Browse > Article
http://dx.doi.org/10.12989/sem.2013.45.5.631

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

Sun, Jun-Yi (College of Civil Engineering, Chongqing University)
Rong, Yang (College of Civil Engineering, Chongqing University)
He, Xiao-Ting (College of Civil Engineering, Chongqing University)
Gao, Xiao-Wei (College of Civil Engineering, Chongqing University)
Zheng, Zhou-Lian (College of Civil Engineering, Chongqing University)
Publication Information
Structural Engineering and Mechanics / v.45, no.5, 2013 , pp. 631-641 More about this Journal
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.
Keywords
axisymmetric deformation; membrane; power series method; Hencky transformation; Hencky solution;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 Alekseev, S.A. (1951), "Elastic annular membranes with a stiff centre under the concentrated force", Engineer Corpus., 10, 71-80. (in Russian)
2 Alekseev, S.A. (1953), "Elastic circular membranes under the uniformly distributed loads", Engineer Corpus., 14, 196-198. (in Russian)
3 Arjun, A. and Wan, K.T. (2005), "Derivation of the strain energy release rate G from first principles for the pressurized blister test", Int. J. Adhes. Adhes., 25(1), 13-18.   DOI   ScienceOn
4 Chen, S.L. and Zheng, Z.L. (2003), "Large deformation of circular membrane under the concentrated force", Appl. Math. Mech. (English Ed.), 24(1), 28-31.   DOI   ScienceOn
5 Chien, W.Z. (1948), "Asymptotic behavior of a thin clamped circular plate under uniform normal pressure at very large deflection", The Science Reports of National Tsinghua University, 5(1), 193-208.
6 Chien, W.Z. and Chen, S.L. (1985), "The solution of large deflection problem of thin circular plate by the method of composite expansion", Appl. Math. Mech. (English Ed.), 6(2), 103-118.   DOI
7 Chien, W.Z., Wang, Z.Z., Xu, Y.G. and Chen, S.L. (1981), "The symmetrical deformation of circular membrane under the action of uniformly distributed loads in its portion", Appl. Math. Mech. (English Ed.), 2(6), 653-668.   DOI
8 Chucheepsakul, S., Kaewunruen, S. and Suwanarat, A. (2009), "Large deflection analysis of orthotropic, elliptic membranes", Struct. Eng. Mech., 31(6), 625-638.   DOI   ScienceOn
9 Ersoy, H., Ozpolat, L. and Civalek, O. (2009), "Free vibration of circular and annular membranes with varying density by the method of discrete singular convolution", Struct. Eng. Mech., 32(5), 621-634.   DOI   ScienceOn
10 Hao, J.P. and Yan, X.L. (2006), "Exact solution of large deformation basic equations of membrane under central force", Appl. Math. Mech. (English Ed.), 27(10), 1333-1337.   DOI   ScienceOn
11 Hencky, H. (1915), "Uber den spannungszustand in kreisrunden platten mit verschwindender biegungssteifigkeit", Zeitschrift Fur Mathematik und Physik, 63, 311-317.
12 Jin, C.R. (2008a), "Large deflection of circular membrane under concentrated force", Appl. Math. Mech. (English Ed.), 29(7), 889-896.   DOI   ScienceOn
13 Jin, C.R. (2008b), "Analysis of energy release rate and bending-to-stretching behavior in the shaft-loaded blister test", Int. J. Solids Struct., 45(25-26), 6485-6500.   DOI   ScienceOn
14 Sun, J.Y., Hu, J.L., He, X.T. and Zheng, Z.L. (2010), "A theoretical study of a clamped punch-loaded blister configuration: The quantitative relation of load and deflection", Int. J. Mech. Sci., 52(7), 928-936.   DOI   ScienceOn
15 Jin, C.R. and Wang, X.D. (2008), "A theoretical study of a thin-film delamination using shaft-loaded blister test: Constitutive relation without delamination", J. Mech. Phys. Solids., 56(9), 2815-2831.   DOI   ScienceOn
16 Lee, K.S. and Han, S.E. (2011), "Geodesic shape finding of membrane structure with geodesic string by the dynamic relaxation method", Struct. Eng. Mech., 39(1), 93-113.   DOI   ScienceOn
17 Plaut, R.H. (2008), "Linearly elastic annular and circular membranes under radial, transverse, and torsional loading. Part I: large unwrinkled axisymmetric deformations", Acta Mech., 202(1-4), 79-99.
18 Sun, J.Y., Hu, J.L., He, X.T., Zheng, Z.L. and Geng, H.H. (2011), "A theoretical study of thin film delamination using clamped punch-loaded blister test: Energy release rate and closed-form solution", J. Adhes. Sci. Technol., 25(16), 2063-2080.   DOI
19 Xu, W., Ye, J.H. and Shan, J. (2009), "The application of BEM in the membrane structures interaction with simplified wind", Struct. Eng. Mech., 31(3), 349-365.   DOI   ScienceOn
20 Zhao, M.H., Zheng, W.L. and Fan, C.Y. (2010), "Mechanics of shaft-loaded blister test for thin film suspended on compliant substrate", Int. J. Solids Struct., 47(18-19), 2525-2532.   DOI   ScienceOn
21 Zheng, Z.L., Xu, Y.P., Liu, C.J., He, X.T. and Song, W.J. (2011), "Nonlinear aerodynamic stability analysis of orthotropic membrane structures with large amplitude", Struct. Eng. Mech., 37(4), 401-415.   DOI   ScienceOn