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Structural Engineering and Mechanics Volume 45, Number 5, March10 2013 , pages 631-641 DOI: https://doi.org/10.12989/sem.2013.45.5.631 |
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Power series solution of circular membrane under uniformly distributed loads: investigation into Hencky transformation |
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Jun-yi Sun, Yang Rong, Xiao-ting He, Xiao-wei Gao and Zhou-lian Zheng
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| 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 | ||