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The numerical results show the advantage of the method.
      
The numerical results show the advantages of such method.
      
Global convergence and locally quadratic convergence are obtained,and numerical results are given.
      
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Utilizing analysis of similarity (ANOSIM) on the ten pharmaceutical descriptors provides a discrete numerical result that indicates overall dissimilarity among these agents.
      
The asymptotic solution is compared with the numerical result, and the range of applicability of the asymptotic equations is established.
      
Representative numerical result is given for effective isotropic radiated power contour-plot of the western zone coverage of Chinese territory by the 7-element array illumination.
      
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The binary cavitating flow field distribution obtained from digital processing of the original cavitation image showed a good agreement with the numerical result.
      
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In this paper, formulas for the calculation of the elastic-plactic stress field near a crack with blunt tip under the conditions of plane stress and plane strain are derived. These formulas are obtained from the exact solution of the elastic stress field of an elliptic crack. In Irwin's Theory, when yielding happens in the region direct near the sharp crack tip, in order to satisfy the equilibrium condition the stress field must be relaxed by moving the elastic zone near the tip with the shape of the original...

In this paper, formulas for the calculation of the elastic-plactic stress field near a crack with blunt tip under the conditions of plane stress and plane strain are derived. These formulas are obtained from the exact solution of the elastic stress field of an elliptic crack. In Irwin's Theory, when yielding happens in the region direct near the sharp crack tip, in order to satisfy the equilibrium condition the stress field must be relaxed by moving the elastic zone near the tip with the shape of the original elastic stress field remaining unchanged. Irwin has also assumed that during the parallel motion of the elastic stress field, the stress intensity factor K maintains constant. In this paper, the assumption of SIF K maintaining constant is discarded, and the analytical results thus obtained are more restrict than that of the Irwin's Theory. Though the calculating formulas in this paper rather complex, yet numerical results will be easily obtained by using high speed computer. The analytical results show that for the case of plane stress the outcomes of the two theories are quite different, while for the case of plane strain they are quite near. When using the analytical method proposed by this paper, how the blunting effect of the crick tip affects the small scale yielding stress field during the increasing of the load can be considered. Besides, bow the shape of the elastic-plastic zone near the tip is affectd by different loading conditions can also be considered. All these discussions and analytical results mentioned above will be hardly obtained by Irwin' sor others' theories.

本文从钝角裂纹应力场的精确解出发,分析了Irwin理论在用平移法计算小范围屈服应力场中的近似性和精确程度,得出了计算钝角裂纹的平面应力和平面应变的弹塑性应力场的公式。在本文中放弃了Irwin理论认为应力强度因子K1在应力场中是一个常量的假定,而是采用了广义应力强度因子KIg理论的概念[1],认为在裂纹应力场中各点的KIg是一个多变量函数。这样所获得的结果,在理论上将比Irwin理论严格。虽然本文的计算公式要比 Irwin理论复杂得多,但是在运用电子计算机之后就容易获得数值结果。本文的计算结果表明,在平面应力情况下两种理论的结果有较大的差别,而平而应变的结果则比较接近。但是,运用本文的方法可以考虑裂纹在钝化过程中的应力场的变化规律,同时也可以考虑不同的载荷条件(例如,孔内受均压张开和双向均匀拉伸)在尖角裂纹的钝化过程中对于塑性区的形状和大小的影响。所有这些分析用奇性解理论是难以做到的。

Various influence factors of solid boundaries on discontinuuties in the gas molecular distribution function are considered and a bimodal two-stream relaxing distribution is suggested. In applying it to the heat conduction problem between two parallel plates by Maxwell transport equation we obtained a closed solution. According to the theory suggested in this paper, in the linear case, the calculated heat transfer is close to that given by existing theory. In the nonlinear case (when the temperature ratio of...

Various influence factors of solid boundaries on discontinuuties in the gas molecular distribution function are considered and a bimodal two-stream relaxing distribution is suggested. In applying it to the heat conduction problem between two parallel plates by Maxwell transport equation we obtained a closed solution. According to the theory suggested in this paper, in the linear case, the calculated heat transfer is close to that given by existing theory. In the nonlinear case (when the temperature ratio of two plates is equal to four), the difference between Willis precise numerical results and ours is less than 2.5%. This is an obvious improvement as compared with the Liu-Lees theory. Furthermore, temperature calculations demonstrate the existence of a Knudsen layer.

分析了固体边界对分子分布函数不连续性的各种影响因素;提出了双峰二向流弛豫分布,将它应用于麦克斯韦输运方程以研究二平行平板间的热传导,得到了封闭解.根据本文提出的理论,在线性情况,计算得到的热流值与现有的理论结果相近;在非线性情况(两壁温度比为4),与Willis的精确数值结果相差小于2.5%.这与具有代表性的Liu-Lees的理论结果相比有较大改进.此外,温度分布计算显示出了Knudsen层的存在.

This paper deals with the motion of viscous liquid column with finite length and two free surfaces in a vertical straight capillary tube. It is assumed that the fluid is Newtonian. Linearizing the boundary conditions, analytic expressions in the form of infinite series have been obtained for velocity, pressure and free surface at low Reynolds number. The numerical calculation is carried out for a set of the cylinder's length of water and blood. It has been revealed that there are considerable circulating currents...

This paper deals with the motion of viscous liquid column with finite length and two free surfaces in a vertical straight capillary tube. It is assumed that the fluid is Newtonian. Linearizing the boundary conditions, analytic expressions in the form of infinite series have been obtained for velocity, pressure and free surface at low Reynolds number. The numerical calculation is carried out for a set of the cylinder's length of water and blood. It has been revealed that there are considerable circulating currents at the upper and lower meniscuses. Its maximum velocity is about 57% of the average velocity of the mainstream. Inertial effect is also studied in this paper. Using the time-dependent method in finite-difference techniques, numerical solutions of the corresponding nonlinear equation at Re-24.5 are computed. Comparing it with the analytic exact solutioa at low Reynolds number shows that inertia! effect is negligible providing Re<24.5

本文考虑了竖直毛细管中具有两个自由面的有限长液柱的粘性流体运动.假设流体是牛顿的对边界条件进行线性化后,得到了小雷诺数情形下速度、压力和自由面形状的级数形式的分析表达式,对水和血液在多种液柱长度下求出了数值结果.分析表明在上下弯月面处有强回流.最大回流速度可达主流平均速度57%左右此外,本文还研究了惯性效应.采用时间相关的有限差分法求出了R_e=24.5时非线性方程的数值解.将此数值解和小雷诺数时的分析解进行比较表明,当R_e≤24.5时惯性效应不大.

 
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