圆柱型各向异性弹性力学平面问题

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。

The Plane Problems of Cylindrical Anisotropic Elasticity

A new stress function G and displacement function Q are presented for the plane problems ofcylindrical anisotropic elasticity. The fundamental equations of the plane problems of cylindrical elas-ticity are adapted so that the new linear partial differential operators with constant coefficient becomean exchangeable ring for multiplication and addition. Thus the fundamental equations can be rewrittenas this form : AX= 0 where A is an operator matrix and X is the vector consists of stress and displace-ment component. Then , based on the theory of linear algebra,the displacement function Q can be ob-tained which satisfies a governing equation of a four order partial differential equation. At the sametime, after adequately conforming the equilibrium equation, we obtain the new stress function G,which satisfies the same governing equation as the one of the displacement function Q. The governingequation is simplier than the governing equation of the stress function F in the reference 1]. Thus,the particular solution to this sovernins equation is easier to get and P is equivalent to rG.After thoroughly study of the governing equation , we obtain a series of particular solutions ofboth separation variable and non-separable variable. By taking these particular solutions into applica-tion, we sucessfully resolve several classic problems including an infinite plane under a concentratedforce, a wedge under a concentrated force , an orthotropic curved bar under a load of sine or cosinedistribution. Both the displacement and stress components of these classic problems are presented here. In this article . the displacement function Q can be used to solve the problems of mixed boundaryvalues (both loads and constraints). In the previous papor3-6] the displacement function of theplane problems of rectilinearity anisotropic elasticity has been presented , but, there is no direct appli-cation of ttiat function.