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Closed‐form solution of elastic circular membrane with initial stress under uniformly‐distributed loads: Extended Hencky solution
Author(s) -
Sun Junyi,
Lian Yongsheng,
Li Yingmin,
He Xiaoting,
Zheng Zhoulian
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400032
Subject(s) - exact solutions in general relativity , stress (linguistics) , membrane , closed form expression , cylinder stress , mathematics , transverse plane , deformation (meteorology) , constant (computer programming) , mechanics , mathematical analysis , materials science , ultimate tensile strength , physics , composite material , structural engineering , chemistry , engineering , computer science , philosophy , biochemistry , linguistics , programming language
The well‐known Hencky solution is only applicable to the problem of deformation of the elastic circular membrane without initial stress under transverse uniformly‐distributed loads. The problem considered here is a more general case: an initial tensile or compressive stress has been present in the initially flat circular membrane before the membrane is subjected to the transverse loads. The closed‐form solution of the considered problem was presented and all the expressions obtained here for displacements, strains and stresses have the same form as those in the well‐known Hencky solution. The initial stress plays an important role in the determination of numerical value of the integral constant controlling membrane equation. The solution obtained here can be regressed into the well‐known Hencky solution when the initial stress is equal to zero, and it is therefore called extended Hencky solution.