Influence of the root radius of crack-like notches on the fracture load of brittle components

Narrow notches often cause damage that can lead to the destruction of components. The stress field in the vicinity of such crack-like notches in two-dimensional (2D) structures is similar to the stress field around equivalent cracks. Therefore similar investigations are necessary to predict the fracture load for components with cracks or narrow notches. Thus, the asymptotical stress field for a narrow notch with a rounded notch root is deduced from an Airy’s stress function. Based on this stress field a fracture criterion is developed. Comparing the theoretical fracture limit curves derived from the fracture criterion with experimental results it can be shown that for brittle material the local stress state at the fracture initiation point is the same for mode I, mixed-mode and mode II loading.     

RESEARCH ON SOIL PRESSURE IN NINE CABINS OF OPENED BOTTOM ELLIPTICAL BARREL STRUCTURE USING PENETRATION OF NEGATIVE PRESSURE METHOD

An investigation is made on the soil pressure in a nine cabin opened bottom elliptical barrel structure. The calculation models using the penetration of negative pressure method have been developed. The first calculation model is is for the construction stage involving three zones,namely, passive, transitional, and active established for the soil pressure in cabins. The other calculation model is based on the use stage, with the two(passive and active) zones for the soil pressure in cabins. The height of zones and the theoretical analytical solutions of inner soil pressure are derived. The analytical formulas of the models are proved using the finite element method and experimental data, and the formulas are analyzed in the inner soil pressure in the same condition.The calculation models can be used for other multi-position structural design or construction.     

Secondary flows and particle centrifugation in slightly tilted rotating pipes

A theoretical analysis is presented of viscous incompressible laminar flow in a pipe which rotates around an axis held at small angle with respect to its symmetry-axis. Analogous to the results of Barua and Benton [1, 2], solutions in closed-form are given for circulatory flows in the cross-sectional plane of the pipe due to Coriolis forces in combination with Hagen-Poiseuille flow through the pipe. The solutions are used to derive analytical expressions for trajectories of solid or liquid particles entrained in the gas and being subject to centrifugation and the said secondary flows. It is shown that despite centrifugation, particles can be locked into circulatory trajectories thus remaining suspended in the gas flowing through the pipe.     

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width.Using a similar approach to that in Rienstra (2003) [13], a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when ?, the parameter characterising the slow variations of the guide’s walls, is relatively large.     

A new theoretical approach for structural modelling of riveted and spot welded multi-spot structures

A general theoretical approach based on theory of elasticity is presented in order to define the structural behaviour of riveted and spot welded joints. The new closed form solutions lead to the definition of a joint element useful to FE models of riveted or spot welded multi-spot structures. The objective is an accurate evaluation of the local elastic stiffness of spot joints in FE analysis, which is fundamental to perform a reliable simulation of multi-joint structures and, consequently, a good estimate of loads acting on spots; this makes it possible to introduce structural stress or new general criteria allowing, for example, to predict fatigue behaviour. On the other hand, a low entry of degrees of freedom is needed when several spot joints are present in a complex structure. The goal is to reach a reliable spot region model which can be used as the basis to develop a spot element in FE analysis. In the present paper, based on new closed form solutions, a spot element is introduced, so as to precisely evaluate both local and overall stiffness both of spot welded joints and riveted joints. Based on the stress function approach and the Kirchhoff plate theory in linear elastic hypotheses, closed-form in-plane stress, displacement, moment and transverse shear force solutions are derived for a new bidimensional model, subjected to various types of loads. The capability to simulate spot welds or rivets depends on the definition of two elastic parameters intrinsic in closed form solutions, that tunes the theoretical model according to actual joint behaviour.The proposed joint element combines the precision in the simulation with a very limited number degrees of freedom in the overall finite element model of an actual multi-spot structure.The results obtained using the introduced theoretical framework and spot element approach perfectly match those obtained using very refined FE models and experimental data.     

库仑土压力的变分法研究

以滑动体静力平衡的两个力平衡方程为基础,引入拉氏乘子,将土压力问题以变分学观点来描述,转化为确定含有两个函数自变量的泛函极值问题。依据泛函取极值时必须满足的欧拉方程,得出了主动土压力和被动土压力在取极值时,墙后土体的破坏是沿平面滑动。然后,将土压力的泛函极值问题进一步转化为带有约束的函数极值问题。这种函数极值可利用M atlab6.1优化工具箱提供的fm incon函数进行求解。当土体的粘聚力等于0时,土压力计算结果与库仑土压力理论解完全一致;而当土体的粘聚力不等于0时,归纳给出了相应的土压力计算公式。     

界面裂纹的路径选择与数值模拟

利用界面断裂能和荷载混合度的概念研究界面裂纹的扩展路径，利用有限元数值方法模拟界面裂纹的扩展过程，再现界面断裂的各种几何构型．研究表明，界面的断裂能和混合度完全控制了裂纹在界面附近的扩展过程．数值预测的裂纹路径与理论结果一致     

Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.     

Self-sustained slip pulses of finite size between dissimilar materials

The problem of a steady-state slip pulse of finite size between dissimilar materials is studied. It is shown that for a Coulomb friction law, there is a continuous set of possible solutions for any slip propagation velocity and any slip length. These solutions are, however, nonphysical because they show a singular behaviour of the slip velocity at one extremity of the pulse, which implies a crack-like behaviour. In order to regularize these solutions, we introduce a modified friction law due to Prakash and Clifton (Experimental Techniques in the Dynamics of Deformable Solids, Vol. AMD-165, pp. 33-48; J. Tribol. 120 (1998) 97), which consists in introducing in the Coulomb friction law a relaxation time for the response of the shear stress to a sudden variation of the normal stress. Then, we show that even for a slip velocity-dependent characteristic time, the degeneracy of the solutions is not suppressed and a physical pulse is not selected. This result shows the absence of steady state self-healing pulses within the modified friction law and is consistent with recent finite-difference calculations (J. Geophys. Res. 107 (2002) 10).     

The stress intensity factor history for an advancing crack in a transversely isotropic solid under 3-D loading

The mode I extension of a half plane crack in a transversely isotropic solid under 3-D loading is analyzed. Firstly, the fundamental problem that the crack is subjected to a pair of unit point loads on its faces is considered. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener–Hopf technique. The Cagniard–de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Based on the fundamental solution, the stress intensity factor history due to general loading is then obtained. Some features of the solutions are discussed through numerical results.     

Stress-driven morphological instability and catastrophic failure of microdevices

In microdevices, the competition between surface energy and elastic energy could lead at the phenomenon known as stress-driven morphological instability (MI), causing an increase of surface roughness with time. Several different mass transport mechanisms can trigger such a morphological alteration and operate simultaneously: surface and bulk diffusion, evaporation and condensation, chemical reactions. Unstable solids could eventually evolve towards crack-like surfaces thus altering mechanical, electrical and optical properties of the devices or even leading to catastrophic failures by supercritical crack propagation. In this work, a more general kinetic law is employed to estimate the onset of MI, considering the effect of the stress field on the atomic mobility. A more intuitive and straightforward approach is used to determine the stability conditions, where the rate of atomic mass motion is introduced as a stability parameter. The critical loads and wavelengths for the onset of MI, determined as a function of material parameters α and β, are compared with the limiting conditions for the supercritical crack propagation (SC) of a crack-like surface in order to asses if and under which situations catastrophic failures by SC can be observed. Two practical cases are investigated: fixed wavelength (Case I) and arbitrary rough surface with a fixed remote load (Case II). In Case I, absolute and relative threshold loads are found below which MI could never occur and a transitional wavelength over which MI would always lead to SC is introduced. In Case II, it is shown that dominant perturbation for MI would always lead to SC given enough time for the surface to evolve towards a crack-like profile. The influence of the material properties α and β on the critical parameters is also addressed.     

桥梁多模态耦合抖振控制方法研究

目前已证实调谐质量阻尼器(TM D)可以有效控制桥梁抖振响应,并已在工程中得到应用。然而,传统桥梁抖振被动控制理论是基于单模态叠加SRSS法,无法考虑多模态参与作用和模态间气动耦合效应,本文基于Scan lan多模态耦合抖振理论和多重调谐质量阻尼器(M TM D)被动控制理论,提出一种桥梁多模态耦合抖振M TM D控制方法,该方法可以考虑多模态参与作用、模态间气动耦合效应和单模态中各模态位移分量的气动耦合,且对各TM D在主梁上的安装位置没有任何限制。本文最后采用时域仿真方法对该方法进行了验证,两者计算结果吻合良好,表明本文所提出的方法的正确性。     

Frictional sliding modes along an interface between identical elastic plates subject to shear impact loading

Frictional sliding along an interface between two identical isotropic elastic plates under impact shear loading is investigated experimentally and numerically. The plates are held together by a compressive stress and one plate is subject to edge impact near the interface. The experiments exhibit both a crack-like and a pulse-like mode of sliding. Plane stress finite element calculations modeling the experimental configuration are carried out, with the interface characterized by a rate and state dependent frictional law. A variety of sliding modes are obtained in the calculations depending on the impact velocity, the initial compressive stress and the values of interface variables. For low values of the initial compressive stress and impact velocity, sliding occurs in a crack-like mode. For higher values of the initial compressive stress and/or impact velocity, sliding takes place in a pulse-like mode. One pulse-like mode involves well-separated pulses with the pulse amplitude increasing with propagation distance. Another pulse-like mode involves a pulse train of essentially constant amplitude. The propagation speed of the leading pulse (or of the tip of the crack-like sliding region) is near the longitudinal wave speed and never less than times the shear wave speed. Supersonic trailing pulses are seen both experimentally and computationally. The trends in the calculations are compared with those seen in the experiments.     

Post-bifurcation analysis of a thin-walled hyperelastic tube under inflation

We consider the problem of bulging, or necking, of an infinite thin-walled hyperelastic tube that is inflated by an internal pressure, with the axial stretch at infinity maintained at unity. We present a simple procedure that can be used to derive the bifurcation condition and to determine the near-critical behaviour analytically. It is shown that there is a bifurcation with zero mode number and that the associated axial variation of near-critical bifurcated configurations is governed by a first-order differential equation that admits a locally bulging or necking solution. This result suggests that the corresponding bifurcation pressure can be identified with the so-called initiation pressure which featured in recent experimental studies. This is supported by good agreement between our theoretical predictions and one set of experimental data. It is also shown that the Gent material model can support both bulging and necking solutions whereas the Varga and Ogden material models can only support bulging solutions. Relevance of the present method to the study of non-linear wave propagation in a fluid-filled distensible tube is also discussed.     

The Fundamental Solution of the Linearized Navier–Stokes Equations for Spinning Bodies in Three Spatial Dimensions – Time Dependent Case

Explicit formulae for the fundamental solution of the linearized time dependent Navier–Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L^p(R³), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.     

Simulation of partial closure of a crack-like cavity with cohesion between the faces in an isotropic medium

A mathematical model for the closure of a crack-like cavity with cohesive end zones in an isotropic medium is constructed using methods of elastic theory. It is assumed that the interaction between the surfaces of the crack-like cavity under the action of body and surface forces can lead to the formation of contact zones on their surfaces. Determination of the unknown parameters characterizing the closure of the crack-like cavity reduces to a system of singular integrodifferential equations. The integral equations are converted to a system of nonlinear algebraic equations which is solved by the method of successive approximations. The contact stresses, the interaction forces between the faces of the crack-like cavity, and the size of the contact zone in which the faces of the crack-like cavities are closed are determined.     

Effective Molecular Dynamics Model of Ionic Solutions for Large-Scale Calculations

A model of ionic solutions is proposed which can be used to calculate aqueous salt solutions in different nanostructures. The interaction potential of the model includes the Lennard-Jones potential and angularly averaged dipole–dipole and ion–dipole interactions. Lennard-Jones potential parameters for different ions are obtained. Characteristics of aqueous solutions at different salt concentrations are calculated using the molecular dynamics method. It is shown that the calculated values of the hydration shells of ions parameters are in good agreement with the theoretical and experimental data at a salt concentration of 1 mol/kg. The computational scheme used in the calculations is described. It is shown that calculations using the proposed model require less computing resources compared with the standard models of ionic solutions.     

Mode transition and oscillation suppression in supersonic cavity flow

Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation(DNS). For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter Ⅱ mode and then to the Rossiter Ⅲ mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation.The oscillation frequencies obtained from a global dynamic mode decomposition(DMD)approach are consistent with the local power spectral density(PSD) analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter Ⅱ mode to the Rossiter Ⅲ mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.     

THE ELASTIC SOLUTION OF CONCENTRATED FORCE ACTING IN ORTHOGONAL ANISOTROPIC HALF-PLANE AND CON-STANT ELEMENT FUNDAMENTAI FORMULAE OF BOUNDARY ELEMENT METHOD

In this paper, the elastic solutions of concentrated force acting in orthogonal anisotropic half-plane are derived by imaginal method and the formulae of coefficient matrix for constant element are put forward. To solve half-plane problems numerically by BEM, this paper provides the necessary formulae. Because the expressions of fundamental solutions are very simple, the object functions could be obtained for every integral of constant element and higher order element of indirect BEM. Thus, the procedure of integration could be avoided in calculation program     

连续分层流体中垂直薄板的水动力特性

研究了在线性连续分层流体中水波与半潜式刚性垂直薄板相互作用的问题. 在 Boussinesq近似下,基于分离变量法,导出了具有自由面的平面前进波的色散关系,建立 了半潜式刚性垂直薄板的反射与透射能量、水平波浪力的计算方法. 对给定的频率,当它大 于浮力频率时,流场中只有一种模态的平面前进波,当它小于浮力频率时,流场 中有无数多个模态的平面前进波,并证明了对每一种模态的入射波,其它每个模态水波的反射与透射能量是 相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量,以及作用在薄板上的水平波浪力 进行了数值计算分析,表明了流体的线性连续分层效应对这些水动力的影响是不可忽视 的. 特别地,在入射波频率小于浮力频率时,与第1模态入射波的能量转化量及其对薄板产 生的水平波浪力相比,其它模态入射波的能量转化量及其对薄板产生的水平波浪力都要大得 多.