Damage and Failure of Metal/Fibre-Reinforced Polymer Tensile Specimens with Inelastic Interface

Hybrid specimens of metal and fibre-reinforced polymer are applied in automotive and aerospace industry. The simulation and analysis of damage of such engineering structures is the focus of this research. The investigation includes a computation of the extension of single lap tensile specimen, produced by ultrasonic metal welding. The specimen is manufactured from CF-PA66 - fibre-reinforced polymer and AlMg3 (AA5754), which is used as a metallic joining partner. The aluminium substrate is treated as an elastoplastic material. The polymer composite generally shows an orthotropic elastic behaviour. The interface material has been numerically modeled as an elastoplastic material with linear hardening, coupled with Lemaitre-type damage. The finite element method is used for the investigation of so-called interface elements. The geometry of the interface is a consequence of the welding sonotrode geometry. The behaviour of specimens with square and ring interface geometry are analysed. The influence of the interface geometry on the mechanical properties of the joint is shown. The increase of the damage parameter and the development of failure are described for both cases. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parallel multi-frontal solver for p adaptive finite element modeling of multi-physics computational problems

The paper presents a parallel direct solver for multi-physics problems. The solver is dedicated for solving problems resulting from adaptive finite element method computations. The concept of finite element is actually replaced by the concept of the node. The computational mesh consists of several nodes, related to element vertices, edges, faces and interiors. The ordering of unknowns in the solver is performed on the level of nodes. The concept of the node can be efficiently utilized in order to recognize unknowns that can be eliminated at a given node of the elimination tree. The solver is tested on the exemplary three-dimensional multi-physics problem involving the computations of the linear acoustics coupled with linear elasticity. The three-dimensional tetrahedral mesh generation and the solver algorithm are modeled by using graph grammar formalism. The execution time and the memory usage of the solver are compared with the MUMPS solver.     

A bayesian approach to the probability density estimation

Summary A Bayesian procedure for the probability density estimation is proposed. The procedure is based on the multinomial logit transformations of the parameters of a finely segmented histogram model. The smoothness of the estimated density is guaranteed by the introduction of a prior distribution of the parameters. The estimates of the parameters are defined as the mode of the posterior distribution. The prior distribution has several adjustable parameters (hyper-parameters), whose values are chosen so that ABIC (Akaike's Bayesian Information Criterion) is minimized. The basic procedure is developed under the assumption that the density is defined on a bounded interval. The handling of the general case where the support of the density function is not necessarily bounded is also discussed. The practical usefulness of the procedure is demonstrated by numerical examples. The Institute of Statistical Mathematics     

On optimal control problems connected with eigenvalue variational inequalities

The eigenvalue optimization problem for a variational inequality over the convex cone is to be dealt with. The control variable appears in the operator of the unilateral problem. The existence theorem for the maximum first eigenvalue optimization problem is stated and verified. The necessary optimality condition is derived. The applications to the optimal design of unilaterally supported beams and plates are presented. The variable thickness of a construction plays the role of a design variable. The convergence of the finite elements approximation is proved. Copyright © 2001 John Wiley & Sons, Ltd.     

自由表面与粘性尾迹的相互作用

解析地研究了无限深不可压粘性流体中运动物体产生层流尾迹与自由表面波的相互作用．以定常的Oseen方程模拟受扰流动,对于小振幅自由表面波则采用线性化的运动学和动力学边界条件．在数学描述上,运动物体以Oseen极子模拟,受扰流场分解成表述粘性尾迹的无界奇异Oseen流和描述自由面效应的有界正则Oseen流之和．通过积分变换法,得到自由表面波的精确解．借助Lighthill的两步格式,导出了自由面波高带有附加校正项的渐近解．所得对称解显示了波动的振幅因粘性和潜深的存在而呈指数衰减．     

A group invariant solution for a pre-existing fluid-driven fracture in permeable rock

The propagation of a two-dimensional pre-existing fracture in permeable rock by the injection of a viscous, incompressible Newtonian fluid is considered. The fluid flow in the fracture is laminar. By the application of lubrication theory, a partial differential equation relating the half-width of the fracture to the fluid pressure and leak-off velocity is derived. The model is closed by the adoption of the PKN formulation in which the fluid pressure is proportional to the fracture half-width. The partial differential equation admits four Lie point symmetries provided the leak-off velocity satisfies a first order linear partial differential equation. The solution of this equation yields the leak-off velocity as a function of the distance along the fracture and time. The group invariant solution is derived by considering a linear combination of the Lie point symmetries. The boundary value problem is reformulated as a pair of initial value problems. The model in which the leak-off velocity is proportional to the fracture half-width is considered. The working condition of constant pressure at the fracture entry is analysed in detail.     

An optimal control problem for a pest, predator, and plant system

The paper is devoted to an optimal control problem for a system of three nonlinear parabolic equations from population dynamics. The equations model a trophic chain consisting of a predator, a pest and a plant species. The existence and uniqueness of the positive solution for the system are proved. The control variable is connected with the action of a pesticide. Our goal is to minimize the density of the pest and to maximize the plant density. The existence of the optimal solution is proved. The first and second order optimality conditions are established.     

Supercomputer simulation of viscous noncompressible flow past bodies of complex shape

The article reports the results of numerical analysis of viscous thermally conducting noncompressible flow past bodies of complex shape. The effect of physico-chemical processes is ignored. Flow past bodies with various nose cone designs is examined. The process is described using a system of Navier–Stokes equations augmented with the energy equation. The continuity equation is used to control the numerical accuracy. The simulation results are reported in the form of vector fields and surface components of the velocity vector in various channel sections. The results are analyzed for various body configurations.     

Nonaxisymmetric Free Convection Flow over a Rotating Disk in a Viscoelastic fluid with Magnetic Field

The non axisymmetric motion produced by a buoyancy-induced secondary flow of a viscoelastic fluid over an infinite rotating disk in a verticalplane with a magnetic field applied normal to the disk has been studied.The governing Navier Stokes equations and the energy equation admit a self similar solution. The system of ordinary differential equations has been solved numerically using Runge-Kutta Gill subroutine.The turning moment for the viscoelastic fluid is found to be less than that of the Newtonian fluid but the turning moment is increased due to the magnetic parameter. The resultant force due to the buoyancy-induced secondary flow increases with the magnetic parameter but reduces as the viscoelastic parameter increases. The quantity of fluid, which is pumped outwards due to the centrifuging action of the disk, for the viscoelastic fluid is more than that of the Newtonian fluid. The buoyancy-induced secondary flow boundary layer is much thicker than the primary boundary layer thickness. The thermal boundary layer due to the primary flow increases with the magnetic parameter decreases as the viscoelastic parameter increases. The heat transfer increases with the viscoelastic parameter but decreases as the magnetic parameter increases. The effect of the viscoelastic parameter is more pronounced on the secondary flow than on the primary flow.     

车路耦合非线性振动高阶Galerkin截断研究

将移动车辆模型化为运动的两自由度质量-弹簧-阻尼系统,道路模型化为立方非线性黏弹性地基上的弹性梁,并将路面不平度设定为简谐函数．通过受力分析,建立车路非线性耦合振动高阶偏微分方程．采用高阶Galerkin截断结合数值方法求解耦合系统的动态响应．首次研究不同截断阶数对车路耦合非线性振动动态响应的影响,确定Galerkin截断研究车路耦合振动的收敛性．研究结果表明,对于软土地基的沥青路面,耦合振动的动态响应,需要150阶以上的截断才能达到收敛效果．并通过高阶收敛的Galerkin截断研究了系统参数对车路耦合非线性振动动态响应的影响.     

空泡起始和溃灭阶段的噪声

本文对孤立空气-水蒸汽空泡,在起始和溃灭阶段的噪声进行了分析.导出了噪声声压及振速的表达式,并进行了具体的计算.计算结果表明:从自由气核发育的起始时刻到空泡溃灭的整个过程中均伴有噪声.空泡噪声主要发生在溃灭阶段的晚期,其声压的数量级可以达到100分贝以上. 在基本声学假定下[1],考虑理想、不可压流体中,孤立空气-水蒸汽空泡在起始和溃灭阶段的噪声,并计及液体的表面张力的影响.     

The modified jump problem for the Laplace equation and singularities at the tips

The boundary value problem for the Laplace equation outside several cuts in a plane is studied. The jump of the solution of the Laplace equation and the boundary condition containing the jump of its normal derivative are specified of the cuts. The unique solution of this problem is obtained. The problem is reduced to the uniquely solvable Fredholm equation of the second kind and index zero. The singularities at the ends of the cuts are investigated.     

Laplace方程有孔椭圆区域边值问题的解析解

本文利用相似流动替换方法 ,解决了中心有圆孔的椭园形区域上 Laplace方程第一类边值问题 ;采用分区域解法 ,给出了中心有椭园孔的椭园形区域上 Laplace方程第一类边值问题的解析通解 .这一结果在许多工程领域有重要应用 ,本文给出了油藏工程实例     

Water waves diffraction by a circular plate

The interaction of water waves with circular plate within the framework of a linear theory is considered. The plate lies on the free surface in water of finite depth. The integral transform technique is used to solve this problem. The problem is reduced to a system of dual integral equations for a spectral function. The way to solve these equations consists in converting them into Fredholm integral equation of the second kind. The asymptotic solutions of this equation are obtained. Representations for diffraction field and for the forces on the plate are given.     

Studium der Eigenschwingungen eines zylindrischen Plasmas mit der Methode der finiten Elemente

The eigenmodes of a cylindrical homogeneous plasma may be calculated analytically. There are three classes of solutions. The eigenvalues of the first class are well separated, those of the second class have a point of accumulation. The eigenvalue of the third class is infinitely degenerated. The eigenvalues and eigenmodes of the corresponding discrete finite element problem tend towards the true solution. The convergence properties are discussed.     

Associations and dissociations with time-dependent reaction coefficients in finite polymer mixtures: The model and analytical-numerical method for solution by successive approximations

The work deals with the association and dissociation reactions with time-dependent coefficients in finite mixtures of polymers dispersed in fluid media with solid components. The polymers are regarded to be formed by identical units, polymer-forming units (PFUs) and, thus, present homopolymers. The model takes into account the porosity of the dispersion-medium/polymer-mixture system. The work derives the model for the reactions in the finite mixtures. The model presents a non-autonomous quadratic finite ODE system in a time-independent hyperplane and is based on the conservation law for the total number of PFUs. A variety of engineering applications of the derived finite-mixture model are discussed. The simplest case of the finite mixtures, i.e., the monomer-dimer mixtures with time-independent reaction coefficients is completely analyzed. An analytical-numerical (AN) method of the successive-approximations (SA) type is proposed for solving the derived model. The AN/SA method includes explicit analytical expressions for each of the approximations in terms of the preceding approximation. The method is exact in the dissociation-only case. The approximations are expected to converge if the association-reaction coefficients are not too large and the zeroth approximations are not very far from the solution. The AN/SA method comprises two sequences of the approximations. If the first one converges uniformly in the entire time axis, then the limit function is a steady-state (or “dynamic equilibrium”) solution of the non-autonomous quadratic ODE system. The second sequence presumes that the first sequence is convergent in the above mentioned sense. The second sequence is intended for calculation of the solutions of initial-value problems for the above ODE system in a semi-infinite time interval. The main differences from common computational methods are formulated. The AN/SA method is quantitatively illustrated with a few examples of the settings in the aforementioned case of monomer-dimer mixtures, also in comparison with the explicit Euler method. The form of the AN/SA method allows especially efficient implementation on multi-processor/multi-core personal computers with graphic processing units even if the dimension of the state space is large. The developed model and method form a constructive framework for analysis or design of polymer mixtures dispersed in fluid-solid media. An application to prospective manufacturing of spatially heterogeneous polymer products is noted. A few directions for future research are proposed as well.     

Modular-function representation of the solutions of the problem of two fixed centres

The problem of two fixed centres can be integrated in quadratures by using Stoeckel's theorem in spheroidal coordinates. The elliptic coordinates of the meridian plane satisfy equations that define a complex elliptic curve. The solution can be written down by using the uniformization formula of the elliptic curve. The constants defining the result in terms of doubly periodic functions are calculated successively from the initial data. The half-period ratio is determined by solving a complex transcendental equation using modular functions. The magnitude of the half-period of least absolute value is determined using -functions of the zero argument, using invariants of the Weierstrass -function.     

Exact solution of thermal stress problem of an inhomogeneous hygrothermal piezoelectric hollow cylinder

The closed-form exact solution for the hygrothermal response of inhomogeneous piezoelectric hollow cylinders is obtained. The interaction of electric potentials, electric displacement and elastic deformations is presented. The present cylinder is subjected to both a mechanical load and an electric potential. The material properties coefficients of the present cylinder are assumed to be changed in the radial direction by different distribution forms. The field quantities like displacement, stresses and electric potentials in the inhomogeneous piezoelectric cylinders are determined. The significant of influences of material inhomogeneity, initial temperature, final moisture, and the load and electric ratios in the field quantities are investigated. The concluding remarks and suitable discussions are made.     

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??Hidden Markov model is widely used in statistical modeling of time, space and state transition data. The definition of hidden Markov multivariate normal distribution is given. The principle of using cluster analysis to determine the hidden state of observed variables is introduced. The maximum likelihood estimator of the unknown parameters in the model is derived. The simulated observation data set is used to test the estimation effect and stability of the method. The characteristic is simple classical statistical inference such as cluster analysis and maximum likelihood estimation. The method solves the parameter estimation problem of complex statistical models.     

关于建立玉米叶片的数学模型的几种方法的讨论

分别运用拉格朗日插值法、最小二乘的三次多项式拟合法和经典三次样条插值法建立了玉米叶片的数学模型,并从收敛性、稳定性、光滑性等方面对三种方法进行了对比分析,通过对所给实例的绘图效果进行比较,指出了拉格朗日插值法、最小二乘的三次多项式拟合法和经典三次样条插值法在描述玉米叶片形态特征的效能上的利弊.