弹性基础上对称叠层厚板的基本解

利用平面波分解法将弹性地基础上计入剪切变形的对称叠层厚板的偏微分方程组转化常微分方程组，然后利用Ｈ¨ｏｒｍａｎｄｅｒ算子法将常微分方程组转化为一个六阶的常微分方程，以定积分的形式提出了弹性基础上对称叠层厚板的基本解．     

四边简支正交各向异性圆柱扁壳的后屈曲和非线性振动

本文在几何非线性三维弹性理论的基础上,通过量级分析导出了考虑横向剪切效应的正交各向异性纤维增强复合材料扁壳的基本方程,并应用伽略金方法求得了四边可动简支正交各向异性圆柱形扁壳后屈曲变形和非线性自由振动问题的数值解。计算结果表明:对于复合材料而言,横向剪切效应是值得注意的。     

厚板结构抗爆炸分析的有限条法

所取厚板条考虑横向剪切变形和转动惯量,并取它的各阶振型为条向连续函数。在厚板条的横向,三个独立变量(挠度和二向转角)采用四次多项式。厚板条的质量矩阵计入转动惯量。用这种厚板条法分析厚板结构在爆炸荷载(或静荷载)作用下的动(静)位移和动(静)内力。给出不同模型的数值结果,并与解析解、有限元解进行比较,表明本文的方法用于厚板结构抗爆炸分析具有精度高、自由度少的特点。     

用有限厚条法计算弹性厚板振动

取考虑横向剪切变形和转动惯量的厚板条的各阶振型作为有限厚条的条向连续函数,在板条的横向每一边采用四次多项式的三个独立变量(挠度和二向转角),质量矩阵计入转动惯量的有限厚条法被用来分析矩形弹性厚板的横向振动。给出了不同模型的数值结果,并与解析解、有限元解和一般有限条解等进行比较,表明本文的方法具有精度高,自由度少的特点。     

各向异性弹性厚板的振动

本文推导了一种具有一个弹性对称面的各向异性厚板的一般性动力方程,给出了适用于各种边界条件正交异性矩形厚板振动问题的一般解。     

加权残数配点法解正交各向异性板的积分方程

本文推导了一般各向异性板弯曲的积分方程,运用加权残数配点法求解了正交各向异性板弯曲的积发方程,本文将部分配点取在边界上,另一部分配点取在域外,只用关于找度的基本积分方程,而不用关于转角的补充积分方程,简化了方程求解和计算程序,由于正交各向异性板没有争析形式的、实用的基本解,本文提出了两种新的近似基本解;加权双三角级数;广义各向同性板解析形式的基本解和加权双三角级数的叠加,算例表明,本文提出的解法和近似基本解适用于各类边界条件的正交各向异性板,具有简单、可靠、精度高等优点。     

变系数渗流场的正交各向异性边界元分析

本文给出了计算复杂渗流场的简化方法.首先由加权余量法得到变系数渗流问题的积分方程.再将区域及边界剖分,对各单元使用形心处的渗透系数而化为正交各向异性问题.最后用正交各向异性问题的基本解,得到对应于边界单元法的线性代数方程组.算例表明方法可靠.     

横观各向同性介质中椭圆夹杂受非弹性剪切变形引起的弹性场的确定

本文求解了横观各向同性介质中椭圆夹杂内受非弹性剪切变形引起的弹性场。采用各向异性弹性力学平面问题的复变函数解法，结合保角变换，获得夹杂内应变能和基体内边界的应力分布和相应的应变能的表达式。进一步，根据最小应变能原理，获得表征夹杂平衡边界的两个特征剪切应变，从而得到了弹性场的解析解。通过应力转换关系，验证了应力解满足夹杂边界上法向正应力和剪应力的连续条件，表明了该解的正确性。本文解可用于复合材料断裂强度的分析中。     

用Tchebychev多项式逼近边界元法中的基本解

正交各向异性板动力问题的边界元法之难点在于找不到其封闭形式的基本解。因此。寻找一种适用性强,精度高、使用方便的求近似基本解的方法,在边界元法的应用中具有重要意义。本文用Tchebychev多项式组成广义双Fourier级数逼近问题的基本解,由算例表明该方法是令人满意的。     

动力边界元法的正交多项式函数的近似基本解研究

为了克服在用边界元法求解正交各向异性板的动力问题时寻求相应的基本解的困难,本文探讨了二种类型的近似基本解:级数形式及迭加修正形式的近似基本解。前者由正交函数系组成,本文中采用了Hermite正交多项式。后者由相近问题(广义各向同性板静力弯曲问题)的解析基本解迭加上用以修正的级数项组成。一些算例说明了近似基本解方法的可行性和有效性。迭加修正形式的解具有较高精度和较快收敛性,比单纯的级数形式解来得优越。     

Boundary element method for orthotropic thick plates

The fundamental solutions of the orthotropic thick plates taking into account the transverse shear deformation are derived by means of Hörmander's operator method and a plane-wave decomposition of the Dirac δ-function in this papey. The boundary integral equations of the thick plates have been formulated which are adapted to arbitrary boundary conditions and plane forms. The numerical calculation of the fundamental solutions is discussed in detail. Some numerical examples are analyzed with BEM.     

Multiple mode large amplitude vibration of thick orthotropic circular plates

This paper is analytically concerned with the large amplitude vibration of thick orthotropic circular plates incorporating the effects of transverse shear and rotatory inertia. Von Kármán-type field equations written in terms of the three displacement components of the plate are utilized to obtain solutions to clamped stress-free and immovable plates. By means of Galerkin's technique and a numerical Runge-Kutta procedure a multiple-mode analysis is carried out in both cases. Exact solutions are reported for two of the three governing equations. Effects of transverse shear deformation and modal interaction are found to be significant for orthotropic thick plates. The method given here could be extended to the multiple-mode analysis of circular plates with other boundary conditions.     

BOUNDARY INTEGRAL EQUATIONS FOR BENDING PROBLEM OF REISSNER'S PLATES ONTWO-PARAMETER FOUNDATION

I.IntroductionThickplatesonelastict'oundationarewidelyusedinengineering,suchasthebottomplatesofoffShorestructures,surfaceplatesonrunwayofairportsandfoundationsofhigh-risebuildingsandthelike.Itisextremelydifficulttoobtainanalyticalsolutiontarathickplatewithcomplicatedshapeorcomplicatedboundaryconditiononelasticfoundation.Inrecentyears,theboundaryelementmethod(BEM)hasbeensuccessl'ullyusedtoanalyzethebendingproblemofplatesoneverykindofelasticfoundation(Ref.[l,2.3]).Butthereareonlyfewreferences…     

Boundary integral equations for bending problem of Reissener's plates on two-parameter foundation

Two fundamental solutions for bending problem of Reissner's plates on two-parameter foundation are derived by means of Fourier integral transformation of generalized function in this paper. On the basis of virtual work principles, three boundar integral equations which fit for arbitrary shapes, lods and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates. It provides the fundamental theories for the application of BEM. A numerical example is given for clamped, simply supported and free boundary conditions. The results obtained are satisfactory as compared with the analytical methods. Project supported by the P.H.D. Foundation of National Education Committee of China     

Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effects

Based on the Reddy ‘s theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature ( DQ ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert ( DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.     

A boundary integral equation formulation for the Reissner's plates resting on two-parameter foundation

In this paper a boundary integral equation formulation for the Reissner's plates resting on a two-parameter foundation is established. With the aid of the Hormander Operator method, the equations of the corresponding fundamental solutions are converted into a sixth order partial differential equation with a scale function as an unknown. In order to reduce the equation further, two auxiliary functions are introduced. They satisfy a second and a fourth order equation respectively. The expressions of the auxiliary functions can be derived easily. The fundamental solutions of the Reissnei's plates on the two-parameter foundation arc expressed by a linear combination of the auxiliary functions and their derivatives. The boundary integral equations are formulated by the use of the weighted residual procedure. The fundamental solutions obtained are taken as the kernel functions of the boundary integral equations. A few examples are studied. The numerical results show high accuacy and efficiency of the present formulation.This work was supported by the National Natural Science Foundation of China.     

板结构计算模型的新发展

现代复合材料层合板具有高强和轻型的突出优点，从而在军工和民用等诸多领域发挥着重要作用。这种板结构的特点是随着纤维走向的不同，层间材料的物理-力学特性发生剧烈变化。沿板厚方向变形的梯度比较陡峭，并在层间结合面处发生强不连续，呈现zig-zag （锯齿状）现象。这导致横向剪应变在板的静态和动态响应中发生重要作用，不计横向变形的经典组合板计算模型CLPT难以适应现代多层板计算分析的需要。考虑横向剪切变形影响的板的计算模型得到重视和发展。需要指出，现有各种考虑剪切变形影响的计算模型虽然有了很大的发展，但在全面和准确性上仍然存在一定的不足，难以适应现代多层组合板横向力和物理性能多变的情况。模型预测的沿板厚方向位移和应力的变化规律难以通过严格的检验。本文提出的以比例边界有限元为基础的正交各向异性板的数值计算模型，同时可适用于各种薄板与厚板的分析，对现代复合材料层合板的分析具有特殊的优越性。所得到的板的位移、正应力和剪应力沿板厚方向的变化，与三维弹性理论的标准解高度吻合。数值算例进一步表明，随着层间纤维走向的变化，板内位移场和应力场沿板厚方向剧烈变化所呈现的锯齿现象均可以精准地进行模拟。据此，本文建议方法对现代板分析的广泛适应性和高度准确性得到了充分论证。     

SH波在正交各向异性功能梯度无限长条中心裂缝处的散射

研究了正交各向异性功能梯度材料无限长条中心裂缝对SH波的散射问题,为方便起见,材料两个方向的剪切模量和密度假定为指数模型.通过Fourier积分变换,将问题转化为对偶积分方程的求解.然后,用Cop-son方法求解对偶积分方程,定义了标准动应力强度因子,通过数值算例,讨论了在SH波作用下,裂缝尖端的标准动应力强度因子与入射波的频率、材料参数之间的关系.     

Time-harmonic Green's function and boundary integral formulation for incremental nonlinear elasticity: dynamics of wave patterns and shear bands

Superimposed dynamic, time-harmonic incremental deformations are considered in an elastic, orthotropic and incompressible, infinite body, subject to plane, homogeneous—but otherwise arbitrary—deformation. The dynamic, infinite body Green's function is found and, in addition, new boundary integral equations are obtained for incremental in-plane hydrostatic stress and displacements. These findings open the way to integral methods in incremental, dynamic elasticity. Moreover, the Green's function is employed as a dynamic perturbation to analyze interaction between wave propagation and shear band formation. Depending on anisotropy and pre-stress level, peculiar wave patterns emerge with focussing and shadowing effects of signals, which may remain undetected by the usual criteria based on analysis of weak discontinuity surfaces.