一种考虑界面相物性影响的界面单元法

界面是由复杂的界面相简化而成的,界面破坏实际是界面相材料的破坏。数值计算为了方便,如经典模型和内聚力模型等,都把很薄的界面相作无厚度化处理。导致只能考虑界面的面力,而无法考虑界面相内的应力(平行于界面方向的应力)。使界面失效准则先天性地排除了界面相内部应力的影响,从界面相材料失效机理的角度来看这是不够严谨的。本文将界面相材料等效为一种弹性连续体,由界面本构关系推导得到了一种新的界面单元。该单元具有界面参数易确定、对界面相物性可以进行等效描述等优点。通过商用有限元软件ABAQUS和用户子程序UEL实现了数值分析,并与直接物理模型的数值模拟结果进行对比,证明了本方法的简便及准确性。通过对不同界面相厚度结构的进一步分析,探讨了本文方法的可行范围。     

Interaction of an Ellipsoidal Inclusion with an Elliptic Crack in an Elastic Material under Triaxial Tension

The interaction of an elastic ellipsoidal inclusion with an elliptic crack in an infinite elastic medium under triaxial loading is analyzed. The stress state in the elastic space is represented as a superposition of the principal state and perturbed states, which are due to the presence and interaction of the inclusion and the crack. The analytical solution of the problem is found using the method of equivalent inclusion, the potential of an inhomogeneous ellipsoid, and a system of harmonic functions for an elliptic crack. The effect of triaxial loading on the stress intensity factors is analyzed     

Using a Smoothing Averaging Operator to Evaluate Macroscopic Parameters in Structurally Inhomogeneous Materials

A smoothing averaging operator is used in passing from structural to macroscopic modeling of the stress–strained state of an article from a composite material taking into account finite strains. A model is constructed using an integral operator, in which the macroscopic laws of conservation of energy and mass and the equation of motion have the ordinary form used to describe processes in homogeneous materials. As an example, macroscopic parameters are evaluated in a system consisting of an ensemble of inclusions in an infinite matrix.     

SH波对浅埋弹性圆柱及裂纹的散射与地震动

采用Green函数、复变函数和多极坐标等方法研究含圆柱形弹性夹杂的弹性半空间中任意位置、任意方位有限长度裂纹对SH波的散射与地震动. 构造了含圆柱形弹性夹杂的半空间对SH波的散射波,并求解了适合本问题Green函数,即含有圆柱形弹性夹杂的半空间内(表面)任意一点承受时间谐和的出平面线源载荷作用时位移函数的基本解答. 利用裂纹``切割'方法在任意位置构造任意方位的裂纹,可以得到基体中圆柱形弹性夹杂和裂纹同时存在条件下的位移场与应力场. 通过数值算例,讨论各种参数对夹杂上方地表位移的影响.      

深埋椭圆形片状裂纹的偏折扩展

基于无限大弹性基体深埋椭圆形片状裂纹的变形场,推导了椭圆形片状裂纹的能量释放率,采用能量平衡方法建立了椭圆形片状裂纹承受拉应力和剪应力时的复合断裂准则. 考虑裂纹在拉-剪应力作用下的偏折扩展,分析了裂纹的偏折方向,提出了椭圆形片状裂纹发生偏折扩展时的初始偏折位置的确定方法.      

Self-Similar Unsteady Viscous Flow

Four examples of self-similar flows of a viscous fluid are considered: separated flow over an expanding plate immersed in an unbounded unsteady viscous flow, the evolution of the velocity field induced by a vortex-source, the flow near an unsteadily moving permeable flat plate, and the flow near an unsteadily rotating disc. For the first example, a numerical solution is constructed. For the next two examples, an analytical solution is found, while the solution of the last problem is reduced to a system of ordinary differential equations.     

Optimal spacecraft terminal attitude control synthesis by the quaternion method

We consider an optimal control problem of spacecraft retargeting from an arbitrary initial position to a given terminal angular position. The objective is to minimize a path functional. Using the quaternion method, we obtain an analytic solution of this problem and present formalized equations and computational expressions for synthesizing an optimal manoeuvre program. We also present an example and the results of mathematical simulation of the spacecraft motion dynamics under an optimal control, which demonstrate the practical implementability of the control method developed in the present paper.     

Experimental Investigation of the Interaction between an Electric Arc and a Gas Flow

The results of investigating the shape of an electric arc carrying an electric current of less than 100 A and exposed to an air, nitrogen, or argon stream at a stream velocity of from zero to 20 m/s, when the interelectrode gap is less than 20 mm, are reported. The shape of the arc is qualitatively investigated as a function of the gas type, blowing velocity, and interelectrode gap. It is shown that an arc burning in a channel with insulated walls is much more stable under these conditions than an arc with the same parameters burning in free space.     

A partially implicit method for simulating viscous aerofoil flows

A partially implicit method for the unsteady compressible Navier-Stokes equations is developed. The method is based on an explicit treatment of streamwise fluxes and an implicit treatment of normal fluxes. This leads to a linear system which is generated by an efficient finite difference procedure and which is block pentadiagonal. The method is tested on a shock-induced oscillatory flow over an aerofoil. Parallel implementations of an explicit, fully implicit and partially implicit method are investigated.     

压电复合材料中的Eshelby夹杂问题

通过采用解析延拓和共形映射技术，获得了压电复合材料中有关Eshelby夹杂几个典型问题的精确弹性解答，即横观各向同性压电介质中任意形状的Eshelby夹杂与圆柱异相夹杂间相互作用；一般各向异性压电介质中任意形状的Eshelby夹杂与双压电材料所形成界面的相互作用．成功求解这些问题的关健在于构造一个辅助函数．与Ru所采用的方法不同，所引入的辅助函数在无穷远点不存在极点，从而使得所展开的分析更加自然合理．分析结果清楚地揭示出Eshelby夹杂的存在对压电复合材料机电耦合响应将产生不容被忽视的影响．很典型的一个例于是当一个Eshelby椭圆夹杂与圆柱异相夹杂相互作用时，每个夹杂体内部的应力场和电场都将是不均匀的；另一个例于是位于界面附近的Eshelby夹杂有可能是界面发生损伤的一个重要原因．     

Surface tension-induced stress concentration around an elliptical hole in an anisotropic half-plane

We examine the surface tension-induced stress concentration around an elliptical hole inside an anisotropic half-plane with traction-free surface. Using conformal mapping techniques, the corresponding complex potential in the half-plane is expressed in a series whose unknown coefficients are determined numerically. Our results indicate that the maximum hoop stress around the hole (which appears in the vicinity of the point of maximum curvature) increases rapidly with decreasing distance between the hole and the free surface. In particular, for an elliptical or even circular hole in an anisotropic half-plane we find that, with decreasing distance between the hole and the free surface, the hoop stress can switch from compressive to tensile at certain points on the hole's boundary and from tensile to compressive at others. This phenomenon is absent in the case of an elliptical or even circular hole in the corresponding case of an isotropic half-plane.     

Elastic Anisotropic Material with Purely Longitudinal and Transverse Waves

The simplest form of the matrix of elasticity moduli of an anisotropic material conducting purely longitudinal and transverse waves with an arbitrary direction of the wave normal is obtained. A generic solution of equations in displacements is represented in terms of three functions satisfying independent wave equations. In the case of planar deformation, this solution yields a complex representation coinciding with the Kolosov–Muskhelishvili formulas for an isotropic material. The formulas in the present work also determine an anisotropic material with Young's modulus identical for all directions, as in an isotropic medium.     

基于实测挠度、转角和曲率的细长梁分段抗弯刚度识别研究

静载试验是获得结构真卖特性的重要方法和途径，具有直观、可靠的特点。本文基于静载试验实测的挠度、转角和曲率，建立目标函数，通过优化的方法，实现结构分段截面抗弯刚度参数的识别。研究了优化目标函数的建立、优化算法的选取与实现；通过数值算例和一片简支梁静载试验实例分析，对方法的正确性与可行性进行了验证，所得结果可用于结构损伤识别和安全性能评估。     

A wave-oriented meshless formulation for acoustical and vibro-acoustical applications

Simulating acoustical or vibro-acoustical waves within the medium frequency range is still an open problem today. In this paper, we first demonstrate that it is possible to formulate an improved element-free Galerkin method (I-EFGM) for the uncoupled acoustical problem applied to three-dimensional complex geometries. Then, we develop a partition of unity formulation extended for the elastodynamics (PUM-dyn). Finally, by coupling both formulations with an appropriate formulation for 2D vibro-acoustical coupled problems, we demonstrate that an I-EFGM coupled to the PUM-dyn seems to be an excellent way to reach the medium frequencies accurately and with an acceptable CPU time.     

Deformations of an elastic pipe submitted to gravity and internal fluid flow

This paper describes the deformation of an elastic pipe submitted to gravity and to an internal fluid flow. The pipe is clamped horizontally at one end and free at the other end. As the fluid velocity increases, the shape changes from an elastic beam deflected by its own weight towards an horizontal position. The shape of the pipe is characterized experimentally and is compared with a theoretical model based on the Euler–Bernoulli approximation and the conservation of the fluid momentum. We study how the determination of the pipe deformation provides an estimation of the conveyed fluid flow. Finally, the vertical force produced by the conveyed fluid to lift off a mass is deduced.     

Convective self-oscillations near an air-bubble surface in a horizontal rectangular channel

The concentration convection in an isothermal fluid near an air bubble clamped between the vertical walls of a horizontal channel with a rectangular cross-section is studied experimentally and numerically. The channel is filled with an aqueous solution of a surfactant with a nonuniform concentration. As a result of the competition between the gravitational convection in the cavity volume and the Marangoni convection near the bubble surface, an oscillation flow regime is established. This regime is observed experimentally over several hours. In the numerical experiment, the oscillations are obtained in the presence of an initial horizontal surfactant concentration gradient. Against the background of gravitational convection, short bursts of Marangoni convection with ten times greater intensity are observed. The convective flow patterns and the oscillation periods obtained experimentally and numerically are in fairly good agreement.     

Uniform difference scheme for a singularly perturbed linear 2nd order hyperbolic problem with zeroth order reduced equation

In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.     

On a novel expression of the field scattered by an arbitrary constant impedance plane

The electromagnetic field scattered by an impedance plane is generally given by its plane wave expansion (Fourier representation). Here we derive an alternative expression which is more suitable for point source illumination. For this, we consider an original expression of the Hertz potentials for the incident field and express the scattered potentials in a novel form. A special function then involved can be expressed in an integral which is in turn expanded in a convergent series. The expression presented also permits us to express complete asymptotics. Our development considers an arbitrary impedance, passive or active.     

Non-linear argumental oscillators: Stability criterion and approximate implicit analytic solution

The behaviour of a space-modulated, so-called “argumental” oscillator, is studied. The oscillator is submitted to an external harmonic force, which is amplitude-modulated by the oscillator's position in space. An analytic expression of a stability criterion is given. Using the averaging method, an integrating factor and a Van der Pol representation in the (amplitude, phase)-space, an exact implicit analytic solution is given when there is no damping, and an approximate implicit analytic solution is given when there is damping, allowing the plotting of the separatrix curve. An attractor is identified.     

Analysis of piezoelectric ceramic multilayer actuators based on an electro-mechanical coupled meshless method

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. In this method, an element free Galerkin (EFG) formulation, an enriched basic function and some special shape functions that contain discontinuous derivatives are employed. Based on the moving least squares (MLS) interpolation approach, the EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional finite element method (FEM) is avoided. The numerical results show that the proposed method can yield an accurate near-tip stress field in an infinite piezoelectric plate containing an interior hole. In another example studying a ceramic multilayer actuator, the proposed model was found to be accurate in the simulation of stress and electric field concentrations arround the abrupt end of an internal electrode. The project supported by the National Natural Science Foundation of China (10025209, 10132010, and 90208002), and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7203/03E). The English text was polished by Yunming Chen.