Power series solution of circular membrane under uniformly distributed loads: investigation into Hencky transformation

Jun-yi Sun , Yang Rong , Xiao-ting He , Xiao-wei Gao , Zhou-lian Zheng

Abstract

In this paper, the problem of axisymmetric deformation of the circular membrane fixed at its perimeter under the action of uniformly-distributed loads was resolved by exactly using power series method, and the solution of the problem was presented. An investigation into the so-called Hencky transformation was carried out, based on the solution presented here. The results obtained here indicate that the well-known Hencky solution is, without doubt, correct, but in the published papers the statement about its derivation is incorrect, and the so-called Hencky transformation is invalid and hence may not be extended to use as a general mathematical method.

Key Words

axisymmetric deformation; membrane; power series method; Hencky transformation; Hencky solution

Address

Jun-yi Sun — College of Civil Engineering, Chongqing University, Chongqing 400045, PR China; Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400030, PR China
Yang Rong — College of Civil Engineering, Chongqing University, Chongqing 400045, PR China
Xiao-ting He — College of Civil Engineering, Chongqing University, Chongqing 400045, PR China; Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400030, PR China
Xiao-wei Gao — College of Civil Engineering, Chongqing University, Chongqing 400045, PR China
Zhou-lian Zheng — College of Civil Engineering, Chongqing University, Chongqing 400045, PR China; Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400030, PR China

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