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.     

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.     

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     

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.     

线性分布载荷作用下功能梯度各向异性悬臂梁的解析解

对功能梯度各向异性弹性悬臂梁在线性分布载荷作用下的弯曲问题进行了研究．从平面应力问题的基本方程出发,假定应力函数为梁长度方向的多项式形式,由应力函数求导给出应力,利用协调方程和边界条件可完全确定应力函数．将解析解与有限元数值方法的结果进行了对比,两者吻合良好．     

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．     

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.     

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.     

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.     

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.     

带刚性限位的双层隔振系统的离散随机模型

研究由多刚体组成的带刚性限位的双层隔振系统,对其冲击后受到周期性外激励和低强度噪声扰动共同作用下可能会产生的碰撞进行了分析．基于单向约束多体动力学理论,导出了此隔振系统的最大Poincaré映射,建立了其冲击后的零次近似随机离散模型和一次近似随机离散模型．通过对一MTU公司的柴油机隔振系统冲击作用后振动响应的调查指出,由于可能发生间歇性碰撞,该系统呈现复杂的非线性特性．零次近似模型和一次近似模型有较大的区别,低强度的噪声也会对系统产生较大的影响．得到的结果对如何正确设计带刚性限位的双层隔振系统提供了理论参考依据．     

Nonlinear electrohydrodynamic Kelvin-Helmholtz and Marangoni instabilities near the marginal state

The effects of surface tension and adsorption on the electrohydrodynamic Kelvin-Helmholtz instability are studied. The system is stressed by a normal electric field such that it allows for the presence of surface charges at the interface. The method used is that of multiple scales. The nonlinear Schrödinger equation describing the behavior of the disturbed system is derived. The stability of the perturbed system is discussed both analytically and numerically and the stability diagrams are obtained. At the critical point, a generalized formulation of the evolution equation is developed, which leads to the nonlinear Klein-Gordon equation. The various stability criteria are derived from this equation.     

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.     

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.     

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.     

Couette flow of a non-homogeneous fluid

The two dimensional Couette flow of a non-homogeneous viscous fluid is studied. The plane boundaries of the channel are maintained at different temperatures. The upper plane moves with a uniform horizontal velocity and the lower plane is at rest. The fluid is subjected to suction and injection at the boundaries. Thesteady equations are solved by introducing similarity variables which are expanded in series of powers of a small stratification parameter. The non-linear theory predicts that the temperature depends on the distancex from the throat section, an observation which is not predicted by the linear theory. The non-linear effects on velocity and temperature are studied. The rate of heat transfer is discussed.     

虚拟解法分析浸入边界法的精度

浸入边界法是对流固耦合系统进行建模和模拟的有效工具,在生物力学领域的应用尤为广泛．该文的工作主要包含两个部分:程序验证和精度分析．前者证明了程序的正确性,后者给出了浸入边界法的精度．两部分工作均使用虚拟解法作为研究工具．在程序验证部分,使用二阶空间离散格式进行数值计算,通过分析各种变量的离散误差,得到的程序计算精度阶是二阶,与理论精度阶一致,证明了数值计算所使用程序的正确性．精度分析部分工作在此基础上展开．引入压强跳跃,在动量方程中加入相应源项,通过分析带有源项的控制方程中各物理量的离散误差,证明浸入边界法只具有一阶精度．同时可以得出以下结论:粗网格无法敏感地捕捉浸入边界的影响;当Euler网格固定时,增加Lagrange标志点的数目并不会改善计算误差．     

Dynamic analysis of a micro-resonator driven by electrostatic combs

The dynamic response of a micro-resonator driven by electrostatic combs is investigated in this work. The micro-resonator is assumed to consist of eight flexible beams and three rigid bodies. The nonlinear partial differential equations that govern the motions of the flexible beams are obtained, as well as their boundary and matching conditions. The natural matching conditions for the flexible beams are the governing equations for the rigid bodies. The undamped natural frequencies and mode shapes of the linearized model of the micro-resonator are determined, and the orthogonality relation of the undamped global mode shapes is established. The modified Newton iterative method is used to simultaneously solve for the frequency equation and identify repeated natural frequencies that can occur in the micro-resonator and their multiplicities. The Gram-Schmidt orthogonalization method is extended to orthogonalize the mode shapes of the continuous system corresponding to the repeated natural frequencies. The undamped global mode shapes are used to spatially discretize the nonlinear partial differential equations of the micro-resonator. The simulation results show that the geometric nonlinearities of the flexible beams can have a significant effect on the dynamic response of the micro-resonator.     

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