平面弹性裂纹分析的一种有效边界元方法

提出了一种简单而有效的平面弹性裂纹应力强度因子的边界元计算方法．该方法由Crouch与Starfield建立的常位移不连续单元和闫相桥最近提出的裂尖位移不连续单元构成A·D2在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界．算例(如单向拉伸无限大板中心裂纹、单向拉伸无限大板中圆孔与裂纹的作用)说明平面弹性裂纹应力强度因子的边界元计算方法是非常有效的．此外,还对双轴载荷作用下有限大板中方孔分支裂纹进行了分析．这一数值结果说明平面弹性裂纹应力强度因子的边界元计算方法对有限体中复杂裂纹的有效性,可以揭示双轴载荷及裂纹体几何对应力强度因子的影响．     

Vibration of a pre-stressed plate on a transversely isotropic multilayered half-plane due to a moving load

This paper presents an analytical research on the dynamic interaction problem between a pre-stressed plate and a transversely isotropic multilayered half-plane subjected to a moving load. The pre-stressed plate is governed by the Kirchhoff plate theory, and the transversely isotropic multilayered half-plane is solved by the analytical layer-element method. Combining the frictionless contact and displacement compatibility conditions between the plate and the soil, the contact stress and the deflection of plate in the Fourier transform domain are derived. With the aid of the inverse Fourier transform, the actual solutions can be further achieved. Numerical examples are given to illustrate the influence of load speed, the rigidity of plate, the axial force applied on the plate and the stratified character of the soil.     

A new boundary element technique for solving plane problems of linear elasticity: improved theory and an application to fracture mechanics

An improved boundary element method for solving plane problems of linear elasticity theory is described. The method is based on the Muskhelishvili complex variable representation for the displacement and stress fields. The paper shows how to take account of symmetry about the x and/or y axes.The potential accuracy of the method is illustrated by its application to the calculation of stress intensity factors associated with cracks in both a square and a circular plate. The crack problem is solved using a Gauss-Chebyshev representation of a singular integral equation by a set of linear algebraic equations. The integral equation involves an analytic function which takes account of the presence of the external boundary. This function is determined directly using the boundary element method.Numerical results are believed to be more accurate than the existing published values which are quoted to four significant figures.     

Interaction of multiple cracks in a rectangular plate

This paper is concerned with interaction of multiple cracks in a finite plate by using the hybrid displacement discontinuity method (a boundary element method). Detail solutions of the stress intensity factors (SIFs) of the multiple-crack problems in a rectangular plate are given, which can reveal the effect of geometric parameters of the cracked body on the SIFs. The numerical results reported here illustrate that the boundary element method is simple, yet accurate for calculating the SIFs of multiple crack problems in a finite plate.     

基于液晶引流效应的上板游离态液晶盒数值计算研究

以小分子液晶Leslie-Ericksen理论为基础,建立液晶盒上基片游离状态的计算模型,在给出边界初始条件的基础上,运用二阶Runge-Kutta(龙格-库塔)法与中心差分法对方程组进行时空离散,通过MATLAB编写计算程序,调整计算参数得出液晶盒厚度、液晶盒两端所施加电场参数对液晶引流的影响.结果表明:液晶指向矢的大小随液晶盒上下基板所施加电场的交变而交变,并引起液晶引流速度大小交变;随着液晶盒厚度的增加,液晶盒上基片在一个周期内移动的位移也在增加;液晶盒两端所施加电场的占空比基本上不影响液晶盒上基片速度的大小,对液晶盒上基片速度最大值出现的时间点影响很大;通过与实验数据相对比,液晶盒上基片位移数值大小在同一个数量级,运动轨迹比较吻合.     

含孔薄板弯曲波动的双互易边界元法

采用双互易边界元法对开孔无限大薄板弹性波的散射与动应力集中问题进行理论分析和数值计算．基于功的互等定理,采用静力基本解建立了薄板弯曲波动问题的双互易边界积分方程．作为数值算例,计算了圆孔附近的动应力集中系数,通过与已有结果进行比较,表明该方法简单有效并能够保证计算精度．     

纯扭各向异性复合材料板断裂分析的复变函数方法

对受纯扭载荷作用的线弹性各向异性纤维复合材料板裂纹尖端附近的应力场进行探讨.选取带复参数的挠度函数,利用复变函数方法和待定系数法,借助边界条件,确定复参数,从而推出了裂纹尖端附近的弯矩、扭矩、应力和位移计算公式.所得到的公式在有关的断裂分析中有一定的实用价值和参考作用,最后给出了数值算例.     

任意形状孔口单边裂纹问题的边界配位解法

本文提出了一组复应力函数,采用边界配位方法对不同形状孔口(包括圆、椭圆、矩形及菱形孔口)的单边裂纹平板的应力强度因子进行了计算.计算结果表明,对长度和宽度远大于孔口和裂纹几何尺寸的试件,配位法与用其他方法所得的无限大板含圆或椭圆孔边裂纹问题的解符合得很好.同时,对其他孔口问题,特别是有限大板情形,本文给出了一系列计算结果.本文所提出的函数及计算过程可以应用于任意形状孔口单边裂纹平板的计算.     

Asymptotic analysis of three-dimensional dynamic equations of a thin plate : PMM vol. 38, n 6, 1974, pp. 1072–1078

Two-dimensional dynamic equations of thin plate vibrations are obtained from the three-dimensional dynamic equations of elasticity theory on the basis of an asymptotic method [1 – 3], Such an approach permits establishing the limits of applicability of the two-dimensional dynamic equations and the corresponding boundary and initial conditions, and indicating the means of obtaining refined results.The question of the construction of an inner state of stress of a thin plate under dynamic conditions is examined herein. The possibility of considering states of stress with distinct variability in time and in the coordinates and with a distinct relationship between the displacement intensities, is taken into account.     

Semianalytical methods for analyzing stress concentrations in thick-walled multilayered composites

For analyzing the stress, strain, and displacement fields in thick-walled anisotropic multilayered composites, sophisticated semianalytical solution methods based on a first-order shear deformation theory have been developed at the Insitut für Leichtbau und Kunststofftechnik and validated in a great number of numerical finite-element simulations and extensive experimental tests. A comparison of results obtained by the different methods for general multilayered composites made from unidirectional, bidirectional, and textile-reinforced layers show a good agreement.     

对称迭层矩形板的平面应力分析

常用的对称迭层板为各向异性板．根据平面应力问题的基本方程精确地用应力函数解法求得了各向异性板的一般解析解．推导出平面内应力和位移的一般公式,其中积分常数由边界条件来决定．一般解包括三角函数和双曲函数组成的解,它能满足4个边为任意边界条件的问题．还有代数多项式解,它能满足4个角的边界条件．因此一般解可用以求解任意边界条件下的平面应力问题．以4边承受均匀法向和切向载荷以及非均匀法向载荷的对称迭层方板为例,进行了计算和分析．     

On the magnitude of surface stresses of buckled plates

Considering a simply supported plate under uni-axial compression it is well-known that after buckling the stress concentrates at the unloaded boundaries as the out-of-plane displacement at the buckle causes an in-plane relaxation, i.e. a decrease of the mid-plane stress. This stress distortion is described by the so-called effective width. The knowledge of the effective width allows the calculation of the stress at the unloaded boundaries, which is usually considered as the highest stress in the plate. However, the out-of-plane displacement also bends the plate, which produces additional stresses. This article analysis the fundamental question, if the total stress at the surface of the buckle is higher than the stress at the unloaded boundaries. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

纯扭正交异性复合材料板的断裂分析

对受纯扭载荷作用的线弹性正交异性复合材料板裂纹尖端附近的断裂性态进行探讨。利用复变函数方法，通过求解偏微分方程的边值问题，推出了裂纹尖端附近的弯矩、扭矩、应力和位移的表达式，最后给出了数值算例。     

Solution of some plate bending problems using the boundary element method

Some fundamental aspects of the boundary element method of the Kirchhoff theory of thin plate flexure are given. The direct boundary integral equation method with higher conforming properties (using first-order Hermitian interpolation for plate displacement ω, and zero-order Hermitian interpolation for angle of rotation θ, the moment M andthe equivalent shear V) are used for several computational examples. They are: square plate with simply-supported or clamped edges, the same square plate with square central opening and the cantilevered triangular plates. The results of computation as compared with some known experimental and theoritical results showed that the numerical schemes seemed to be satisfactory for the practical applications.     

Inverse Design of a Displacement Body with a discrete Adjoint Method

Wind tunnel experiments at German Aerospace Center (DLR) for the analysis of laminar turbulent transition showed that a nearly linearly decreasing pressure distribution at a plate is able to suppress Tollmien-Schlichting boundary layer instabilities. Nevertheless, this pressure distribution leads to the growth of nonlinear instabilities in cross flow direction. Within up-ucoming research projects at DLR it is intended to further investigate this cross flow boundary layer instabilities. The experimental setup consists of a flat plate, a displacement body mounted above the plate and an additional supporting wing. The supporting wing prevents flow separations. The displacement body imposes the particular pressure distribution upon the upper side of the plate. However, contour and position of the displacement body is not known by detail. Therefore, the given pressure distribution is to be recreated by an inverse design procedure. The task can be seen as a design optimisation to a given pressure function. To provide a fast evaluation the discrete adjoint method of the TAU-Code is used. The problem's cost function is regarded as the residual of the current and the target pressure. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

3D elasticity analytical solution for bending of FG micro/nanoplates resting on elastic foundation using modified couple stress theory

This paper addresses a 3D elasticity analytical solution for static deformation of a simply-supported rectangular micro/nanoplate made of both homogeneous and functionally graded (FG) material within the framework of modified couple stress theory. The plate is assumed to be resting on a Winkler–Pasternak elastic foundation, and its modulus of elasticity is assumed to vary exponentially along thickness. By expanding displacement components in double Fourier series along in-plane coordinates and imposing relevant boundary conditions, the boundary value problem (BVP) of plate system, including its governing partial differential equations (PDEs) of equilibrium are reduced to BVP consisting only ordinary ones (ODEs). Parametric studies are conducted among displacement and stress components developed in the plate and FG material gradient index, length scale parameter, and foundation stiffnesses. From the numerical results, it is concluded that the out-of-plane shear stresses are not necessarily zero at the top and bottom surfaces of plate. The results of this investigation may serve as a benchmark to verify further bending analyses of either homogeneous or FG micro/nanoplates on elastic foundation.     

Hamilton力学下框筒结构剪滞翘曲位移模式研究北大核心CSCD

以等效连续化方法为基础,在Hamilton力学体系下进行框筒结构剪滞翘曲位移函数精度研究.选用不同类型的函数描述翼缘板的剪滞翘曲位移,考虑等效板的剪切变形以及纵向翘曲,得到不同位移函数下结构的总势能及对应的Lagrange函数.区别于传统变分法,该文在Hamilton力学体系下进行问题研究,导出框筒结构弯曲问题的Hamilton正则方程并利用精细积分法求解,进而计算出柱轴力并进行精度分析.算例验证结果表明:使用该方法分析框筒结构的剪力滞后效应是简单可行的;不同翘曲位移函数的选择对侧移计算结果影响不大,对轴力求解结果影响较大,二次抛物线最能反映等效翼缘板的实际翘曲位移;对比不同形式荷载作用下等效翼缘板中应力分布可知,随着外荷载合力作用点位置的升高,结构顶部负剪力滞后效应逐渐减弱至消失.     

一种有效的分析弹塑性问题的边界元法

本文提出了一组有效的边界元公式.该公式通过利用一个新的变量,使核函数仅具有lnr(r为源点和场点的距离)的较低阶奇异性,从而,在积分点的传统位移和应力公式的奇异性得到降低,且原公式中影响应力计算精度的边界层效应得到消除.同时,也避免了难于计算的参数C.将该方法应用到弹塑性分析中,数值分析结果表明该公式具有明显的优势.     

轴对称圆板(含叠层板)的三维非线性分析

本文提出了轴对称固支圆板(含叠层板)受均布横向载荷作用下的三维非线性摄动解答.文中所考虑的是一种中等大挠度的几何非线性,并采用一种发展的摄动方法对复杂的三维非线性平衡微分方程进行求解.该方法的基本思想是以二维解答为基础,对板的厚度参数进行摄动而求得相应的三维解答.文中给出了一般板及叠层板的三维非线性理论结果及数值结果,并图示出了各个应力的分布情况.而且,该三维非线性结果能退化为完全一致的相应的二维板理论非线性结果.结果表明,该方法对板的三维非线性分析是一种行之有效的方法.     

Analytical solution of piezolaminated rectangular plates with arbitrary clamped/simply-supported boundary conditions under thermo-electro-mechanical loadings

This paper extends an analytical method for static analysis of general cross-ply piezolaminated rectangular plates with any combination of clamped/simply-supported boundary conditions under uncoupled thermo-electro-mechanical loadings. This method is based on the novel superposition method and the first-order shear deformation theory (FSDT). The FSDT enables this expanded method to consider the effect of shear deformation of the plate. The process of applying electrical and thermal resultants causes some advantages due to its simplicity and less computational process. In this analysis displacement components are written in terms of unknown force and moment resultants. Using Fourier series for displacement components, mechanical, thermal, and/or electrical stress resultants, the complex governing differential equations of the plate are reduced to a set of linear algebraic equations with non-trivial solution. The obtained equations may be solved analytically to determine the unknown stress resultants. Several examples are proposed, and their obtained numerical results are compared with those available in the literature to verify the convergence, high accuracy, and the capability of the present method to analyze the static behavior of piezolaminated plates. It is found that there is high agreement between the present results with those obtained by other investigators.