Method for determining elastic energy of circular film under condition that maximum deflection is limited by elasticity

Abstract

The invention discloses a method for determining elastic energy of a circular film under condition that maximum deflection is limited by elasticity. The method comprises the following steps of: applying a uniform load q to a circular film with a Young's modulus of E, a Poisson's ratio of v, a thickness of h, a radius of a, and a self-weight of q0 per unit area, which is initially flat and fixedlyclamped at the periphery, to enable the circular film to produce axisymmetric deformation; pushing a rigid circular plate which has a radius of a and a center on the same axis as the center of the circular film, is always parallel to the circular film which is flat at the middle, and has a smooth surface to move a distance of wm in parallel; forming an contact area with a radius b between the axisymmetrically deformed circular film and the rigid circular plate; compressing a spring having a stiffness coefficient of k from the original length L by wm by the parallelly moving rigid circular plate; and after ignoring the self-weight of the rigid circular plate, using the measured value of the load q to determine the elastic energy U of the axisymmetrically deformed circular film based on a static balance analysis of the axisymmetrically deformed circular film.

Description

technical field [0001] The invention relates to a method for determining the elastic energy 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 transversely uniformly distributed 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 ...

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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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