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Structural Engineering and Mechanics   Volume 31, Number 6, April 20 2009, pages 625-638
DOI: https://doi.org/10.12989/sem.2009.31.6.625
 
Large deflection analysis of orthotropic, elliptic membranes
Somchai Chucheepsakul, Sakdirat Kaewunruen and Apiwat Suwanarat

 
Abstract     [Buy Article]
    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 inplane 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.
 
Key Words
    membrane structures; elliptic membranes; circular membranes; nonlinear static analysis; large deflections; large static tension; Rayleigh-Ritz method; energy minimization.
 
Address
Somchai Chucheepsakul: Department of Civil Engineering, King Mongkut
 

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