Short-and resonant-range interactions between scales in turbulence and their applications

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the shortrange viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation ( LES ) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.     

One-dimensional consolidation of layered soils with impeded boundaries under time-dependent loadings

On the basis of Terzaghi‘s one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under timedependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method, the results from the method illustrated are more accurate.     

Torsional impact response of a penny-shaped crack in a functional graded strip

The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived. And it is shown that, as crack driving force, they are equivalent for the present crack problem. Investigated are the effects of material nonhomogeneity and strip‘s highness on the dynamic fracture behavior.Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the dynamic behavior varies little with the adjusting of the strip‘ s highness.     

横观各向同性含液饱和多孔介质中应力波传播的特征分析

根据广义特征理论,对横观各向同性含液饱和多孔介质中应力波传播特性进行了特征分析．给出了特征曲面的微分方程以及沿次特征线的相容条件,得到了波阵面的解析表达式．详细地讨论了应力波在横观各向同性含液饱和多孔介质中传播时,其速度曲面和波阵面的形状及性质．分析结果亦表明,纯固体中应力波传播的特征方程,是含液饱和多孔介质中应力波特征方程的特例．     

固体介质中力学参数传递观念及其工程应用

通过定性的力学分析、原理性的模型试验、工程动载试验、数值计算分析4个方面的研究,论述了在地层介质中应力、加速度的传递与介质的相对刚度密切相关,提出固体介质中应力、加速度传递的观念,及其相应的广义复合结构体系;在地下工程、防护工程建设中,若能正确的运用这种观念,就能大幅度提高工程的生存能力．     

单轴拉伸条件下细观非均匀性岩石损伤局部化和应力应变关系分析

岩石在拉应力状态下的力学特性不同于压应力状态下的力学特性．利用细观力学理论研究了细观非均匀性岩石拉伸应力应变关系包括:线弹性阶段、非线性强化阶段、应力降阶段、应变软化阶段.模型考虑了微裂纹方位角为Weibull分布和微裂纹长度的分布密度函数为Rayleigh函数时对损伤局部化和应力应变关系的影响,分析了产生应力降和应变软化的主要原因是损伤和变形局部化.通过和实验成果对比分析验证了模型的正确性和有效性．     

湍流不同尺度间的近程和共振作用规律及应用

从Navier-Stokes方程出发,研究了湍流不同尺度间的相互作用规律,给出相近尺度间近程粘性应力的积分和微分表达式．引入极相近尺度之间共振相互作用的概念,得到共振粘性应力的微分表达式．利用共振粘性应力张量获得不含经验关系和常数、近似封闭的大涡模拟（LES）方程组．利用近程和共振粘性应力张量获得不含经验关系和常数、近似封闭的湍流多尺度方程组．讨论了湍流多尺度方程的性质及用于湍流计算的优点,尺度间相互作用的近程特性说明:多尺度模拟是湍流计算很有价值的方法,并列举了算例．     

双材料界面裂纹平面问题的半权函数法

应用半权函数法求解双材料界面裂纹的平面问题．由平衡方程、应力应变关系、界面的连续条件以及裂纹面零应力条件推导出裂尖的位移和应力场,其特征值为lambda及其共轭．设置特征值为lambda的虚拟位移和应力场,即界面裂纹的半权函数A·D2由功的互等定理得到应力强度因子KⅠ和KⅡ以半权函数与绕裂尖围道上参考位移和应力积分关系的表达式．数值算例体现了半权函数法精度可靠、计算简便的特点．     

应用离散偶应力单元分析弹性Cosserat介质

讨论了平面弹性偶应力问题的有限元方法,提出了离散偶应力单元的理论和构造方法,其特点是独立假设单元的位移和微观转角,偶应力理论中微观转角和宏观转角相等的假设在单元中以离散形式强加.该类单元列式简单,易于编程,且有满意的精度.并构造了一个三角形九自由度离散偶应力单元DCT9(discrete Coss-erat triangular).数值结果表明该单元能够较好地描述Cosserat介质的力学性质.     

颗粒Reynolds正应力轨道模型及后台阶两相流动数值模拟

用随机过程理论建立气固两相耦合脉动量Lagrange方程,并建立了气固两相流随机颗粒轨道模型中颗粒Reynolds正应力的Lagrange方程.将新的模型运用于各向同性的湍流衰减的流场中,模拟颗粒的湍流扩散特性,与文[1]中的模型和实验结果作比较,并使用新模型模拟了后台阶两相流动.