CN105956379B - The determining method of the annular membrane maximum stress of center band rigid plate under uniform load - Google Patents

Abstract

The invention discloses a method for determining the maximum stress of an annular film with a rigid plate in the center under a uniformly distributed load: a clamping device with an inner radius of a is used, and the thickness is h, Young's modulus of elasticity is E, Poisson's ratio is ν, The annular membrane with a rigid plate with a radius b in the center is fixed and clamped to form an axisymmetric annular membrane with a rigid plate in the center with an outer radius a and an inner radius b fixed and clamped, and a uniform load is applied to it in the transverse direction q, based on the static equilibrium analysis of this axisymmetric deformation problem, and using the measured value of the uniformly distributed load q, the maximum stress σ _m of the annular membrane can be determined.

Description

Method for Determination of Maximum Stress of Annular Membrane with Rigid Plate in the Center under Uniform Load

technical field

The invention relates to a method for determining the maximum stress of an annular film with a rigid plate in the center under a uniformly distributed load.

Background technique

The analytical solution to the axisymmetric deformation problem of the annular membrane with a rigid plate in the center under a uniform load is of great significance to the development of sensors, instruments and meters. Since the film is a flexible material, it usually exhibits a large deflection under a uniform load, so its deformation problem has a strong nonlinearity, and these nonlinear problems are usually difficult to solve analytically. The present invention is devoted to the analytical research on the axisymmetric deformation problem of the annular film with the rigid plate in the center under uniform load, and obtains the analytical solution of the problem, and on this basis, provides the annular film with the rigid plate in the center under uniform load Determination of maximum stress.

Contents of the invention

The determination method of the maximum stress of the annular membrane with a rigid plate in the center under a uniform load: using a clamping device with an inner radius of a, the thickness is h, Young’s modulus of elasticity is E, Poisson’s ratio is ν, and the radius of the central band is The annular membrane of the rigid plate of b is fixed and clamped to form an axisymmetric annular membrane with a rigid plate in the center fixed and clamped around the outer radius a and inner radius b, and a uniform load q is applied to it in the transverse direction, based on this Static force balance analysis of the axisymmetric deformation problem, the analytical relationship between the maximum stress σ _m of the annular film and the uniformly distributed load q can be obtained as

in,

While β=(a+b)/2a, the values of _c1 and _c2 are given by the equation

and

OK, among them,

In this way, as long as the value of the applied uniform load q is accurately measured, the maximum stress σ _m after deformation of the annular membrane can be determined. Among them, all parameters are in SI units.

Description of drawings

Figure 1 is a schematic diagram of the loading structure of an annular film with a rigid plate in the center fixed and clamped around it under a uniform load, in which, 1-annular film, 2-rigid plate, 3-clamping device, and a represents the inner part of the clamping device Radius and the outer radius of the annular membrane, b indicates the radius of the rigid plate and the inner radius of the annular membrane, r indicates the radial coordinate, w(r) indicates the transverse coordinate at point r, q indicates the transverse uniform load, w _m indicates the membrane maximum deflection.

Detailed ways

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

As shown in Figure 1, using a clamping device with an inner radius a=20mm, the thickness h=0.06mm, Young’s modulus of elasticity E=7.84MPa, Poisson’s ratio ν=0.47, and the rigidity of the central belt radius b=5mm The rubber film of the plate is fixed and clamped to form an axisymmetric annular film with a rigid plate in the center fixed and clamped around the outer radius a=20mm and inner radius b=5mm, and a uniform load q is applied to it in the transverse direction, and measured q = 0.01 MPa. Adopt the method that the present invention provides, by equation

and

Then c ₁ =-0.7026607165, c ₂ =-0.6927450924 can be obtained, where,

β=(a+b)/2a=0.625,

Finally, by the equation

Then the maximum stress σ _m =0.74044MPa of the annular membrane can be obtained, where,

Claims (1)

1. The method for determining the maximum stress of the annular film with the rigid plate at the center under uniformly distributed loads is characterized by comprising the following steps of: fixedly clamping an annular film of a rigid plate with the thickness of h, the Young's modulus of elasticity of E, the Poisson ratio of v and the radius of a central zone of b by adopting a clamping device with the inner radius of a to form an axisymmetric annular film of the rigid plate with the central zone, the periphery of which is fixedly clamped and the outer radius of a and the inner radius of b, transversely applying an evenly distributed load q to the axisymmetric annular film, measuring the value of the applied evenly distributed load q, and determining the maximum stress sigma of the annular film by the following formula_m：

Wherein,

and β ═ a + b)/2a, c₁And c₂Is given by the equation

And

determining, wherein,

all parameters adopt an international system of units.