A study of emulsion expansion by a boundary integral method

A new implementation of the conventional three-dimensional boundary-integral formulation for deformable drops in a viscous medium at low Reynolds numbers is presented. We describe a scheme to generate concentrated emulsions and a numerical procedure for computing interactions among deformable drops. Direct numerical simulations are used to describe the expansion of an ordered emulsion at dispersed-phase volume fraction up to 0.98. We also study the viscoelastic response of a monodisperse emulsion which have been concentrated up to 0.68. The results have demonstrated the feasibility of simulating high-volume fraction emulsions, and the method can readily be extended to explore three-dimensional foam problems.     

Solution of the laminar duct flow problem by a boundary integral equation method

Summary A boundary integral equation method is proposed for approximate numerical and exact analytical solutions to fully developed incompressible laminar flow in straight ducts of multiply or simply connected cross-section. It is based on a direct reduction of the problem to the solution of a singular integral equation for the vorticity field in the cross section of the duct. For the numerical solution of the singular integral equation, a simple discretization of it along the cross-section boundary is used. It leads to satisfactory rapid convergency and to accurate results. The concept of hydrodynamic moment of inertia is introduced in order to easily calculate the flow rate, the main velocity, and the fRe-factor. As an example, the exact analytical and, comparatively, the approximate numerical solution of the problem of a circular pipe with two circular rods are presented. In the literature, this is the first non-trivial exact analytical solution of the problem for triply connected cross section domains. The solution to the Saint-Venant torsion problem, as a special case of the laminar duct-flow problem, is herein entirely incorporated.     

SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION

IntroductionThereweresomeresultsofstudyingonboundaryvalueproblemsforfunctionaldifferentialequation[1～6 ]byemployingthetoplolgicaldegreetheoryandsomefixedpointprinciplesinrecentyears.Buttheworktostudyboundaryvalueproblemsfordelaydifferentialequationwithsmallparameterbymeansofthetheoryofsingularperturbationrarelyappeared[7～11].Thereasonforitisthattheworktoconstructtheuppersolutionandlowersolutionforthecaseofdifferentialequationwithdelayisdifficult.Theauthorhasstudiedakindofboundaryvalueproblem…     

Radial integral boundary element method for simulating phase change problem with mushy zone

A radial integral boundary element method(BEM) is used to simulate the phase change problem with a mushy zone in this paper. Three phases, including the solid phase, the liquid phase, and the mushy zone, are considered in the phase change problem. First, according to the continuity conditions of temperature and its gradient on the liquid-mushy interface, the mushy zone and the liquid phase in the simulation can be considered as a whole part, namely, the non-solid phase, and the change of latent heat is approximated by heat source which is dependent on temperature. Then, the precise integration BEM is used to obtain the differential equations in the solid phase zone and the non-solid phase zone, respectively. Moreover, an iterative predictor-corrector precise integration method(PIM) is needed to solve the differential equations and obtain the temperature field and the heat flux on the boundary. According to an energy balance equation and the velocity of the interface between the solid phase and the mushy zone, the front-tracking method is used to track the move of the interface. The interface between the liquid phase and the mushy zone is obtained by interpolation of the temperature field.Finally, four numerical examples are provided to assess the performance of the proposed numerical method.     

A boundary element method for a non-linear free surface problem

In this paper a numerical method to compute the wave resistance of a body submerged in a free stream of finite and infinite depth is presented. Non-linear effects on the free surface are taken into account by an iterative procedure; the solution is in the form of a single-layer potential. For the 2D problem, results are shown for both the cases of finite and infinite depth of the fluid domain, with special emphasis on the supercritical flow in which the consistency of the scheme is pointed out. The method is also extended to the 3D case of a spheroid submerged in deep water. All the results presented are compared with experimental data and analytical solutions available in the literature.     

基于广义非线性统一强度理论的隧道塌落拱分析

基于广义非线性统一强度的剪切破坏理论,在平面应变状态下,根据极限上限定理和隧道顶部的围岩塌落机制,在耗散能中引入了包含曲线型破裂面方程的目标函数,建立了围岩中任意断面的隧道顶部围岩的塌落机制。基于塑性位势理论,考虑塑性应变增量与塑性势函数的应力梯度成正比,由此得出了在速度间断线上任意点内能的耗散率;再运用虚功原理,建立内能耗散率和外力做功相等的关系式,从而通过变分原理得出了隧道顶部塌落面的解析表达式,由该表达式计算出隧道顶部塌落面的形状。以圆形断面隧道为例,对影响塌落拱形状的隧道半径和中间主剪应力系数等相关参数进行了讨论分析。由此得出:在平面应变状态下,隧道顶部围岩塌落体的宽度和高度随着中间主剪应力系数的不断增大而减小;塌落面的高度随着广义非线性统一强度参数的不断增大而增大,而塌落面的宽度则不断减小;塌落宽度和塌落高度随隧道半径的增大而增大。     

基于非线性梁理论的有限质点法

有限质点法是以向量式力学为基础,用有限数量的质点来模拟结构的变形行为,质点的运动由牛顿运动定律来计算。在有限质点法中,质点通过构件相连,构件约束着质点的运动,并且其内力由质点的运动变量来描述。基于向量式力学的基本思想和非线性梁理论,提出了一种新的有限质点法,该方法在共旋单元坐标系中描述梁的非线性变形。以空间梁系结构为例,推导了计算构件内力的非线性公式,并考虑了弯扭耦合变形。通过两个连续欧拉角的变换公式得到共旋坐标系的旋转矩阵。与传统的有限质点法相比,本文提出的方法避免了刚体虚转动分析。通过四个结构的数值求解,验证了本文方法在计算结构大变形响应时具有较高的精度。     

Approximate solutions of a nonlinear boundary value problem

Archive for Rational Mechanics and Analysis -     

A perturbation boundary integral equation method for analysis of interaction between foundation and nonlinear rock and soil medium

A scheme is developed for analysing the interaction between a foundation and a nonlinear rock and soil medium, in which the foundation is considered as a linear elastic body and a typical boundary integral equation method (BIEM) is employed. On the basis of taking the nonlinear properties of the medium into account, a perturbation BIEM is developed. The fundamental equations for the nonlinear coupling analysis are formulated, and typical problems are solved and discussed by the present method.     

On a boundary layer problem for the nonlinear Boltzmann equation

This article deals with a boundary-layer problem arising in the kinetic theory of gases when the mean free path of molecules tends to zero. The model considered here is the stationary, nonlinear Boltzmann equation in one dimension with a slightly perturbed reflection boundary condition. We restrict our attention to the case of hard spheres collisions, with Grad's cutoff assumption. Existence, uniqueness and asymptotic behavior are derived by means of energy estimates.     

A spectral boundary integral method for inviscid water waves in a finite domain

In this paper, we show how the spectral formulation of Baker, Meiron and Orszag can be used to solve for waves on water of infinite depth confined between two flat, vertical walls, and also how it can be modified to take into account water of finite depth with a spatially varying bottom. In each case, we use Chebyshev polynomials as the basis of our representation of the solution and filtering to remove spurious high‐frequency modes. We show that spectral accuracy can be achieved until wave breaking, plunging or wall impingment occurs in two model problems. Copyright © 2016 John Wiley & Sons, Ltd.     

A simplified nonlinear theory of the generalized plane strain

A finite deformation theory of plane strain is formulated for transversely isotropic, homogeneous bodies with nonlinear stress-strain law. A new set of simplified field equations, which is valid in the case of some deviations from Hooke's law, is derived systematically with the help of the method of order estimation. For illustration purposes, a circular hole in a body under generalized plane strain is considered, together with the solution of an example problem by perturbation techniques.     

A boundary integral equation method for the solution of a class of crack problems

A boundary integral equation method for the solution of an important class of crack problems in elasticity is outlined. The method is applicable for deformations in which the crack faces remain in contact. Specific numerical examples are considered to illustrate the application of the method.