Theory of gradient-elastic membranes and its application in the wrinkling analysis of stretched thin sheets

Dadgar‐Rad, Farzam; Imani, Arash

doi:10.1016/j.jmps.2019.103679

Cited by 10 publications

(2 citation statements)

References 41 publications

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“…Previous studies mostly focused on uniform membrane structures [6][7][8], but current membrane structures are usually heterogeneous, such as membrane antenna structures with rigid components [9,10] or flexible electronic devices with rigid circuits in aerospace engineering [11,12]. Yan et al studied the wrinkle characteristics of thin films with local microstructures, such as square rigid elements and circular holes [13,14], but the calculation method of the non-uniform stress field they proposed is based on infinite thin plates.…”

Section: Introductionmentioning

confidence: 99%

Wrinkling Patterns and Stress Analysis of Tensile Membrane with Rigid Elements

et al. 2022

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Heterogeneous membrane structures with rigid elements are often used in flexible electronic and aerospace structures. In heterogeneous membrane structures under tension, the disturbance stress caused by the rigid element changes the stress distribution of the membrane, and it is difficult to calculate the stress distribution of the heterogeneous membrane structure using the traditional stress functions method. In this article, we propose a method for calculating the non-uniform stress field based on the Eshelby elastic inclusion theory, which states that tension membrane structures contain square rigid elements. The wrinkle distribution of the rigid element at different positions is predicted by a stress analysis, and the influence of the position and size of the rigid element on the wrinkle distribution of the membrane is studied by a finite-element simulation. The research results show that the wrinkle pattern of the stretched membrane can be controlled by changing the position of the rigid element to meet some special needs.

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Section: Introductionmentioning

confidence: 99%

Wrinkling Patterns and Stress Analysis of Tensile Membrane with Rigid Elements

et al. 2022

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“…Membranes are increasingly being used in a wide variety of applications [1][2][3][4]. In our earlier work [5], the statics problem of fluid-structure interaction of a peripherally fixed circular membrane subjected to liquid weight loading is investigated analytically.…”

Section: Introductionmentioning

confidence: 99%

Large Deflection Analysis of Peripherally Fixed Circular Membranes Subjected to Liquid Weight Loading: A Refined Design Theory of Membrane Deflection-Based Rain Gauges

Sun

Zhang

et al. 2021

Materials

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The anticipated use of elastic membranes for deflection-based rain gauges has provided an impetus for this paper to revisit the large deflection problem of a peripherally fixed circular membrane subjected to liquid weight loading, a statics problem when the fluid–structure interaction of membrane and liquid reaches static equilibrium. The closed-form solution of this statics problem of fluid–structure interaction is necessary for the design of such membrane deflection-based rain gauges, while the existing closed-form solution, due to the use of the small rotation angle assumption of the membrane, cannot meet the design requirements for computational accuracy. In this paper, the problem under consideration is reformulated by giving up the small rotation angle assumption, which gives rise to a new and somewhat intractable nonlinear integro-differential equation of the governing out-of-plane equilibrium. The power series method has played an irreplaceable role in analytically solving membrane equations involving both integral and differential operations, and a new and more refined closed-form solution without the small rotation angle assumption is finally presented. Numerical examples conducted show that the new and more refined closed-form solution presented has satisfactory convergence, and the effect of giving up the small rotation angle assumption is also investigated numerically. The application of the closed-form solution presented in designing such membrane deflection-based rain gauges is illustrated, and the reliability of the new and more refined closed-form solution presented was confirmed by conducting a confirmatory experiment.

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