Abstract
In this paper, the static problem of equilibrium of contact between an axisymmetric deflected circular membrane and a frictionless rigid plate was analytically solved, where an initially flat circular membrane is fixed on its periphery and pressurized on one side by gas such that it comes into contact with a frictionless rigid plate, resulting in a restriction on the maximum deflection of the deflected circular membrane. The power series method was employed to solve the boundary value problem of the resulting nonlinear differential equation, and a closed-form solution of the problem addressed here was presented. The difference between the axisymmetric deformation caused by gas pressure loading and that caused by gravity loading was investigated. In order to compare the presented solution applying to gas pressure loading with the existing solution applying to gravity loading, a numerical example was conducted. The result of the conducted numerical example shows that the two solutions agree basically closely for membranes lightly loaded and diverge as the external loads intensify.
Highlights
As structures or structural components, elastic membranes have played important roles in many fields
The vesicle membrane for targeted drug delivery [1] and cell membrane adhered onto substratum [2] are of practical importance in biological science, the electrostatically driven diaphragm membranes play important roles in micro-electro-mechanical systems (MEMS) [3,4], and the membrane structures in bulge tests [5,6,7] or blister tests [8,9,10,11,12,13,14] are designed for characterizing the mechanical properties of thin films or film/substrate interfaces
Let us address the plane problem of axisymmetric deformation of the plane radial stretched or compressed circular membrane in the central contact region 0 ≤ r ≤ b, where the radial displacement at r = b is denoted by u(b)
Summary
As structures or structural components, elastic membranes have played important roles in many fields. If the uniform pressure is applied on one side of an initially flat peripherally fixed circular membrane, such that the circular membrane deflects axisymmetrically and comes into contact with a flat surface parallel to the initially flat circular membrane, this is the so-called contact problem between circular membranes and rigid plates [26,27,28]. Such a contact problem is reminiscent of the constrained blister test [11,12], but the debonding does not occur at the edge of the blistering film, because the edge of the blister is clamped.
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