Abstract
The large deflection phenomenon of an initially flat circular membrane under out-of-plane gas pressure loading is usually involved in many technical applications, such as the pressure blister or bulge tests, where a uniform in-plane stress is often present in the initially flat circular membrane before deflection. However, there is still a lack of an effective closed-form solution for the large deflection problem with initial uniform in-plane stress. In this study, the problem is formulated and is solved analytically. The initial uniform in-plane stress is first modelled by stretching or compressing an initially flat, stress-free circular membrane radially in the plane in which the initially flat circular membrane is located, and based on this, the boundary conditions, under which the large deflection problem of an initially flat circular membrane under in-plane radial stretching or compressing and out-of-plane gas pressure loading can be solved, are determined. Therefore, the closed-form solution presented in this paper can be applied to the case where the initially flat circular membrane may, or may not, have a uniform in-plane stress before deflection, and the in-plane stress can be either tensile or compressive. The numerical example conducted shows that the closed-form solution presented has satisfactory convergence.
Highlights
A thin elastic film is, in mechanics, called a “membrane” when used as a structure or a structural component, because it usually has no resistance to bending and is usually in a stress state of full tension
The analytical solutions are necessary in the field of mechanical properties characterization for freestanding thin films, or thin-film/substrate systems based on pressured bulge or blister tests [8,14,15,17,18,19,20,21,22], and can provide these technical applications with a required analytical relationship between loads and stress or deflection, or an analytical relationship between radius and deflection of a blister that is gradually getting larger
From the in-plane equilibrium equation established by Campbell, it can be seen that the horizontal component of the applied gas pressure, which is neglected in the well-known Hencky solution, was still not included
Summary
A thin elastic film is, in mechanics, called a “membrane” when used as a structure or a structural component, because it usually has no resistance to bending and is usually in a stress state of full tension. From the in-plane equilibrium equation established by Campbell, it can be seen that the horizontal component of the applied gas pressure, which is neglected in the well-known Hencky solution, was still not included This means that the solution obtained by Campbell is still not suitable for the circular membrane problem under gas pressure loading. Since in the existing literature there is no such closed-form solution as the one presented in this paper, which considers pre-stress and gas pressure loading, the mechanical properties characterization based on pressured bulge or blister tests [8,14,15,17,18,19,20,21,22] has to use the well-known Hencky solution or its modified solutions, which are suitable for uniform lateral loading, rather than the gas pressure loading.
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