Large deflection analysis of orthotropic, elliptic membranes
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Author list: Chucheepsakul S., Kaewunruen S., Suwanarat A.
Publisher: Techno-press Ltd
Publication year: 2009
Journal: Structural Engineering and Mechanics (1225-4568)
Volume number: 31
Issue number: 6
Start page: 625
End page: 638
Number of pages: 14
ISSN: 1225-4568
Languages: English-Great Britain (EN-GB)
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Abstract
Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes - subject to gravitational, uniform pressures often found in nano-sensors - is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to in-plane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.
Keywords
Circular membranes, Elliptic membranes, Energy minimization, Large deflections, Large static tension, Membrane structures, Nonlinear static analysis, Rayleigh-ritz method
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