CN106644682B - The determination method of annular membrane elasticity energy under combined load with hard core - Google Patents

Abstract

The invention discloses the determination methods for the annular membrane elasticity energy that hard core is had under combined load: being laterally applied to a uniform load q to the annular membrane with hard core that the periphery for being ν with a thickness of h, outer radius a, inside radius b, Young's modulus of elasticity E, Poisson's ratio fixes to clamp, wherein the radius of hard core is also b, and apply a lateral concentrfated load F simultaneously at the center of hard core, based on the standing balance analysis to this On Axisymmetric Deformation of A, using the measured value of uniform load q and concentrfated load F, then it can determine that the deformed elasticity of the annular membrane can U.

Description

Method for determining the elastic properties of annular films with hard cores under compound loading

technical field

The invention relates to a method for determining the elastic properties of a ring-shaped thin film with a hard core which is fixed and clamped at the periphery under the action of compound loads.

Background technique

The ring-shaped thin film structure has a wide range of applications in the fields of mechanics, electronics, and biological engineering. A ring-shaped membrane structure with a hard core, which is fixed and clamped around the periphery, can be used for the development of capacitive pressure sensors, in which the ring-shaped membrane and the hard core will be under the action of pressure at the same time (under the action of a uniform load). But in fact, under the action of small pressure, the self-weight of the hard core element is a non-negligible load for the annular film, which changes the mechanical behavior of the annular film structure, thus affecting the accuracy of the sensor. If the load effect of the hard core element's own weight on the annular film is considered, this is actually a problem of axisymmetric deformation of the annular film with a hard core fixed and clamped around it under the action of a compound load. From the results of the literature search, this problem has not been solved analytically, which affects the refined development of the sensor.

SUMMARY OF THE INVENTION

The invention analytically solves the axisymmetric deformation problem of the annular film with a hard core that is fixedly clamped around the periphery under the action of the composite load, and on this basis, gives the results of the composite load Methods for determining elastic properties under combined action.

Determination method of elastic properties of annular film with hard core under compound load: for a fixed and clamped peripheral with thickness h, outer radius a, inner radius b, Young's modulus of elasticity E, and Poisson's ratio ν A uniform load q is applied laterally to the annular film with a hard core, where the radius of the hard core is also b, and a lateral concentrated load F is simultaneously applied at the center of the hard core, then based on the static force for this axisymmetric deformation problem Equilibrium analysis, the analytical relationship between the elastic energy U of the annular film and the applied uniform load q and concentrated load F can be expressed as

where π is the pi,

β=(a+b)/(2a),

α=(F-πb ² q)/(πa ² q), the values of c ₁ and c ₂ are given by the equation

and

is determined, and the value of _c0 is determined by the formula

Sure. Among them, all parameters are in the International System of Units.

In this way, as long as the applied uniform load q and concentrated load F are measured, the elastic energy U after the deformation of the annular film can be determined.

Description of drawings

Figure 1 is a schematic diagram of the loading structure of an annular film with a hard core that is fixed and clamped around the periphery, wherein 1-deformed annular film, 2-hard core, 3-clamping device, and a represents the inner radius of the clamping device and The outer radius of the annular film, b is the radius of the hard core and the inner radius of the annular film, q is the transverse uniform load, F is the transverse concentrated load, and w _m is the maximum deflection of the film.

Detailed ways

Below in conjunction with Fig. 1, the technical scheme of the present invention is described in further detail:

The transverse direction of the annular rubber film with a hard core fixed and clamped to the periphery of the thickness h=0.5mm, outer radius a=20mm, inner radius b=5mm, Young's modulus of elasticity E=7.84MPa, Poisson's ratio ν=0.47 A uniform load q is applied, wherein the radius of the hard core is also b=5mm, and a lateral concentrated load F is simultaneously applied at the center of the hard core. Measured q=0.01MPa, F=1.178N. Using the method provided by the present invention, α=(F-πb ² q)/(πa ² q)=0.03125, β=(a+b)/(2a)=0.625, through the equation

and

That is, the equation

and

in,

It can be obtained that c ₁ =-0.729227258 and c ₂ =-0.645917810. Then, by the formula

That is, the formula

This results in c ₀ =0.375442416. Finally, by the formula

That is, the formula

It can be obtained that when the uniform load q is 0.01MPa and the concentrated load F is 1.178N, the elastic energy of the annular rubber film is U=30.19N·mm=30.19×10 ^-3J .

Claims (1)

1. The method for determining the elastic properties of a ring-shaped thin film with a hard core under a composite load, characterized in that: the thickness is h, the outer radius is a, the inner radius is b, the Young's modulus of elasticity is E, and the Poisson's ratio is ν A uniformly distributed load q is applied laterally to the annular film with a hard core fixed and clamped at the periphery of The value of the uniform load q and the concentrated load F, the elastic energy U of the annular film under the combined action of the uniform load q and the concentrated load F is determined by the following formula, where π is the pi, β=(a+b)/(2a), α=(F-πb ² q)/(πa ² q), the values of c ₁ and c ₂ are given by the equation and is determined, and the value of _c0 is determined by the formula OK, all parameters are in the International System of Units.