Dr. Fuzhang Zhao Profile

Dr. Fuzhang Zhao

Mechanical Design Engineer at Celerity Inc

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Proceedings Article | 3 April 2008 Paper

Nonlinear solutions for circular membranes and thin plates

Fuzhang Zhao

Proceedings Volume 6926, 69260W (2008) https://doi.org/10.1117/12.775511

KEYWORDS: Partial differential equations, Mathematical modeling, Numerical analysis, MATLAB, Sensors, Electroluminescence, Gas sensors, Radar, Optical telescopes, Optical instrument design

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Plates, with many applications, can be classified into membranes, thin plates, and thick plates based on different aspect ratios of the hydraulic diameter to the plate's thickness. The existing nonlinear models for circular membranes and thin plates are reviewed. It is desirable to have analytical or approximate analytical models for the nonlinear deflections, strains, and stresses of membranes because of their maneuverable and insightful forms albeit the available numerical solutions. The new nonlinear models for prestretched and post-heated circular membranes under uniform pressure by both the Ritz method and the Galerkin method have been derived. The new nonlinear membrane model has been validated and compared to other related existing models. Furthermore, the condition of the pre-tensioned stress to minimize the maximum equivalent stress of membranes has been obtained. The solutions for thin plates have also been extended to include pretension and post-heating. The truncation error of the stretching factor of thin plates is corrected. For circular membranes and thin plates, both the Ritz method and the Galerkin method give the same answer if both the radial and axial displacements derived from the Galerkin method are used. The computer software MATLAB has also been used to verify the derivations of new membrane and thin plate models.

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