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1.
平面弹性问题的另一种通解形式   总被引:2,自引:0,他引:2  
本文得到了平面问题以双调和混合函数表示的新的通解形式.用该函数可以同时表示出应力和位移分量,克服了用Airy 应力函数不易表示位移分量的缺点.  相似文献   

2.
<正> 求解弹性力学的空间问题,可归结为构造各种三维双调和函数.构造二维双调和函数已有许多结果.更精采的就是平面问题的复变函数方法.用任意两个解析函数将二维双调和函数表示出来.依照二维方法,本文用复变函数求解三维双调和方程,从而给出该方程的解.  相似文献   

3.
弹性力学平面问题的应力函数的选择   总被引:1,自引:0,他引:1  
弹性力学平面问题的应力解法,归之为求解满足边界条件的双调和方程.要从纯数学上来求出双调和方程的通解是很困难的,也是不必要的.所以弹性力学中不得不采用逆解法和半逆解法,来试凑出一个满足边界条件和双调和方程的解.但是,要从众多的函数中,选择一个既满足边界条件,又满足双调和方程的应力函数,谈何容易,这常使一些初学者感到束手无策.如果我们从边界上的已知应力分布规律出发,就很容易找到所需的应力函数了.例如,在直角坐标解法中,双调和方程为...  相似文献   

4.
弹性力学平面问题的应力解法,归之为求解满足边界条件的双调和方程.要从纯数学上来求出双调和方程的通解是很困难的,也是不必要的.所以弹性力学中不得不采用逆解法和半逆解法,来试凑出一个满足边界条件和双调和方程的解.但是,要从众多的函数中,选择一个既满足边界条件,又满足双调和方程的应力函数,谈何容易,这常使一些初学者感到束手无策.如果我们从边界上的已知应力分布规律出发,就很容易找到所需的应力函数了.例如,在直角坐标解法中,双调和方程为  相似文献   

5.
杨连枝  高阳 《应用力学学报》2012,29(6):666-669,772
通过将分解形式从弹性梁板推广到磁弹性广义平面问题,得到了磁弹性板的分解定理,表明表面不受外力的板内的应力状态可以分解为四部分:平面应力状态、剪切状态、Papkovich-Fadle(P-F)状态、磁应力状态。通过引入并证明了四个引理,简明直接地给出了分解定理的一个严格数学证明。此证明不依赖于双调和函数的P-F本征函数展开,且在证明过程中只应用了一些基本的数学方法,更易于理解。  相似文献   

6.
<正> 1.引言用应力函数求解弹性力学平面问题,关键在于如何选取应力函数,常用逆解法或半逆解法选取应力函数,有时进行量纲分析和应力函数在边界上的力学意义确定应力函数,或以泛复函为工具,引入双调和  相似文献   

7.
本文在文献[2]工作的基础上,首先给出严密的平面应力状态的概念,深入地研究三维问题的协调方程组,给出了平面应力状态按Airy应力函数求解时,解答应满足的协调方程组。  相似文献   

8.
<正> 按应力求解弹性力学平面问题,如果不计体力,应力函数应满足双调和方程,即▽(?)=0 (1)将其分离变量((?)=X·Y)后,可得常微分方程组  相似文献   

9.
本文以泛复变函数(简称泛复函)为工具,通过引入双调和数,构造出直角坐标和极坐标下平面应力函数的一系列特解,其中有些是以往文献中尚未出现的。  相似文献   

10.
在极坐标中构造平面弹性力学特解的一种方法   总被引:1,自引:0,他引:1  
在极坐标中构造平面弹性力学的特解,曾引起不少作者的注意,本文补充讨论了解法,并指出用Gousat公式来表示双调和函数的方法,不仅是构造特解的一个简单有效的方法,而且能方便地写出相应的位移和应力。  相似文献   

11.
板弯曲求解新体系及其应用   总被引:39,自引:3,他引:36  
钟万勰  姚伟岸 《力学学报》1999,31(2):173-184
建立平面弹性与板弯曲的相似性理论,给出了板弯曲经典理论的另一套基本方程与求解方法,然后进入哈密顿体系用直接法研究板弯曲问题.新方法论应用分离变量、本征函数展开方法给出了条形板问题的分析解,突破了传统半逆解法的限制.结果表明新方法论有广阔的应用前景.  相似文献   

12.
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   

13.
Stress calculation formulae for a ring have been obtained by using Airy stress function of the plane strain field with the decomposition of the solutions for normal stresses of Airy biharmonic equation into two parts when it is loaded under two opposite inside forces along a diameter. One part should fulfill a constraint condition about normal stress distribution along the circumference at an energy valley to do the minimum work. Other part is a stress residue constant. In order to verify these formulae and the computed results, the computed contour lines of equi-maximal shear stresses were plotted and quite compared with that of photo-elasticity test results. This constraint condition about normal stress distribution along circumference is confirmed by using Greens’ theorem. An additional compression exists along the circumference of the loaded ring, explaining the divorcement and displacement of singularity points at inner and outer boundaries.  相似文献   

14.
In the present paper,the compatibility equation for the plane stress problems of power-law materials is transformed into a biharmonic equation by introducing the so-calledcomplex pseudo-stress function,which makes it possible to solve the elastic-plastic planestress problems of strain hardening materials described by power-law using the complexvariable function method like that in the linear elasticity theory.By using this generalmethod,the close-formed analytical solutions for the stress,strain and displacementcomponents of the plane stress problems’of power-law materials is deduced in the paper,which can also be used to solve the elasto-plastic plane stress problems of strain-hardeningmaterials other than that described by power-law.As an example,the problem of a power-law material infinite plate containing a circular hole under uniaxial tension is solved byusing this method,the results of which are compared with those of a known asymptoticanalytical solution obtained by the perturbation method.  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.
1 StressFunctionEquationsofPlanarElasticBodyandConditionsofDefiniteSolutions  Analyticfunctionshavemanyimportantapplicationstotheproblemsofplanarelasticmechanicsandfluidmechanics[1~ 3].Inordertomakeacarefulstudyofthevectorfieldswithsourcesandcurls,thebia…  相似文献   

17.
In the present paper a stress general solution is obtained for the generalized plane stress problem with planar body forces, and it is demonstrated that only body force of biharmonic type ensures the compatibility with the generalized plane stress assumptions (σ 33=0). Inspired by the Filon perspective of average values, two more generalized plane stress problems with weak assumptions on the out-of-plane stress averages (\(\bar{\sigma}_{33}=0\) or \(\nabla^{2} \bar{\sigma}_{33}=0\)) are studied, and the averages of the corresponding stress fields are expressed by the Airy stress functions. The authors also provide an alternative proof of the Gregory decomposition theory.  相似文献   

18.
A boundary integral representation of plane biharmonic function is established rigorously by the method of unanalytical continuation in the present paper. In this representation there are two boundary functions and four constants which bear a one to one correspondence to biharmonic functions. Therefore the set of boundary integral equations with indirect unknowns based on this representation is equivalent to the original differential equation formulation.  相似文献   

19.
A general series solution to the magnetoelastic problem of interacting circular inclusions in plane magnetoelasticity is provided in this paper. By the use of complex variable theory and Laurent series expansion method, the general expression of the magnetic and the magnetoelastic complex potentials for the circular inclusion problem is derived. Expanding the definition of the Airy’s stress function of pure elastic field into the magnetoelastic field and applying the superposition method, the general expression then can be reduced to a set of linear algebraic equations and solved in a series form. An approximate closed form solution for the case of two arbitrarily located inclusions is also provided. For illustrating the effect of the pertinent parameters, the numerical results of the interfacial magnetoelastic stresses are displayed in graphic form.  相似文献   

20.
I.IntroductionThereareimportantapplicationsfortheor}:ofplanea'iscoelasticit}'Inthefieldsofgeology,miningandconstructingetc.,butformostproblemsofviscoelastici[}'.theirsolutionsareobtainedfromthecorrespondingelasticsolutionsb}'"leansofthecorrespondenceprinc…  相似文献   

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