GENERAL SOLUTION OF MULTI-VALUED DISPLACEMENT PROBLEM OF AN ECCENTRIC CIRCULAR RING

In this paper.by using N.I.Muskhelishvili’s method a mul-ti-valued displacement problem is Considered for an eccentriccircular ring.The gereral expression of stress function isderived in the bipolar coordinate system and its application isexplained.     

The Bending of Elastic Circular Ring of Non-homogeneous and Variable Cross Section under the Actions of Arbitrary Loads

On the basis of the stepped reduction method suggested in[1],we investigatethe problem of the bending of elastic circular ring of non-homogeneous andvariable cross section under the actions of arbitrary loads.The general solutionof this problem is obtained so that it can be used for the calculations of strengthand rigidity of practical problems such as arch,tunnel etc.In order to examineresults of this paper and explain the application of this new method,an exampleis brought out at the end of this paper.Circular ring and arch are commonly used structures in engineering.Timo-shenko,S.,Barber,J.R.,Tsumura Rimitsu et al.have studied theseproblems of bending,but,so far as we know,it has been solely restricted to thegeneral solution of homogeneous uniform cross section ring.The only knownsolution for the problems with variable cross section ones has been solelyrestricted to the solution of special case of flexural rigidity in linear functionof coordinates.On account of fundamental equations of the non-homoge     

General solution of multi-valued displacement problem of an eccentric circular ring

In this paper, by using N.I, Muskhelishvili’s method a multi-valued displacement problem is considered for an eccentric circular ring. The general expression of stress function is derived in the bipolar coordinate system and its application is explained.     

The bending of elastic circular ring of non-homogeneous and variable cross section under the actions of arbitrary loads

On the basis of the stepped reduction method suggested in [1], we investigate the problem of the bending of elastic circular ring of non-homogeneous and variable cross section under the actions of arbitrary loads. The general solution of this problem is obtained so that it can be used for the calculations of strength and rigidity of practical problems such as arch, tunnel etc. In order to examine results of this paper and explain the application of this new method, an example is brought out at the end of this paper. Circular ring and arch are commonly used structures in engineering. Timoshenko, S.^[2], Barber, J. R.^[3], Tsumura Rimitsu^[4] et al. have studied these problems of bending, but, so far as we know, it has been solely restricted to the general solution of homogeneous uniform cross section ring. The only known solution for the problems with variable cross section ones has been solely restricted to the solution of special case of flexural rigidity in linear function of coordinates. On account of fundamental equations of the non-homogeneous variable cross section problem being variable coefficients, it is very difficult to solve them. In this paper, we use the stepped reduction method suggested in [1] to transform the variable coefficient differential equation into equivalent constant coefficient one. After introducing virtual internal forces, we obtain general solution of an elastic circular ring with non-homogeneity and variable cross section under the actions of arbitrary loads.     

非均匀变截面弹性圆环在任意载荷下的弯曲问题

本文在等刚度弹性圆环的初参数公式的基础上,利用[2]提出的阶梯折算法,进一步研究非均匀变截面弹性圆环的弯曲,得到了这类问题的通解,应当指出,这组通解对非均匀变截面圆柱拱的相应问题也是适用的.为验证所得的公式并说明这种方法的应用,文末给出了示例并进行了求解,圆环、圆拱是工程上经常采用的结构,它们的弯曲,Timoshenko,S.[5],Barber,J.R.[3],Roark,R J[4],津村利光[6]等曾作过很多研究.然而,迄今只求得了均匀材料、等截面圆环的通解。对变截面问题,仅仅求得了抗弯刚度是坐标的线性函数这一特殊情况的解.由于非均匀变截面问题常常导出变系数微分方程,它们的求解遇到很大的数学困难.本文通过阶梯折算法把非均匀变截面弹性圆环弯曲问题的变系数微分方程转化成一等效的等刚度圆环弯曲的常系数微分方程.为保证内力连续,引入虚拟内力,并以[1]导出的初参数公式为影响函数,通过积分构造出了非齐次解,从而求得了非均匀变截面弹性圆环弯曲问题的通解.     

偏心圆环多值位移问题的一般解

本文利用И.И.Мусхелишвили的复函数方法,研究了平面偏心圆环多值位移问题,得到了以双极坐标表示的应力函数的一般表达式,文中对表达式的应用作了说明.