Determination of Maximum Stress of Circular Membrane under Uniform Transverse Load

Abstract

The invention discloses a method for determining the maximum stress of a circular thin film under the action of transverse uniform load: use a clamping device with an inner radius a to clamp a film with thickness h, Young's modulus of elasticity E, and Poisson's ratio ν The film is fixed and clamped, so as to form a circular film structure with a radius of a fixed and clamped around the periphery, and a uniform load q is applied to the circular film in the transverse direction, so that the circular film produces axisymmetric deformation, then based on the circle Static force balance analysis of the axisymmetric deformation of a circular thin film, using the measured value of the load q, the maximum stress σ after the axisymmetric deformation of the circular thin film can be determined m .

Description

technical field [0001] The invention relates to a method for determining the maximum stress of a circular thin film whose periphery is fixed and clamped under the action of transverse uniform load. Background technique [0002] The axisymmetric deformation of a circular membrane fixed and clamped around the periphery under a uniform lateral load has applications in many engineering and technical fields, for example, it is used to study the adhesion energy measurement of the membrane / substrate system, and to develop various instruments and instruments. Various sensors, etc. According to the results of the novelty search in the literature, in the process of solving the axisymmetric deformation problem of a circular film, the so-called assumption of a small film rotation angle (that is, the assumption that the film rotation angle θ satisfies sinθ≈tanθ) is abandoned to improve the calculation accuracy, for example Invention patent "A Method for Determining the Maximum Stress of...

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Problems solved by technology

According to the results of the novelty search in the literature, in the process of solving the axisymmetric deformation problem of a circular film, the so-called assumption of a small film rotation angle (that is, the assumption that the film rotation angle θ satisfies sinθ≈tanθ) is abandoned to improve the calculation accuracy, for example Invention patent "A Method for Determining the Maximum Stress of a Large-Angle Circular Film under Uniform Load" (Patent No.: ZL201510194408.1), but when establishing the geometric equation of this mechanical problem, some assumptions were used to establish an approximate geometry Equation e r =du / dr+1 / 2(dw / dr) 2 (e r represents the radial strain of the circular film, r represents the radial coordinate of the circular film, u and w represent the radial displacement and deflection of the circular film respectively), where it is assumed that the curve elements selected on the geometric middle surface of the circular film are The length is approximately equal before and after deformation. However, when the external load is large and the deflection of the film is large, this assumption is no longer applicable. Therefore, the analytical solution obtained based on this approximate geometric equation can only be used for small external loads. situation

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