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1.
A theory of elasticity for the bending of orthogonal anisotropic beams has been developed by analogy with the special case, which can be obtained by applying the theory of elasticity for bending of transversely isotropic plates to the problems of two deminsions. In this paper, we present a method to solve the problems of bending of orthogonal anisotropic beams and a new theory of the deep-beam whose ratio of depth to length is larger. It is pointed out that Reissner's theory to account for the effect of transverse shear deformation is not very approximate in the components of stress,  相似文献   

2.
A fundamental solution for half-plane problems which will play a key role incalculation of the stress concentration around a hole embedded in half-plane is derived by amethod combining images with direct integrations. It is more intuitive than the Fouriertransform method used by Gladwell. In addition, the principle and procedure of boundaryelement method to solve the half-plane problems are also presented by means of Betti’sreciprocal theorem in this paper.It is shown that the computing procedure for half-plane problems is much moreconvenient using the fundamental solution presented here than the one adopted by C.A.Brebbia.  相似文献   

3.
In this paper the outcome of axisymmetric problems of ideal plasticity in paper[39],[19]and[37]is directly extended to the three-dimensional problems of ideal plasticity,andget at the general equation in it.The problem of plane strain for material of ideal rigid-plasticity can be solved by putting into double hormonic equation by famous Pauli matricesof quantum electrodynamics different from the method in paper[7].We lead to the eigenequation in the problems of ideal plasticity,taking partial tenson of stress-increment aseigenfunctions,and we are to transform from nonlinear equations into linear equation inthis paper.  相似文献   

4.
According to Iliushin's small elastic-plastic deformation theory, in this paper, we derive the basic equations of planestrain problems in a power hardening and incompressible material. In addition, this paper presents two methods to solve these basic equations, i.e. the displacement function stress method and the stress function strain method. Two examples have been calculated to illustrate the application of these two methods.  相似文献   

5.
In this paper,the criteria of mixed mode brittle fractureare carefully examined. It has been shown that, the circumfer-ential strain factor criterion is rational and safe.With the exception of opening mode, mixed mode plane strainfracture of comparatively ductile materials (metals), in general,does not follow the theory of linear elastic fracture mechanics.Like the stress intensity factor that which is concerned isplaying an important role in pure opening mode crack problems.We believe that. in mixed mode crack problems, the circumferen-tial strain factor will become a parameter to determine the rateof fatigue crack propagation per cycle. and of stress corrosioncracking per unit time.  相似文献   

6.
In this paper,a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample.The elastic-plastic solutions of the crack tip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field,to calculate the plastic stress intensity factors,are also developed.Therefore,a complete analysis based on the calculation both for the crack tip field and for the whole crack body field is provided.  相似文献   

7.
In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method (F2LFEM). The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor (SIF).  相似文献   

8.
Symmetric laminated plates used usually are anisotropic plates. Based on the fundamental equation for anisotropic rectangular plates in plane stress problem, a general analytical solution is established accurately by method of stress function. Therefore the general formula of stress and displacement in plane is given. The integral constants in general formula can be determined by boundary conditions. This general solution is composed of solutions made by trigonometric function and hyperbolic function, which can satisfy the problem of arbitrary boundary conditions along four edges, and the algebraic polynomial solutions which can satisfy the problem of boundary conditions at four corners. Consequently this general solution can be used to solve the plane stress problem with arbitrary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load, tangential load and nonuniform normal load on four edges is calculated and analyzed.  相似文献   

9.
In this paper. we indicate that after the Liapunov function by using linear combinationof mechanical first integral was suggested by Chetayev in 1946.He and his students solvedstability of conservative system by means of this method. But he had trouble to solve theproblems by means of cut and try.Moreover,the condition of stability is imperfect.Solution by this method is limited for problems of purely imaginary roots.The cases of zeroroots have not been considered Condition of stability secured is more strict.This paper suggests that the differential equation can be transformed into standardform by method of cancellation of cyclic coordinates(method of lowering degree of order),and condition of stability can be determined by energy integral.By this method not only thecomputation is clear and concise.But also zero roots can be considered.Therefore theproblems of two cyclic coordinates can be transformed into second-order system,and we getnew conclusion of the condition of stability simply .As for problem  相似文献   

10.
A fundamental solution for half-plane problems which will play a key role in calculation of the stress concentration around a hole embedded in half-plane is derived by a method combining images with direct integrations. It is wore intuitive than the Fourier transform method used by Gladwell[6]. In addition, the principle and procedure of boundary element method to solve the half-plane problems are also presented by means of Betti’s reciprocal theorem in this paper.It is shown that the. computing procedure for half-plane problems is much more convenient using the fundamental solution presented here than the one adopted by C.A.  相似文献   

11.
For the treatment of plane elasticity problems the use of complex functions has turned out to be an elegant and effective method. The complex formulation of stresses and displacements resulted from the introduction of a real stress function which has to satisfy the 2-dimensional biharmonic equation. It can be expressed therefore with the aid of complex functions. In this paper the fundamental idea of characterizing the elasticity problem in the case of zero body forces by a biharmonic stress function represented by complex valued functions is extended to 3-dimensional problems. The complex formulas are derived in such a way that the Muskhelishvili formulation for plane strain is included as a special case. As in the plane case, arbitrary complex valued functions can be used to ensure the satisfaction of the governing equations. Within the solution of an analytical example some advantages of the presented method are illustrated.  相似文献   

12.
曾祥太  吕爱钟 《力学学报》2019,51(1):170-181
无限平板中含有任意形状单个孔的问题可以使用复变函数方法获得其应力解析解.对于无限平板中含有两个圆孔或两个椭圆孔的双连通域问题,也可以利用多种方法进行求解,比如双极坐标法、应力函数法、复变函数法以及施瓦茨交替法等.其中复变函数中的保角变换方法是获得应力解析解的一个重要方法.但目前尚未见到用此方法求解无限板中含有一个正方形孔和一个椭圆孔的问题.当板在无穷远处受有均布载荷和孔边作用垂直均布压力时,利用保角变换方法可以求解板中含有两个特定形状孔的问题.该方法将所讨论的区域映射成象平面里的一个圆环,其中最关键的一步是找出相应的映射函数.基于黎曼映射定理,提出了该映射函数一般形式,并利用最优化方法,找到了该问题的具体映射函数,然后通过孔边应力边界条件建立了求解两个解析函数的基本方程,获得了该问题的应力解析解.运用ANSYS有限单元法与结果进行了对比.研究了孔距、椭圆形孔大小和两孔布置方位对边界切向应力的影响,以及不同载荷下两孔中心线上应力分布规律.   相似文献   

13.
通过引入Airy应力函数,平面问题可以归结为在给定的边界条件下求解一个双调和方程.因此对双调和函数性质的研究将有利于平面问题的求解.首先给出一个有关双调和函数的引理,并分别从复变和微分两种角度提供该引理的证明.借助这个引理,提出了一种构造极坐标中Airy应力函数的观察法.最后,举例说明了该观察法在几个经典平面问题中的应用.这些例子说明,利用本的观察法可以将某些平面问题应力函数构造的过程简单化。  相似文献   

14.
圆柱型各向异性弹性力学平面问题   总被引:2,自引:1,他引:1  
本文对圆柱型各向异性弹性力学平面问题的基本方程进行了改写。在此基础上,导出了应力函数G和位移函数φ,它们满足相同的控制方程,比文〔1〕的应力函数F的控制方程要简单,便于求得特解,并有F=rG的关系。还对若干经典问题进行了求解。  相似文献   

15.
Two displacement formulation methods are presented for problems of planar anisotropic elasticity. The first displacement method is based on solving the two governing partial differential equations simultaneously/ This method is a recapitulation of the orignal work of Eshelby, Read and Shockley [7] on generalized plane deformations of anisotropic elastic materials in the context of planar anisotropic elasticity.The second displacement method is based on solving the two governing equations separately. This formulation introduces a displacement function, which satisfies a fourth-order partial differential equation that is identical in the form to the one given by Lekhnitskii [6] for monoclinic materials using a stress function. Moreover, this method parallels the traditional Airy stress function method and thus the Lekhnitskii method for pure plane problems. Both the new approach and the Airy stress function method start with the equilibrium equations and use the same extended version of Green's theorem (Chou and Pagano [13], p. 114; Gao [11]) to derive the expressions for stress or displacement components in terms of a potential (stress or displacement) function (see also Gao [10, 11]). It is therefore anticipated that the displacement function involved in this new method could also be evaluated from measured data, as was done by Lin and Rowlands [17] to determine the Airy stress function experimentally.The two different displacement methods lead to two general solutions for problems of planar anisotropic elasticity. Although the two solutions differ in expressions, both of the depend on the complex roots of the same characteristic equation. Furthermore, this characteristic equation is identical to that obtained by Lekhnitskii [6] using a stress formulation. It is therefore concluded that the two displacement methods and Lekhnitskii's stress method are all equivalent for problems of planar anisotropic elasticity (see Gao and Rowlands [8] for detailed discussions).  相似文献   

16.
各向异性介质中SH波引起的裂纹扩展   总被引:3,自引:2,他引:1  
刘殿魁 《爆炸与冲击》1990,10(2):97-106
本文利用Green函数法,求解各向异性介质中半无限长裂纹在SH波作用下,以任意速度扩展的问题。首先,利用Laplace变换和Cagniard-de Hoop反演法求解各向异性介质中反平面问题的Green函数,并利用它建立了求解裂纹扩展问题的积分方程。因为方程为Abel型的,所以可得到在SH波作用下,半无限长裂纹扩展问题的解析解。还可求得裂纹端点附近的应力和裂纹表面上位移的表达式。并对裂纹端点附近的奇异性进行讨论。最后讨论了裂纹尖端附近任一点的能量关系。并应用Griffith的能量准则,对裂纹扩展规律进行了讨论。  相似文献   

17.
本文采用Williams特征展开方法结合Lee伪应力函数方法得到了平面应变状态下不可压缩幂硬化蠕变材料中刚性片状夹杂物的奇异场和局部解.研究发现,夹杂物尖端的应力奇性为r~(-m/2),与幂硬化指数m有关;而应变奇性为r~(-1/2),与幂硬化指数无关.本文通过选择积分路径给出了近尖的局部解,并用显函数的形式给出了近尖应力和位移的角变化.  相似文献   

18.
The method is very efficient by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions to solve some plane-elastic problems under concentrated loads, in Ref.[1], this method is used to deal with the elastic problems of homogeneous plane. In this paper, it is extended to the case of dissimilar materials with co-circular cracks under concentrated force and moment. For several typical cases the solutions of complex stress function in closed form are built up and the stress intensity factors are given. From these solutions, we provide a series of particular results, in which two of them coincide with those in Refs. [1] and [6].  相似文献   

19.
幂硬化介质中平面应力动态裂纹的尖端弹塑性场   总被引:1,自引:0,他引:1  
本文采用塑性动力学方程,对幂硬化介质中平面应力动态裂纹尖端场进行了渐近分析,其结果表明:在裂纹尖端附近,应力具有的奇异性,应变具有的奇异性,其中A是一个与塑性区尺寸有关的常数因子,r是离开裂纹尖端的距离,n为硬化指数,文中给出了尖端场的控制参量D,它依赖于马赫数;并且给出了各物理量的角函数。  相似文献   

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