for an example, the distribution characteristic of electric potential in the electrostatic field was analyzed, namely, the expression of potential function in the electrostatic field was deduced by Laplacian equation. And then, by combining the difference equation with electric potential expression, the numerical solutions of electrostatic force in single electrode mode and trisection circularity electrode mode were disposed. Finally, the calculated figure was compared with the ideal paraboloid and comparison shows that more accuracy would be achieved by multi-electrode control.

根据静电力与薄膜变形载荷作用力之间的平衡关系和静电拉伸薄膜反射镜成形的复杂过程，介绍了薄膜反射镜静电成形的控制原理；以三等分环状电极为例，分析了静电场中空间电势分布特性，即从拉普拉斯方程推导出静态场势函数的表达式；然后，利用差分与电势方程结合的方法，对单电极电场力和三等分环状电极电场力进行了数值求解；最后，将计算面形与理想抛物面进行了比较，结果显示，单电极情况下得到的薄膜反射镜面形不是理想抛物面，若采用多电极控制可获得更高的控制精度。

The control principle of electrostatic shaping was introduced according to the balance between electrostatic force and resulting force formed by membrane deformation and the complex shaping process of SMEC. Then, taking the trisection circularity electrode for an example, the distribution characteristic of electric potential in the electrostatic field was analyzed, namely, the expression of potential function in the electrostatic field was deduced by Laplacian equation. And then, by combining the difference equation with electric potential expression, the numerical solutions of electrostatic force in single electrode mode and trisection circularity electrode mode were disposed.

根据静电力与薄膜变形载荷作用力之间的平衡关系和静电拉伸薄膜反射镜成形的复杂过程，介绍了薄膜反射镜静电成形的控制原理；以三等分环状电极为例，分析了静电场中空间电势分布特性，即从拉普拉斯方程推导出静态场势函数的表达式；然后，利用差分与电势方程结合的方法，对单电极电场力和三等分环状电极电场力进行了数值求解；最后，将计算面形与理想抛物面进行了比较，结果显示，单电极情况下得到的薄膜反射镜面形不是理想抛物面，若采用多电极控制可获得更高的控制精度。

The formation of martensite is accomplished by the immigration of well-defined glissile interface (121)fcc type and its misfit dislocations can produce the lattice invariant deformation on the basis of phenomenal theory of martensitic crystallography, however, LID is retarded slightly after the migration of interphase (121)fcc, i.e.a thin plate-like zone exists without LID in martensite near the well-defined interface. When the temperature reduces to the Ms point, the lattice parameter of austenite matrix is √3/2 times that of the martensite without LID. This critical condition for spontaneous transformation agrees with that the stack fault energy in matrix is less than zero according to Olson and Cohen's nucleation model.

通过模型分析表明：fcc/bcc马氏体形核与长大过程是通过(121)fcc型择优界面推移进行的，界面上的错配位错可以完成马氏体晶体学唯象理论要求的点阵不变变形，但LID要稍滞后于界面迁移，即在马氏体形核与长大过程中推移界面新相一侧存在一未发生LID的新相薄区；当相变温度达到马氏体相变点Ms时，母相奥氏体与这一薄区的晶格常数比为√3/2，这一几何条件和Olson-Cohen形核模型中要求扩展位错层错区界面能γ≤0是等价的。

The pattern of camber die-drawing are optimized. The physical innate character of drawing with camber die is analyzed thoroughly. For the first time, the periodical relation between the limit drawing coefficient and the large longitudinal stress in dangerous section is established. Furthermore, the rationale to judge limit deforming degree is developed. Then, the limit drawing coefficient of drawing with camber die is proposed. Based on the criterion that the large stress in flange is smaller than that of limit value, the formula of drawing with camber die without wrinkles is deduced.

对拉深凹模的型式进行了优化；深入地分析了曲面凹模拉深成形的物理本质，首次定量地确定了极限拉深系数与危险断面最大径向应力的关系，提出了判断极限变形程度的依据，分析了极限承载能力，建立了曲面凹模拉深的极限拉深系数的表达式；以凸缘切向最大压应力小于凸缘切向压应力临界值为准则，推导出了曲面凹模拉深不起皱的理论表达式。

For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted.

对可压缩材料，本文首先采用非规则的对数幂级数渐近展开方法，克服了过去研究中存在的中心扇形区变形率协调方程的高次渐近式不能被满足的困难，并得到了一个切向速度在裂尖前方存在间断的高阶渐近解，该解的主项就是目前被广泛接受的关于可压缩材料的尖端场解。

The detailed comparisons between the higher—order near tip solution and the well—known modified Prandtl field are also given in this paper.For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted.

对可压缩材料，本文首先采用非规则的对数幂级数渐近展开方法，克服了过去研究中存在的中心扇形区变形率协调方程的高次渐近式不能被满足的困难，并得到了一个切向速度在裂尖前方存在间断的高阶渐近解，该解的主项就是目前被广泛接受的关于可压缩材料的尖端场解。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。