• Structural Engineering and Mechanics
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• v.31 no.6
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• pp.625-638
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• 2009

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.

• Coupled systems mechanics
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• v.6 no.2
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• pp.141-155
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• 2017

We present relatively simple derivations of the Helfrich energy potential that has been widely adopted in the analysis of lipid membranes without detailed explanations. Through the energy variation methods (within the limit of Helfrich energy potential), we obtained series of analytical solutions in the case when the lipid membranes are excited through their edges. These affordable solutions can be readily applied in the related membrane experiments. In particular, it is shown that, in case of an elliptic cross section of a rigid substrate differing slightly from a circle and subjected to the incremental deformations, exact analytical expressions describing deformed configurations of lipid membranes can be obtained without the extensive use of Mathieu's function.