反平面弹性中边缘内分叉裂纹的奇异积分方程解法

利用复变函数和奇异积分方程方法,求解反平面弹性中半平面边缘内分叉裂纹问题。提出了满足半平面边界自由的由分布位错密度表示的半平面中单裂纹的基本解,此基本解由主要部分和辅助部分组成。将半平面边缘内分叉裂纹问题看作是许多单裂纹问题的叠加,建立了以分布位错密度为未知函数的Cauchy型奇异积分方程组。然后,利用半开型积分法则求解奇异积分方程,得到了裂纹端处的应力强度因子。文中给出两个数值算例的计算结果。     

半平面多边缘裂纹反平面问题的奇异积分方程

利用复变函数和奇异积分方程方法,求解弹性范围内半平面多边缘裂纹的反平面问题．提出了满足半平面边界自由的由分布位错密度表示的单边缘裂纹的基本解,此基本解由主要部分和辅助部分组成．将半平面多边缘裂纹问题看作是许多单边缘裂纹问题的叠加,建立了一组Cauchy型奇异积分方程．然后,利用半开型积分法则求解该奇异积分方程,得到了裂纹端处的应力强度因子．最后,给出了几个数值算例．     

SH波对浅埋裂纹的半圆形凹陷地形的散射

采用Green函数方法，研究浅埋裂纹和含有圆形凹陷的弹性半空间对入射SH波的散射。首先取含有半圆形凹陷的弹性半空间，任意一点承受时间谐和的出平面线源荷载作用时的位移函数基本解作为Green函数；然后求解含半圆形凹陷的弹性半空间对SH波的散射问题；最后在裂纹实际存在位置利用Green函数实施裂纹的人工切割以恢复存在的裂纹，给出浅埋裂纹的半圆形凹陷弹性空间内的位移函数，进而求解裂纹存在对地表位移的影响。     

含半无限裂纹的各向异性体平面问题基本解

应用复变函数的方法，给出了含半无限裂纹的各向异性平面在任意面内集中载荷作用下的复应力函数和应力强度因子基本解；指出了现有文献中的一些错误结果．     

弹性半平面中边界裂纹研究的新方法

讨论了载荷作用在裂纹面上的弹性半平面边界裂纹问题.研究以线弹性断裂力学为基础,采用复变函数方法以及Riemann-Hilbert(R-H)边值问题的一般理论,将问题分拆为含有限裂纹的全平面问题与无裂纹的半平面问题的叠加,计算得到裂纹尖端的应力强度因子.与文献结果比较,该方法具有精度高的优点.     

一类半平面焊接的界面裂纹问题

利用复变方法和解析函数边值问题的基本理论，研究一类带孔洞的两个半平面焊接的界面裂纹问题。通过适当的函数分解和消元方法，将问题转化为一类简单的Riemann边值问题，从而得到弹性体应力函数的封闭解，给出了裂纹尖端应力强度因子的一般表达式。     

一维六方准晶中椭圆孔边裂纹的静态与动态分析

通过构造保角映射函数,借助复变函数方法,研究了一维六方准晶中椭圆孔边裂纹的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子的解析解.当椭圆的长、短半轴以及裂纹长度变化时,所得结果不仅可以还原为Griffith裂纹的情形,而且得到孔边裂纹问题、T型裂纹问题和半无限平面边界裂纹问题的应力强度因子的解析解.就声子场而言,这些解与经典弹性的结果完全一致.接着对椭圆孔边裂纹的动力学问题进行了研究,并得到了Ⅲ型动态应力强度因子的解析解.当裂纹速度V→0时,动力学解还原为静力学解.这些解在科学与工程断裂中有着潜在的应用价值.     

有限宽板边裂纹上作用一对集中力时的应力强度因子K_1

对于无限大板及半无限大板的带裂纹平面问题,可用积分变换和复变函数等解析方法得到解析解。但是,确定有限尺寸带裂纹体的应力场及应力强度因子,由于数学上存在着很大困难,目前还只能采用数值解法和近似分析解...     

SH波对内含裂纹衬砌结构的散射及动应力集中

当衬砌结构内含裂纹时 ,采用Green函数的方法 ,研究了SH波对裂纹的散射及其动应力集中 ,构造了在含有半圆形衬砌的弹性半空间上 ,在水平面上任一点承受时间谐和出平面线源载荷作用时的位移函数作为Green函数 ;推导了SH波对衬砌内有裂纹的散射定解积分方程组 ,进而求得裂纹尖端的动应力因子 ,重点讨论了衬砌及周围介质对裂纹尖端动应力因子的影响 ,给出了介质参数变化对裂纹尖端动应力因子的影响曲线 ,为工程设计提供了依据。     

带单裂纹弹性半平面问题的几个解答

在论文[1]的基础上,文中提出了弹性半平面多裂纹问题的一个基本解。利用基本解和迭加原理,文中得出了弹性半平面多裂纹问题的Fredholm积分方程组。文中还给出了弹性半平面单裂纹问题的5个算例和解答。     

Thermoelastic buckling behavior of thick functionally graded rectangular plates

Thermoelastic buckling behavior of thick rectangular plate made of functionally graded materials is investigated in this article. The material properties of the plate are assumed to vary continuously through the thickness of the plate according to a power-law distribution. Three types of thermal loading as uniform temperature raise, nonlinear and linear temperature distribution through the thickness of plate are considered. The coupled governing stability equations are derived based on the Reddy’s higher-order shear deformation plate theory using the energy method. The resulted stability equations are decoupled and solved analytically for the functionally graded rectangular plates with two opposite edges simply supported subjected to different types of thermal loading. A comparison of the present results with those available in the literature is carried out to establish the accuracy of the presented analytical method. The influences of power of functionally graded material, plate thickness, aspect ratio, thermal loading conditions and boundary conditions on the critical buckling temperature of aluminum/alumina functionally graded rectangular plates are investigated and discussed in detail. The critical buckling temperatures of thick functionally graded rectangular plates with various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.     

矩形屈曲板受微扰时的浑沌现象

用Ｍｅｌｎｉｋｏ－Ｈｏｌｍｅｓ方法研究四边简支的弹性矩形薄板可能发生浑沌振动的临界条件，所提出的方法适用于具有各种边界条件和载荷工况 大量的其它类似问题。     

An embedding method for modeling micromechanical behavior and macroscopic properties of composite materials

This paper presents a numerical method for modeling the micromechanical behavior and macroscopic properties of fiber-reinforced composites and perforated materials. The material is modeled by a finite rectangular domain containing multiple circular holes and elastic inclusions. The rectangular domain is assumed to be embedded within a larger circular domain with fictitious boundary loading represented by truncated Fourier series. The analytical solution for the complementary problem of a circular domain containing holes and inclusions is obtained by using a combination of the series expansion technique with a direct boundary integral method. The boundary conditions on the physical external boundary are satisfied by adopting an overspecification technique based on a least squares approximation. All of the integrals arising in the method can be evaluated analytically. As a result, the elastic fields and effective properties can be expressed explicitly in terms of the coefficients in the series expansions. Several numerical experiments are conducted to verify the accuracy and efficiency of the numerical method and to demonstrate its application in determination of the macroscopic properties of composite materials.     

INTERACTION OF THREE PARALLEL CRACKS IN RECTANGULAR PLATE UNDER CYCLIC LOADS

This paper presents a numerical approach for modeling the interaction between multiple cracks in a rectangular plate under cyclic loads. It involves the formulation of fatigue growth of multiple crack tips under ruixed-mode loading and an extension of a hybrid displacement discontinuity method （a boundary element method） to fatigue crack growth analyses. Because of an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, remeshing of existing boundaries is not necessary for each increment of crack extension. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, the numerical approach is used to analyze the fatigue growth of three parallel cracks in a rectangular plate. The numerical results illustrate the validation of the numerical approach and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

Enhancement of elementary beam theories in order to obtain exact solutions for elastic rectangular beams

Boley's method is utilized in order to show that the elementary Bernoulli–Euler beam theory can be enhanced such that exact solutions of the plane-stress theory of linear elasticity are obtained for force loaded rectangular beams. An equivalent enhancement is derived for the elementary Timoshenko theory of beams. The enhancement terms act analogous to thermal loadings; they follow from the force loading of the rectangular beam in an explicit form. The resulting boundary value problem of fourth order can be efficiently solved by means of symbolic computer codes. As an illustrative example, a redundant beam is studied, which is simply supported at one end, and which is clamped at the other end. Outcomes for three alternative clamped end boundary conditions are compared.     

非完善板屈曲路径的有限元增量摄动法

本文以Thompson一般稳定性理论为基础,提出非完善结构(有初始几何缺陷)屈曲平衡路径分析的有限元增量摄动法,它克服了增量迭代法及摄动法各自的缺点,利用增量摄动法,还建立了非完善板屈曲平衡路径的数学分析模型,对非完善矩形板在各种边界条件下的屈曲路径实现了数值程序分析,得到了符合实验的结果。     

Thermoelastoplastic Stress-Strain State of Rectangular Plates

A technique is proposed to solve a thermoplastic problem for rectangular plates of varying thickness with arbitrary boundary conditions at all edges. The technique is based on the hypothesis of rectilinear element, the theory of simple loading, and the method of complete systems __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 53–63, October 2005.     

A differential quadrature procedure for three-dimensional buckling analysis of rectangular plates

This paper presents an application of the differential quadrature (DQ) method for three-dimensional buckling analysis of rectangular plates. The governing equations of the plate model are first presented in terms of displacement, stress displacement relationship, and boundary conditions with three-dimensional flexibility. These equations are then normalised and discretised using the DQ procedure. Example problems pertaining to the buckling of rectangular plates with generic boundary conditions are selected to illustrate the efficiency and simplicity of implementing the DQ procedure. The convergence characteristics of the method are first conducted based on numerical studies. The DQ solutions are then compared, where possible, with exact or approximate solutions. It is found that the differential quadrature method yields accurate results for the plate problems under the current investigation. In addition to the above, some parametric studies are carried out by varying the plates aspect ratio, boundary conditions and thickness to width ratio under axial and biaxial loading.     

Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

In this research work, an exact analytical solution for buckling of functionally graded rectangular plates subjected to non-uniformly distributed in-plane loading acting on two opposite simply supported edges is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the classical plate theory based on exact neutral surface position is employed to derive the governing stability equations. Considering Levy-type solution, the buckling equation reduces to an ordinary differential equation with variable coefficients. An exact analytical solution is obtained for this equation in the form of power series using the method of Frobenius. By considering sufficient terms in power series, the critical buckling load of functionally graded plate with different boundary conditions is determined. The accuracy of presented results is verified by appropriate convergence study, and the results are checked with those available in related literature. Furthermore, the effects of power of functionally graded material, aspect ratio, foundation stiffness coefficients and in-plane loading configuration together with different combinations of boundary conditions on the critical buckling load of functionally graded rectangular thin plate are studied.     

Transient response of a rectangular piezoelectric medium with a center crack

The dynamic field intensity factors and energy release rates in a rectangular piezoelectric ceramic medium containing a center crack are obtained for boundary conditions of a permeable and an impermeable crack under electro-mechanical impact loading. An integral transform method is used to reduce the problem to two pairs of dual integral equations, which are then expressed as Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate are obtained to show the dependences upon the geometry and electric field.