变形椭球

This project studies the scale-dependent deformation behavior of the metal matrix composite, the void nucleation and void growth mechanisms at the micron/submicron scale. The main results are:(1) In prophase, growth and coalescence of the void embedded in the graded matrix are analyzed in detailed;(2) Based on the infinite solid model containing a micro-void, coupling effects of the void shape and the void size on the void growth are studied carefully, the results show that it seems to exist a critical equivalent void radius, which is associated with the material length. When radius of a microvoid is close to or smaller than the critical void radius, the micro-void growth rate is essentially eliminated;(3) The coupling effects of the particle shape and size on the mesoscopic stress fields within the particle and matrix are also investigated by introducing the conception of inclusion/matrix interfacial energy. The results show that the stress concentration factors within the particle and on the matrix/particle interface are also strongly size-dependent,so the void nucleation mechanism is size-dependent.(4) By employing a specific orthogonal curve coordinate frame and a 'kernel function' conception, a 'unified method'solving the spheriodal and spherical void problems is suggested; by this unified method, size-dependent plastic potentials of the porous materials containing the spheriodal or spherical voids are obtained, which extend the traditional Gurson model for the spherical void and GLD model for the spheriodal voids to the micron scale.(5) Based on the RVE model containing the spheriodal or spherical particles, the influences of the particle shape and size on the size-dependent mechanical behavior of metal matrix composite are studied.

中文摘要：本项目对金属基复合材料在微细观尺度下的尺度相关变形行为、孔洞形核及长大的机理和模型进行了研究，取得了如下主要结果：1）在前期研究中，探讨了基体的梯度分布对孔洞长大和聚合的影响；2）基于含孔洞的无限大体模型，探讨了孔洞形状和孔洞尺寸对其长大的耦合作用，结果表明：可能存在一个与材料特征长度相关的临界孔洞尺寸，当椭球孔洞的等效半径小于临界孔洞半径时，孔洞的长大受到明显抑制；3）通过引入基体/夹杂界面能的概念，分析了夹杂尺寸、夹杂形状对材料细观应力场的耦合影响，结果表明：颗粒内部和界面上的应力集中因子强烈地依赖于夹杂的尺寸和形状，因此，孔洞的形核机理是尺寸相关的；4）采用一种特殊的正交曲线坐标系和引入"核函数"的概念，"统一"地得到了含椭球和球形孔洞的材料的尺寸相关塑性势，它将传统的Gurson球形孔洞模型和GLD椭球孔洞模型推广到微尺度范围；5）基于含椭球和球形夹杂的体胞模型，初步研究了夹杂形状、夹杂尺寸对金属基复合材料尺寸相关力学行为的影响。

During the progressive uniform deformation, the deformation of the IMP ellipsoid is coincident with that of the structural object. They both follow the same deformation rule.

论证了在均匀的递进变形过程中，构造标志体惯量投影椭球的变形与其自身的变形保持一致，两者遵循同样的均匀变形方程。

Based on weld finite element analysis software SYSWeld, the outer shells on air diffuser of an aeroengine augmentor was modelled.

基于焊接有限元分析软件SYSWeld，建立了某型号航空发动机加力燃烧室扩散器外壁的有限元模型，采用双椭球热源模型，模拟了其环缝电弧焊接的过程，得到了焊接温度场、应力场及焊后变形分布的结果并对其进行了定性分析。

The shape of a real 2p orbital is two separated, distorted ellipsoids.

实2p轨道的形状是两个分开的变形的椭球。

This paper discusses the significance of a new tool, the Inertia Moment Projection ellipsoid, for the deformation description and strain analysis of structural objects with arbitrary shape.

本文讨论了一种新的数学工具，即惯量投影椭球，在具有任意形状构造变形体的变形描述与应变分析中的意义。

It has the same characteristics as the finite strain ellipsoid and can substitute for the structural object for strain analysis.

惯量投影椭球具有有限应变椭球相同的性质，可以用来描述任意形状构造标志体的变形，并可以替代具有任意形状构造标志体进行变形分析。

Concept To describe changes in the relative configuration of rocks, imagine that there is a unit sphere, 1 in radius, in the rock before it is deformed. When the rock is deformed homogeneously, the sphere becomes an ellipsoid. Then this ellipsoid is called strain ellipsoid, whose shape and orientationrepresents the rock's strain condition.

概念 为了形象地描述岩石的应变形态，设想在变形前岩石内有一个半径为1的单位球体、平均变形后成为一个椭球，以这个椭球形态和方位表示岩石应变状态这个椭球称应变椭球。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。