上覆非饱和层的饱和地基稳态响应分析

基于多孔弹性饱和介质及多孔弹性非饱和介质的动力控制方程,研究了上覆非饱和层的饱和半空间成层地基在竖向谐振荷载作用下的稳态响应问题。通过引入位移函数,并利用Cauchy-Reimann条件,分别求得了Fourier变换域内饱和土与非饱和土的位移、应力和孔压的一般解;结合不同的边界条件和连续条件,经过Fourier逆变换,得到竖向简谐荷载作用下成层土的稳态响应积分表达式;当将上覆非饱和层饱和半空间分别退化为均质饱和弹性半空间及上覆弹性层饱和半空间时,结果与已有结果均吻合得较好。通过数值算例分析,着重研究了上覆非饱和土层的饱和度、厚度以及地表透气透水条件对动力响应的影响。     

非饱和土中端承桩纵向振动问题简化解

基于单相流固结理论与Bishop有效应力原理,研究了单相流条件下非饱和土中端承桩的耦合纵向振动问题。建立了简化条件下非饱和土体的动力平衡方程,通过引入拉普拉斯变换和势函数对此方程进行解耦,并采用算子分解理论及分离变量法求得土体纵向振动位移形式解。依据桩土系统的边界和衔接条件,进而得到了桩顶动力响应的闭合形式解,并研究了主要参数对桩顶速度导纳和速度时域响应的影响。结果表明,桩长径比和桩土模量比对桩顶动力响应有着显著的影响,而吸力折减系数对其基本上没有影响。     

深埋圆形隧洞非饱和土-衬砌结构系统的动力特性

采用解析方法在频率域内研究了深埋圆形隧洞非饱和土-衬砌结构系统的动力特性。基于Bishop非饱和土有效应力原理和单相流固结理论,建立了单相流条件下非饱和土的运动方程。通过位移势函数解耦,得到了非饱和土在简谐荷载作用下的动力响应解答。将衬砌结构视为均匀弹性介质,基于弹性理论,得到了简谐荷载作用下圆柱形衬砌结构的稳态形式解答。利用土体与衬砌界面的连续性条件和衬砌结构内边界上的边界条件,确定了表达式的待定系数。在此基础上,考察了饱和度、吸力折减系数、衬砌厚度等参数对非饱和土响应幅值的影响。结果表明:随着衬砌厚度的增加,系统响应幅值逐渐减小;饱和度和吸力折减系数对孔隙水压力幅值的影响较大,而对径向位移和环向应力幅值的影响较小。     

正常固结非饱和黏性土的三剪弹塑性本构模型

基于临界状态土力学框架,采用单应力变量法和双应力变量法非饱和土三剪强度准则,将原饱和土屈服函数中的屈服应力和破坏应力比分别替换成能反映土体饱和度影响的屈服应力和三剪破坏应力比,采用等量代换法和坐标平移法的三剪屈服函数推导出4种三剪弹塑性本构模型.所提本构模型能反映非饱和土全应力状态下土的强度区间效应、拉压强度差及黏聚力...     

正常固结非饱和黏性土的三剪边界面模型研究

将三剪统一强度准则分别与非饱和土的单应力变量理论和双应力变量理论相结合提出了正常固结非饱和黏性土的三剪强度准则,在此基础上采用等量代换法与坐标平移法分别推导出可以反映土体全应力状态效应的三剪破坏应力比。将该三剪破坏应力比引入非饱和黏性土修正剑桥模型的屈服面方程以确定初始边界面,采用径向映射法则确定后续边界面,根据插值函数得到加载面上的塑性模量,据之建立了非饱和黏性土单应力变量和双应力变量下分别采用等量代换法和坐标平移法的4个三剪弹塑性边界面模型并对这4个模型做了单调和循环压缩荷载试验验证。结果表明,所建模型均能较好地反映土的变形特征,但相比之下,双应力变量下建立的模型相对单应力变量下建立的模型更接近试验结果,采用等量代换法建立的模型相对坐标平移法更接近试验结果的特点。真三轴数值模拟结果表明,单调加载时,相同应力条件下中主应力影响系数增大会引起非饱和土强度增大;循环加载时,最小主应力或中间主应力的增大均会引起土体抗剪强度的增大,且荷载振幅越大,非饱和土的轴向应变随之增大。比较4个边界面模型在真三轴应力状态的模拟结果表明,单调加载时,非饱和黏性土在双应力变量下的模拟抗剪强度值相对较大;循环加载时,单应力变量下所得塑性变形相对较大。     

固支三维弹性矩形厚板的精确解

采用有限积分变换和状态空间理论相结合的方法推导出了固支三维弹性矩形厚板的精确解.在分析过程中摒弃以往薄板和中厚板理论中有关应力和位移函数的各种人为假定,完全从三维弹性力学基本方程出发,经过变量代换将关于应力和位移分量的六阶偏微分方程组化为2 个彼此独立的四阶、二阶矩阵微分方程,再利用有限积分变换的方法得到空间状态方程,并由Cayley-Hamilton定理求得应力和位移分量沿板厚度z 方向的传递矩阵,最后利用边界条件定解出待定常数,经过有限积分逆变换解得了固支三维厚板的精确解.通过计算实例验证了该文方法的正确性.     

非饱和土三维固结问题探讨

本文推导了非饱和土三维固结控制方程组，它由三个静力平衡方程、一个连续性方程和一个吸力状态方程组成，包含五个基本未知量（三个位移分量、一个孔隙水应力和一个孔隙气应力）。这是不同于前人思路的一种尝试，饱和度可用其它基本未知量表达，不作为独立变量而只作为方程中的可变参数出现。饱和土的Ｂｉｏｒ固结方程可作为该方程组的一个特例而存在。文中还就方程组求解、本构模型和参数测定等问题提出了一些设想。     

非饱和地基中Love波的传播特性

基于非饱和多孔介质的波动方程,考虑了土中水,气体与土骨架之间的粘性耦合作用,建立了弹性半空间上非饱和土层中Love波的弥散方程。首先分析了饱和度与频率对非饱和孔隙介质中剪切波速的影响。然后运用数值方法得到了不同饱和度下土层中多种Love模态波的弥散特性和位移分布情况,并用图表的形式给出。数值计算结果表明,上覆非饱和土层中Love波的传播速度和衰减系数不仅具有频散性,而且与土层的饱和度有关。在不同饱和度时的高模态(n≥2)的Love波的截止频率值不同。此外,讨论了饱和度对Love波水平位移幅值的影响。     

球对称压电壳的随机最优控制

分析研究球对称压电壳在边界随机激励下的最优控制问题。给出压电壳的机电动力学方程、应力和电位移表达式,建立其随机最优控制问题方程;通过电势积分转化为机械振动控制方程。通过位移变换和Galerkin法,导出关于模态位移的多自由度振动最优控制方程。根据随机动态规划原理,建立HJB方程,得到压电壳的最优控制电势;并给出受控壳系统的频响函数、响应谱密度和相关函数等表达式,以计算其随机响应。最后给出数值结果,显示压电壳的随机最优控制效果。     

饱和地基上弹性圆板的固结位移

 采用Laplace变换及Hankel变换研究弹性圆板在饱和地基上的固结位移．在Laplace变换域上建立了求解弹性圆板固结位移的第二类Fredholm积分方程，由数值反变换获得时域解，给出了对工程实践有参考价值的计算结果．计算结果表明，弹性板的固结位移随饱和土的排水泊松比的减少而增加，而弹性板的初始位移随饱和土的不排水泊松比的减少而增加．     

A mathematical model of pulsatile flows of microstretch fluids in circular tubes

Pulsatile flows of micropolar fluids with stretch whose microelements can undergo expansions and contractions besides translations and rotations in straight circular tubes are considered. The governing field equations for such flows of linear microstretch fluids turn out to be a nonlinear coupled partial differential system. Solutions are sought for this system starting with a reasonable initial approximation for microinertia and the consequent linearization of the field equations. One of the coupled equations governing the microstretch and microinertia is solved approximately by the method of Laplace transforms taken with respect to the time variable. Making use of this approximate solution, the other coupled equation is solved leading to explicit higher order approximation solutions for microinertia, microstretch and micropressure. Next, the coupled equations governing the velocity and the microrotation fields are solved by employing the finite Hankel transform operators on a space variable and their inversions, and higher order approximation solutions are determined. All the above-mentioned explicit solutions are obtained in computationally suitable forms. These solutions have the promise of application to many practically important physical situations such as flows of polymeric fluids with deformable springy suspensions and flows of biological fluids including blood with deformable cell suspensions in small arteries.     

On the relationship between continuum mixture theory and integral averaged equations for immiscible fluids

The local fluid flow equations governing the flow of two immiscible fluids are averaged to obtain the two-component flow equations. A one-to-one correspondence is shown to exist between the averaged two-component flow equations and the continuum theory of mixtures when a proper identification of the mixture free energies has been made in terms of the constituent properties of the fluids comprising the mixture.     

Some simple unsteady unidirectional flows of a binary mixture of incompressible Newtonian fluids

The problems dealing with some simple unsteady unidirectional flows of a mixture of two incompressible Newtonian fluids are investigated. By using the constitutive equations appeared in the literature for binary mixtures of chemically inert incompressible Newtonian fluids, the equations governing the motion of the binary mixture are reduced to a system of coupled partial differential equations. By means of integral transforms, the exact solutions of these equations are obtained for the following three problems: (i) unsteady Couette flow, (ii) unsteady plane Poiseuille flow, (iii) unsteady axisymmetric Poiseuille flow.     

On finite element modelling of surface tension Variational formulation and applications – Part I: Quasistatic problems

This paper describes variational formulation and finite element discretization of surface tension. The finite element formulation is cast in the Lagrangian framework, which describes explicitly the interface evolution. In this context surface tension formulation emerges naturally through the weak form of the Laplace–Young equation.The constitutive equations describing the behaviour of Newtonian fluids are approximated over a finite time step, leaving the governing equations for the free surface flow function of geometry change rather than velocities. These nonlinear equations are then solved by using Newton-Raphson procedure.Numerical examples have been executed and verified against the solution of the ordinary differential equation resulting from a parameterization of the Laplace-Young equation for equilibrium shapes of drops and liquid bridges under the influence of gravity and for various contact angle boundary conditions.     

OPTIMIZATION METHODS FOR SOLVING NON-LINEAR EQUATIONS IN VISCOELASTIC FLOW PROBLEMS

Numerical simulation of complex flows of viscoelastic fluids requires the use of efficient algorithms for solving the non-linear governing equations. In this paper, optimization algorithms, associated to a non-linear least squares methods are considered. The governing equations are written in the context of stream-tube analysis. This method is particularly adapted to handle memory-integral constitutive equations and permits calculation of flows by considering elementary sub-domains in a mapped computational domain where the transformed streamlines are parallel and straight. The procedure used to solve the equations is the Trust Region optimization algorithm, which satisfies a global convergence property. Using an integral codeformational equation, various tests involving the influence of parameters of the algorithms are applied to different flow geometries and underline the robustness and efficiency of the Trust Region algorithm.     

MHD boundary-layer flow of a micropolar fluid past a wedge with variable wall temperature

Summary The steady laminar MHD boundary-layer flow past a wedge immersed in an incompressible micropolar fluid in the presence of a variable magnetic field is investigated. The governing partial differential equations are transformed to the ordinary differential equations using similarity variables, and then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results show that the micropolar fluids display drag reduction and consequently reduce the heat transfer rate at the surface, compared to the Newtonian fluids. The opposite trends are observed for the effects of the magnetic field on the fluid flow and heat transfer characteristics.     

On the determination of response functions for a binary mixture of incompressible newtonian fluids

The equations governing the motion of a mixture of two incompressible inert Newtonian fluids are stated. Some steady 2-dimensional solutions are derived and using these results a procedure is suggested for determining certain combinations of the coefficients which appear in the constitutive equations. A discussion of the boundary conditions appropriate to a free surface and the proof of a uniqueness theorem are also included.     

Analysis of the vacuum infusion moulding process: I. Analytical formulation

The present work is primarily concerned with the analytical formulation of governing equations for flow of incompressible fluids through compacting porous media and their application to vacuum infusion (VI) of composite materials. The literature on VI and the effects of compacting media on permeability and flow is reviewed. A complete development of the proposed governing equation is shown along with a suggested numerical solution. The proposed model is subsequently used to quantify the effect of process parameters such as inlet and outlet pressures, fibre architecture and lay-up. Implications for industrial production are discussed.     

Wave features related to a model of compressible immiscible mixtures of two perfect fluids

Summary The balance equations of a compressible immiscible mixture of two perfect fluids are derived by using a variational principle. It is shown that the equations of such a mixture obey Truesdell's third metaphysical principle. Then the governing equations, specialized by assuming that both phases have the same motion, are studied by means of a suitable asymptotic approach. It is derived an evolution equation representing a generalized Korteweg-de Vries equation containing also nonlinear terms in the higher order derivatives. Finally, the travelling wave solutions of this evolution equation are discussed.     

A particle finite element method for analysis of industrial forming processes

We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing equations for the deformable bodies are written in a unified manner that holds both for fluids and solids. The success of the formulation lays on a residual-based expression of the mass conservation equation obtained using the finite calculus method that provides the necessary stability for quasi/fully incompressible situations. The governing equations are discretized with the FEM via a mixed formulation using simplicial elements with equal linear interpolation for the velocities, the pressure and the temperature. The merits of the formulation are demonstrated in the solution of 2D and 3D thermally-coupled forming processes using the particle finite element method.