Method for determining maximum deflection of circular film with maximum deflection under elastic limitation

Abstract

The invention discloses a method for determining the maximum deflection of a circular film with maximum deflection under elastic limitation. The method comprises the following steps: a uniform load qis applied to the circular film which is initially flat and fixedly clamped at the periphery in the transverse direction, wherein the Young's modulus of elasticity of the circular film is E, the Poisson's ratio is v, the thickness is h, the radius is a, and the self-weight per unit area is q0, the circular film is enabled to generate an axisymmetric deformation so as to push a rigid circular platewith a smooth surface to parallelly move by a distance of wm, wherein the radius of the rigid circular plate is a, the center of the rigid circular plate is on the same axis with the center of the circular film, the rigid circular plate is always parallel to the initially flat circular film, the axially symmetrically deformed circular film forms an interacting contact area with the radius of b with the rigid circular plate, the rigid circular plate moving in parallel compresses a spring with a stiffness coefficient of k by wm from the original length L, and then, after ignoring the self-weight of the rigid circular plate, the maximum deflection wm of the circular film after axially symmetric deformation is determined based on the static balance analysis of the axisymmetric deformation ofthe circular film by utilizing a measured value of the load q.

Description

technical field [0001] The invention relates to a method for determining the maximum deflection of a circular film fixed and clamped around the periphery under the condition that the maximum deflection is limited by elasticity under the action of transverse uniform load. Background technique [0002] Under the condition that the maximum deflection is limited by elasticity, the axisymmetric deformation of a circular film fixed and clamped around the periphery under the action of a transverse uniform load is used and applied in many engineering and technical fields, for example, to study the adhesion of film / substrate systems. Attached to energy measurement, and the development of various instruments and meters and various sensors. Because the film is usually very thin, it often produces a large deflection under the action of lateral uniform load, so it has strong geometric nonlinearity, which brings difficulties to analytical research. Therefore, according to the novelty sear...

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Problems solved by technology

Because the film is usually very thin, it often produces a large deflection under the action of lateral uniform load, so it has strong geometric nonlinearity, which brings difficulties to analytical research. Therefore, according to the novelty search results of existing literature, Under the condition that the maximum deflection is limited by elasticity, the problem of axisymmetric deformation of a circular membrane fixed and clamped around the periphery under a transversely uniform load has not yet been solved analytically

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