Method for determination of maximum deflection of prestressed circular membranes whose deflection is limited by elasticity

Abstract

The invention discloses a method for determining the maximum deflection of a prestressed circular membrane whose deflection is limited by elasticity: Young's modulus of elasticity is E, Poisson's ratio is ν, and prestress is σ 0 , the radius is a, the thickness is h, and the self-weight per unit area is q 0 The prestressed circular film fixed and clamped around the periphery of the prestressed circular film applies a transverse uniform load q, so that the prestressed circular film produces axisymmetric deformation and then pushes a piece of radius a, which is always perpendicular to the transverse uniform load q, and is in line with the circle The coaxial, smooth-surfaced rigid circular plate moves in parallel, so that the maximum deflection of the axisymmetrically deformed prestressed circular membrane reaches w m At the same time, the rigid circular plate also moves in parallel w m distance, and the parallel moving rigid circular plate compresses a spring with original length L and stiffness coefficient k by w m , and an interactive circular contact area with radius b is finally formed between the axisymmetrically deformed prestressed circular film and the rigid circular plate, then after ignoring the self-weight of the rigid circular plate, based on the prestressed circular Static force balance analysis of the axisymmetric deformation of the film, using the measured value of the load q, the maximum deflection w after the axisymmetric deformation of the prestressed circular film can be determined m .

Description

technical field [0001] The invention relates to a method for determining the maximum deflection of a prestressed circular film whose periphery is fixed and clamped under the action of transverse uniform load under the condition that the deflection is limited by elasticity. Background technique [0002] The axisymmetric deformation of a circular film fixed and clamped around the periphery under the action of a transverse uniform load under the condition that the deflection is limited by elasticity is used and applied in many engineering and technical fields, for example, to study the adhesion of film / substrate systems It can measure and develop various instruments and meters and various sensors. However, according to the results of literature search, there are only analytical research results on the axisymmetric deformation of a non-prestressed circular membrane fixed and clamped around the periphery under the action of a transverse uniform load under the condition that the d...

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Problems solved by technology

However, according to the results of literature search, there are only analytical research results on the axisymmetric deformation of a non-prestressed circular membrane fixed and clamped around the periphery under the action of a transverse uniform load under the condition that the deflection is limited by elasticity, while There are no analytical research results on the axisymmetric deformation of prestressed circular membranes fixed and clamped around the perimeter under uniform transverse loads under the condition that the deflection is limited by elasticity

But in fact, when the peripheral fixed clamping is carried out to the circular film, it is easy to cause the circular film after the peripheral fixed clamping to be stretched (or compressed), so that the circular film after the peripheral fixed clamping is Initially stressed in tension (or compression) prior to application of a transverse uniform load (i.e., becomes a prestressed circular membrane with a fixed perimeter clamp)

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