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Closed‐form solution of well‐known Hencky problem without small‐rotation‐angle assumption
Author(s) -
Lian Yongsheng,
Sun Junyi,
Yang Zhixin,
He Xiaoting,
Zheng Zhoulian
Publication year - 2016
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.201600059
Subject(s) - rotational symmetry , rotation (mathematics) , constant (computer programming) , deflection (physics) , mathematics , mathematical analysis , exact solutions in general relativity , axial symmetry , transverse plane , geometry , mechanics , classical mechanics , physics , computer science , structural engineering , engineering , programming language
In this paper, the well‐known Hencky problem, the large deflection problem of axisymmetric deformation of uniformly loaded circular membranes, was resolved, where the small‐rotation‐angle assumption usually adopted in membrane problems was given up. The presented closed‐form solution has a higher accuracy than well‐known Hencky solution, a better understanding of the non‐linear behavior of the considered problem could thus be reached. The presented numerical example shows that, the important integral constant controlling differential equations should change along with the increase of the applied transverse loads, but in well‐known Hencky solution it becomes a constant due to the adopted small‐rotation‐angle assumption, resulting in the calculation error to increase, especially when the applied transverse loads is relatively large the well‐known Hencky solution will no longer apply.