Abstract
In this paper, the problem of fluid–structure interaction of a circular membrane under liquid weight loading is formulated and is solved analytically. The circular membrane is initially flat and works as the bottom of a cylindrical cup or bucket. The initially flat circular membrane will undergo axisymmetric deformation and deflection after a certain amount of liquid is poured into the cylindrical cup. The amount of the liquid poured determines the deformation and deflection of the circular membrane, while in turn, the deformation and deflection of the circular membrane changes the shape and distribution of the liquid poured on the deformed and deflected circular membrane, resulting in the so-called fluid-structure interaction between liquid and membrane. For a given amount of liquid, the fluid-structure interaction will eventually reach a static equilibrium and the fluid-structure coupling interface is steady, resulting in a static problem of axisymmetric deformation and deflection of the circular membrane under the weight of given liquid. The established governing equations for the static problem contain both differential operation and integral operation and the power series method plays an irreplaceable role in solving the differential-integral equations. Finally, the closed-form solutions for stress and deflection are presented and are confirmed to be convergent by the numerical examples conducted.
Highlights
Elastic membrane structures or structural components have applications in various fields [1,2,3,4,5]
Three main loading forms of transverse loads are involved in the existing studies: 1 the uniformly distributed loads applied to the entire circular membrane [14,15,16,17,18,19,20,21,22], 2 the uniformly distributed loads applied to the central portion of the circular membrane [23], and 3 the concentrated force applied to the center of the circular membrane [24,25,26,27,28]
Hencky was the first scholar to deal with the circular membrane problem concerning the first loading form of transverse loads and presented a closedform solution in the form of power series [14]
Summary
Elastic membrane structures or structural components have applications in various fields [1,2,3,4,5]. These applications have provided an impetus for scholars to investigate the phenomena of large deflection of membrane [6,7,8] Such investigations usually give rise to nonlinear equations with differential and even integral operation. The usually so-called circular membrane problem refers to the problem of axisymmetric deformation and deflection of an initially flat, peripherally fixed circular membrane subjected to transverse loads. Analytically dealt with the symmetrical deformation of circular membrane under the action of uniformly distributed loads in its central portion, i.e., the circular membrane problem concerning the second loading form of transverse load. The closed-form solution of this static problem is expected to be used in the development of a new rain gauge [29,30,31] Such a fluid–structure coupling problem will give rise to governing equations containing both differential operation and integral operation.
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