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

<正> 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