Analytical solutions to edge effect of composite laminates based on symplectic dual system

In the symplectic space composed of the original variables, displacements, and their dual variables, stresses, the symplectic solution for the composite laminates based on the Pipes-Pagano model is established in this paper. In contrast to the traditional technique using only one kind of variables, the symplectic dual variables include displacement components as well as stress components. Therefore, the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously. After being introduced into the symplectic dual system, the uniform schemes, such as the separation of variables and symplectic eigenfunction expansion method, can be implemented conveniently to analyze composite laminate problems. An analytical solution for the free edge effect of composite laminates is obtained, showing the effectiveness of the symplectic dual method in analyzing composite laminates.     

SINGULAR PERTURBATIONS OF ROBIN BOUNDARY VALUE PROBLEMS FOB SEMILINEAR SYSTEMS

In this paper, we study the singular perturbations of Robin boundary value problems for semilinear systems using the method and technique of differential inequalities. We assume that the corresponding reduced system has at least one solution which is Iq -stable. This "component-wise" Iq-stability condition will allow us to obtain estimates for each component of the solution.     

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＯＦＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＶＡＬＵＥＦＲＯＢＬＥＭＳＯＦＲＥＡＣＴＩＯＮＤＩＦＦＵＳｌＯＮＥＱＵＡＴＩＯＮＷＩＴＨＤＥＬＡＹＺｈａｎｇＸｉａｎｇ（张祥）（ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ｗｕ...     

AGAIN DISCUSSING ABOUT SINGULAR PERTURBATION OF GENERAL BOUNDARY VALUE PROBLEM FOR HIGHER ORDER ELLIPTIC EQUATION CONTAINING TWO-PARAMETER

In this paper using the method of "The Two-Variable Expansion Procedure" we again discuss the construction of asymptotic expression of solution of general boundary value problem for higher order ellitptic equation containing two-parameter whose boundary condition is more general than [1]. We give asymptotic expression of solution as well as the estimation corresponding to the remainder term.     

BOUNDARY VALUE PROBLEMS OF TWO-DIMENSIONAL ANISOTROPIC BODY WITH A PARABOLIC BOUNDARY

Based upon Stroh formalism we derive a novel and convenient scheme for determiningthe elastic fields of a two-dimensional anisotropic body with a parabolic boundary subject to two kindsof boundary conditions, which are free surface and rigid surface, respectively. The correspondingGreen's functions are found by using the conformal mapping method. When the parabolic curve de-generates into a half-infinite crack or rigid inclusion, the singular stress fields near the tip of defectsare obtained. In particular, those Green's functions for a concentrated moment M_0 applied at a pointon the parabolic curve are also studied. It is easily found that arbitrary parabolic boundary value prob-lems can be solved by using these Green's functions and associate integrals.     

Reissner板弯曲问题的摄动域外奇点法

本文用摄动的方法将Ｒｅｉｓｓｎｅｒ板的变曲问题转化为一系列Ｋｉｒｃｈｏｆｆ板弯曲问题的叠加,并用后者简单的Ｇｒｅｅｎ函数按域外奇步法求解。数值算例表明,这种算法单且精度高。     

A CLASS OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR THE SECOND-ORDER E2 CLASS ELLIPTIC SYSTEMS IN GENERAL FORM

IntroductionThispaperdiscussesaclassofnonlinearboundaryvalueproblems (BVP)forthesecond_orderE2 classellipticsystemsingeneralform ,whichareofgreatimportanceinmathematicalsciencesandengineering ,andattractmoreandmoreinterestsfrommanyresearchersdomesticandabroad .ThesenonlinearBVPwerefirstintroducedbyRussianresearcher,L .V .Wolfersdorf,whereaclassofnonlinearBVPforholomorphicfunctionswasstudiedandsomeefficientresultsderived[1,2 ].LaterSigridKenchtandAliSeifMashimba[3],R .P .Gilbertandthea…     

一种基于直接计算高阶奇异积分的断裂力学双边界积分方程分析法

相对于有限元法,边界单元法在求解断裂问题上有着独特的优势,现有的边界单元法中主要有子区域法和双边界积分方程法.采用一种改进的双边界积分方程法求解二维、三维断裂问题的应力强度因子,对非裂纹边界采用传统的位移边界积分方程,只需对裂纹面中的一面采用面力边界积分方程,并以裂纹间断位移为未知量直接用于计算应力强度因子.采用一种高阶奇异积分的直接法计算面力边界积分方程中的超强奇异积分;对于裂纹尖端单元,提供了三种不同形式的间断位移插值函数,采用两点公式计算应力强度因子.给出了多个具体的算例,与现存的精确解或参考解对比,可得到高精度的计算结果.      

一种边界元分析接触问题的快速迭代算法

弹性摩擦接触问题的接触状态和接触应力的分析需要进行迭代，迭代过程是很费机时的，采用一种快速迭代算法进行迭代计算，其迭代的计算机ＣＰＵ时间约为常用迭代方法时间的１／１０左右。     

THEORETICAL RELATIONS OF BOUNDARY DISPLACEMENT DERIVATIVES AND TRACTIONS AT SINGULAR BOUNDARY POINT FOR 2D ISOTROPIC ELASTIC PROBLEMS

Although boundary displacement and traction are independent field variables in boundary conditions of an elasticity problem at a non-singular boundary point, there exist definite relations of singularity intensities between boundary displacement derivatives and tractions at a singular boundary point. The analytical forms of the relations at a singular smooth point for 2D isotropic elastic problems have been established in this work. By using the relations, positions of the singular boundary points and the corresponding singularity intensities of the unknown boundary field variables can be determined a priori. Therefore, more appropriate shape functions of the unknown boundary field variables in singular elements can be constructed. A numerical example shows that the accuracy of the BEM analysis using the developed theory is greatly increased.     

复合材料及其结构的非线性力学问题

本文根据最近文献及新近进展,讨论了复合材料及其结构的非线性力学问题,这是一个在实用上和理论上很重要并且越来越重要的问题。      

APPLICATION OF THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD TO SOLUTION OF NONLINEAR DIFFERENTIAL EQUATION

In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation ∇² u+u+ɛu ³ =b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method(DRM)in solving nonlinear differential equations.     

SINGULAR SOLUTIONS OF ANISOTROPIC PLATE WITH AN ELLIPTICAL HOLE OR A CRACK

In the present paper, closed form singular solutions for an infinite anisotropic plate with an elliptic hole or crack are derived based on the Stroh-type formalism for the general anisotropic plate. With the solutions, the hoop stresses and hoop moments around the elliptic hole as well as the stress intensity factors at the crack tip under concentrated in-plane stresses and bending moments are obtained. The singular solutions can be used for approximate analysis of an anisotropic plate weakened by a hole or a crack under concentrated forces and moments.They can also be used as fundamental solutions of boundary integral equations in BEM analysis for anisotropic plates with holes or cracks under general force and boundary conditions.     

非线性力学场论的几个基本课题

最近10年,在变形体转动的描述和应用,应变的度量和应用,以及应力,应变的客观性导数这三个非线性力学场论中互相关联的基本课题方面,提出了许多新问题,作出了大量的研究工作.本文综合介绍了其中一些方面的情况,并概述了笔者的相应工作.      

含孔von Karman板中非线性波散射与边值问题

基于ｖｏｎ Ｋａｒｍａｎ板大挠度弯曲理论,利用小参数摄动法,分析研究了含孔ｖｏｎＫａｒｍａｎ板的非线性波散射与动应力集中问题,其中一类可看成是薄板弯曲波动问题的控制方程。当有单频波入射时,由于弯曲应力与膜应力状态的非线性耦合,孔洞会产生高次谐波散射现象。建立了求解本问题的边界积分方程法,利用积分方程法交替求求这两类问题,最终可获得问题的近似分析解。     

边界积分方程中近奇异积分计算的一种变量替换法

准确估计近奇异边界积分是边界元分析中一项很重要的课题,其重要性仅次于对奇异积分的处理. 近年来已发展了许多方法,都取得了一定程度的成功,但这个问题至今仍未得到彻 底的解决. 基于一种新的变量变换的思想和观点,提交了一种通用的积分变换法, 它非常有效地改善了被积函数的震荡特性,从而消除了积分的近奇异性,在不增加计算量的情况 下, 极大地改进了近奇异积分计算的精度. 数值算例表明,其算法稳定,效率高, 并可达到很高的计算精度,即使区域内点非常地靠近边界,仍可取得很理想的结果.     

边界元法在求解复合材料力学问题中的应用

本文讨论了边界元法在求解复合材料的微观力学、宏观力学和结构力学问题中的应用,并指出边界元法用于分析复合材料及其结构的力学问题的优点和局限性。      

功能梯度压电材料圆环在位移和反对称电势边值条件下的解析解

采用了在径向极化情况下横观各向同性的线性本构关系,考虑了材料性质沿径向的梯度分布,对功能梯度压电材料圆环在给定的位移和电势边界条件下,导出了问题的一般解.推导了外壁固定、接地,内壁沿垂向有一微小位移、电势为反对称分布问题的解析解,并计算了该问题在位移和电势作用情况下的位移、电势在不同梯度分布时的数值结果.     

考虑接触应力非线性分布的接触力元模式及其验证分析

在作者提出的非连续变形计算力学模型中,采用接触力元模型描述多体接触界面上的接触特性.由于这种模型中假定接触应力沿接触界面为线性分布,从而得到的接触界面应力分布往往出现跳跃等非光滑性特征,该文对此进行了改进,采用具有高阶光滑性的非线性函数建立了能够考虑界面上接触应力非线性分布的接触力元模式,以期合理地揭示多体系统中界面的接触特性.对某一典型算例进行了数值计算,通过与大型通用非线性有限元结构分析软件ABASQUS的计算结果对比,验证了所建议计算模型的合理性与有效性.两种方法计算得到的界面接触对上的接触力基本相同;而由于采用的应力分布模式的假定不同,接触应力有所差别,由于在该文计算模型中接触对上的接触应力是按照未知量直接求得的,因此按照所建议的非线性接触力元模式所得到的接触应力更为合理.