Determination method for maximum deflection of prestressed round film under transversely uniformly distributed load

Abstract

The invention discloses a determination method for maximum deflection of a prestressed round film under transversely uniformly distributed load. The determination method comprises the following steps: transversely applying a uniformly distributed load q to the prestressed round film with a fixed and clamped periphery, wherein the thickness, radius, Young's modulus, poisson ratio and prestress of the round film are respectively h, a, E, v an sigma 0; analyzing the static equilibrium based on the axial symmetry deformation problem, and determining the maximum deflection wm of the deformed film by utilizing the measured value of the uniformly distributed load q.

Description

technical field [0001] The invention relates to a method for determining the maximum deflection of a prestressed circular membrane fixed and clamped around the periphery under the action of transverse uniform load. Background technique [0002] The analytical solution to the axisymmetric deformation problem of a circular film fixed and clamped around the periphery under the action of lateral uniform load is of great significance to the development of sensors and instruments. According to the results of the novelty search in the literature, there are currently analytical solutions for the axisymmetric deformation of circular membranes fixed and clamped around the periphery under uniform lateral loads when the membrane rotation angle θ is large but there is no prestress in the membrane. For example, The analytical solution used in the invention patent declared by the applicant (“a method for determining the maximum deflection of a circular film with a large rotation angle unde...

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Problems solved by technology

According to the results of the novelty search in the literature, there are currently analytical solutions for the axisymmetric deformation of circular membranes fixed and clamped around the periphery under uniform lateral loads when the membrane rotation angle θ is large but there is no prestress in the membrane. For example, The analytical solution used in the invention patent declared by the applicant (“a method for determining the maximum deflection of a circular film with a large rotation angle under uniform load”, patent application number: 201510193793.8) is based on the assumption that there is no prestress in the circular film It is obtained under the conditions, so it is only applicable to the case of no prestress in the film; it is also suitable for the case of prestress in the film, but the film rotation angle θ is small. The analytical solution to the axisymmetric deformation problem, for example, the analytical solution used in another invention patent ("a method for determining the maximum deflection value of a prestressed circular film under a uniform load", patent application number: 201410238568.7) previously declared by the applicant The solution is obtained under the assumption that there is prestress in the circular film, but the film rotation angle θ is small, that is, the prestress in the film is considered in the solution process of this analytical solution, but the film The rotation angle θ approximately satisfies the assumption of sinθ=tanθ, as we all know, Therefore, it is obvious that only when the film rotation angle θ is small, can there be The approximation of , so this analytical solution is only applicable to the case where the film has prestress, but the film rotation angle θ is small; however, so far, it has not been found that it is suitable for the case where the film rotation angle θ is large, and the film has a Analytical Solution of Axisymmetric Deformation Problem of Circular Membrane Clamped and Clamped Under Transverse Uniform Loading in the Prestressed Case

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