服从二次曲线型莫尔准则的塑性平面应变滑移线场理论

本文初步建立了服从二次曲线型莫尔准则的塑性平面应变滑移线场理论,它以经典的滑移线场理论作为其特例,它可用于金属加工、岩土力学和构造力学平面应变问题的分析.作为初步应用,用数值解确定了半无限体受刚模压入问题的滑移线场及极限载荷,还确定和分析了斜坡层状介质重力滑动问题的滑移线场.     

基于非关联流动法则的圆形隧洞滑移线解答

圆形隧洞的滑移线方程早在20世纪中期苏联学者已给出解答,并在国内广泛应用．推导过程中假设滑移线与速度矢量方向夹角为45°-φ/2是错误的,理论上滑移线与速度矢量方向的夹角与采用的流动法则有关．该文分别从关联流动法则和非关联流动法则出发,推导了圆形隧洞的滑移线方程和水平方向破裂体深度的表达式．通过与模型试验结果进行对比,对岩土材料应采用基于非关联流动法则的滑移线解答.     

滑移和感应磁场对Johnson-Segalman流体蠕动传输的影响

存在感应磁场和滑移条件下,研究Johnson-Segalman(J-S)流体在平面通道中的蠕动流.通道中的流动认为是对称的,并在剪切应力项中考虑了速度的滑移条件.首先给出问题的数学公式,然后在长波长和低Reynolds数近似下,求解该方程组得到摄动解,确定沿管道截面的压力增量、轴向速度、微转动分量、流函数、磁力函数、轴向感应磁场和电流密度分布公式.导出了小数值Weis-senberg数时解的表达式,分析并勾画出诸流动物理量的有趣变化.     

应变空间中的岩土屈服准则与本构关系

本文从Илъюшин公设出发评述了在应变空间中研究岩土弹塑性问题的必要性和特点.建立了应力不变量与弹性应变不变量之间的关系式,实现了应力屈服面到应变屈服面的转换,导出和讨论了十二个以应力表达的屈服准则的应变表达式.应用正交法则导出了十二个与上述应变屈服准则相联系的理想塑性材料的本构关系.本文工作的结果可供实际应用,并有助于应变空间塑性理论的进一步研究.     

极限应变法在圆形隧洞稳定分析中的应用

材料的屈服和破坏是不同的,屈服准则已有大量研究,但缺少严格的破坏准则.理想弹塑性模型用应力表述难以区别屈服与破坏,为此该文提出极限应变破坏判据,可用于判断材料的局部和整体破坏.给出了不同材料极限应变的确定方法,并作为破坏判据用于岩土类材料的稳定分析,称为极限应变法.将极限应变法应用于圆形隧洞,研究隧洞的破坏过程、围岩破坏深度及其安全系数,并与滑移线理论和实际模型试验的结果进行对比.研究表明:极限应变法能够判断圆形隧洞的破坏过程与极限状态,求得准确的安全系数,与滑移线场法和模型试验的结果一致,验证了极限应变法在隧洞中应用的可行性.极限应变判据具有明确的力学意义,能反映材料破坏的全过程,为岩土类材料极限分析提供了一种新的方法.     

各向异性材料中共线刚性线夹杂的纵向剪切问题

本文研究各向异性材料中共线刚性线夹杂，（有时称作“硬裂纹”或“反裂纹”问题）的纵向剪切问题。利用复变函数方法，提出了一般问题的公式和某些实际重要问题的封闭形式解，考察了刚性线端点附近的应力分布．从本文解答的特殊情形，可以直接导出各向同性材料相应问题的公式和结果，包括某些已有的结果￣［７］．     

各向异性材料界面周期刚性线夹杂的反平面问题

研究了两种各向异性材料界面含周期分布刚性线夹杂的反平面剪切问题。运用复变函数方法，获得了封闭形式解答，并给出了刚性线尖端应力场公式，从该文解答的特殊情形，可直接导出各向同性材料界面以及均匀各向异性材料中相应问题的公式，其极限情形与已有的结果吻合。     

初始应力作用下的横向各向同性梁

本文从Novozhilov的非线性弹性理论基本方程出发,经适当的简化,用沿梁横截面积分的方法导出任意非均匀初始应力场作用下的横向各向同性梁的运动方程.当初始应力不存在时,方程退化为经典的Timoshenk。梁方程,作为例子,本文用所得的方程,研究了在初始轴向力、初始弯矩作用下的横向各向同性梁的屈曲及振动特性。     

明渠中变密度变粘度牛顿流体紊动基本方程式

本文利用Navier－Stokes方程及雷诺时均法则,导出了变密度变粘度牛顿流体的紊动微分方程式,并进一步导出了变密度变粘度牛顿流体在明渠中紊流流动时的运动微分方程式.文中首次提出了密度紊动应力与粘度紊动应力的概念.     

静电场理论中微分几何方法的一个应用

引用微分几何的方法导出了静电场中曲面导体表面附近场强的法向分量的法向变化率与曲面两个主曲率的关系式,并作为特例,导出了静电场理论的一个众所周知的经典公式.     

复合挤压力的上限解

本文根据实验和滑移线场拟定复合挤压时的速度不连续刚性三角形,由此得出复合挤压时凸模单位压力的最小上限解的解析式,将此式解值和实测值进行比较,表明上限值可供实际使用.     

Large scale nonlinear effects of fluctuations in relativistic gravitation

The first fully nonlinear mean field theory of relativistic gravitation was developed in 2004. The theory makes the striking prediction that averaging or coarse graining a gravitational field changes the apparent matter content of space-time. A review of the general theory is presented, together with applications to black hole and cosmological space-times. The results strongly suggest that at least part of the dark energy may be the net large scale effect of small scale fluctuations around a mean homogeneous isotropic cosmology.     

Non-linear laws of fluid flow through anisotropic porous media

Non-linear laws of fluid flow through anisotropic porous media are written out in invariant tensor form for all crystallographic point symmetry groups. The equations, as is customary in seepage theory [1, 2], are represented by expressions containing the seepage velocity up to and including the third degree. Expressions defining non-linear flow resistances are given and it is shown that, when one transfers from linear to non-linear seepage laws, the symmetry group of the flow properties may change. For example, the isotropic flow properties manifested in Darcy's law may become essentially anisotropic in a non-linear law and display asymmetry, that is, they may be different along one straight line in the positive and negative directions. It is shown that, compared with linear seepage laws for anisotropic media, when flow properties may be defined by just four essentially different types of equation, in non-linear laws the appearance of anisotropy is highly diversified and the number of distinct types of equation increases considerably.     

横观各向同性饱和地基的三维动力响应

首先引入位移函数,将直角坐标系下横观各向同性饱和土Biot波动方程转化为2个解耦的六阶和二阶控制方程;然后基于双重Fourier变换,求解了Biot波动方程,得到以土骨架位移和孔隙水压力为基本未知量的积分形式的一般解,并用一般解给出了饱和土总应力分量的表达式．在此基础上系统研究了横观各向同性饱和半空间体的稳态动力响应问题,考虑表面排水和不排水两种情况,得到了半空间体在任意分布的表面谐振荷载作用下,表面位移的稳态动力响应,文末给出了算例．     

Numerical models of mosaic homogeneous isotropic random fields and problems of radiative transfer

New algorithms for statistical modeling of radiation transfer through various types of stochastic homogeneous isotropic media are created. For this, a special geometric implementation of a “maximum cross-section method” is developed, which takes into account radiation absorption by an exponential weight factor. Some functionals of the solution to the radiative transfer equation, such as mean passage probability, as functions of the correlation length and field type are studied both theoretically and numerically. A theorem of convergence of these functionals to corresponding functionals for an average field as the correlation length decreases to zero is proved.     

Poroelastodynamic potential method for transversely isotropic fluid-saturated poroelastic media

By introduction of two scalar potentials, an analytical method is developed for the solution of poroelastodynamic boundary value problems in transversely isotropic fluid-saturated poroelastic media. The governing equations of motion are considered in the framework of Biot's complete model without any assumption or simplification. As a case of application, solutions in three dimensions for a transversely isotropic fluid saturated porous half space loaded by an arbitrary distribution of time harmonic tractions at the free surface is derived. The free surface of the half space may be considered either permeable or impermeable. As a particular solution, Green's functions for uniform vertical and horizontal circular patch loads are presented as semi-infinite integrals which may be evaluated by means of an appropriate numerical method proposed. The accuracy of the solutions is verified both analytically and numerically against the preceding solutions. Some numerical results are also presented to clarify the influence of different degrees of anisotropy and frequency of excitation on the response of the medium.     

Integral equations of plane static boundary value problems in the moment elasticity theory of inhomogeneous isotropic media

Boundary value problems in the plane moment and simplified moment elasticity theory of inhomogeneous isotropic media are reduced to Riemann-Hilbert boundary value problems for a quasianalytic vector. Uniquely solvable integral equations over a domain are derived. As a result, weak solutions for composite inhomogeneous elastic media can be determined straightforwardly.