CN109323924A

CN109323924A - Maximum defluxion is limited down the determination method of circular membrane maximum stress by elasticity

Info

Publication number: CN109323924A
Application number: CN201811566941.6A
Authority: CN
Inventors: 何晓婷; 李雪
Original assignee: Chongqing University
Current assignee: Chongqing University
Priority date: 2018-12-20
Filing date: 2018-12-20
Publication date: 2019-02-12
Anticipated expiration: 2038-12-20
Also published as: CN109323924B

Abstract

The invention discloses a kind of maximum defluxions to be limited down the determination method of circular membrane maximum stress by elasticity: being E to Young's modulus of elasticity, Poisson's ratio v, with a thickness of h, radius a, unit area self weight is q₀Original flat and the circular membrane that fixes to clamp of periphery be laterally applied to a uniform load q, allow circular membrane to generate axisymmetric deformation so push one piece of radius be a, its center of circle and circular membrane center of circle on the same axis and the circular membrane that is parallel to original flat always, rigid circular plate that surface is smooth move in parallel w_mDistance, and the contact area for the interaction that a radius is b is formd between the circular membrane and rigid circular plate after axisymmetric deformation, and a stiffness coefficient is had compressed w from original length L for the spring of k by the rigid circular plate moved in parallel_m, then after having ignored the self weight of rigid circular plate, the standing balance analysis based on circular membrane axisymmetric deformation utilizes the measured value of load q, so that it may the maximum stress σ after determining circular membrane axisymmetric deformation_m。

Description

Maximum defluxion is limited down the determination method of circular membrane maximum stress by elasticity

Technical field

The circular membrane that periphery fixes to clamp under conditions of being limited the present invention relates to a kind of maximum defluxion by elasticity is in transverse direction The determination method of maximum stress under Uniform Loads.

Background technique

The circular membrane that periphery fixes to clamp under conditions of maximum defluxion is limited by elasticity is under lateral Uniform Loads Axisymmetric deformation, many field of engineering technology have utilization, application, for example, be used to study the adherency of film/substrate system It is capable of measuring and develops various instrument and meters and various kinds of sensors etc..Since film is usually very thin, thus in lateral uniform load Very big amount of deflection is often generated under effect, thus there is stronger geometrical non-linearity, this brings difficulty to analysis research, so From looking into terms of new result for existing literature, the circular membrane that periphery fixes to clamp under conditions of maximum defluxion is limited by elasticity is in transverse direction On Axisymmetric Deformation of A under Uniform Loads, there is presently no resolved solutions.Therefore, it is necessary to carry out relevant parsing Research work provides convenient and bigger research and development space for the research and development of engineering technology.

Summary of the invention

This invention address that maximum defluxion limited by elasticity under conditions of the circular membrane that fixes to clamp of periphery laterally The analysis research of On Axisymmetric Deformation of A under the effect of cloth load, is analyzed based on standing balance, has obtained the axisymmetric deformation and asked The analytic solutions of topic, and the circular membrane that periphery fixes to clamp under conditions of maximum defluxion is limited by elasticity is given on this basis The determination method of maximum stress under lateral Uniform Loads.

Maximum defluxion is limited down the determination method of circular membrane maximum stress by elasticity: being E, Poisson to Young's modulus of elasticity Than for v, with a thickness of h, radius a, unit area self weight be q₀Original flat and the circular membrane that fixes to clamp of periphery it is lateral Apply a uniform load q, allowing circular membrane to generate axisymmetric deformation and then pushing one piece of radius is a, its center of circle and round The center of circle of film on the same axis and the circular membrane that is parallel to original flat always, rigid circular plate that surface is smooth Move in parallel w_mDistance, and it is b that a radius is formd between the circular membrane and rigid circular plate after axisymmetric deformation The contact area of interaction, and the rigid circular plate moved in parallel presses the spring that a stiffness coefficient is k from original length L Contracted w_m, then after having ignored the self weight of rigid circular plate, the standing balance analysis based on circular membrane axisymmetric deformation, so that it may To obtain the maximum stress σ after applied load q and circular membrane axisymmetric deformation_mBetween parsing relationship

Wherein,

And b, c₀、c₁Value by equation

With

It determines, wherein

As long as in this way, accurately measuring the value of load q, so that it may the maximum stress σ after circular membrane axisymmetric deformation_mReally It decides, wherein parameter a, b, h, L, w_mUnit be millimeter (mm), parameters E, q₀、q、σ_mUnit be every square of newton Millimeter (N/mm²), the unit of parameter k is Newton per millimeter (N/mm), and parameter v, c₀、c₁、c₂、c₃、c₄、c₅、c₆、d₁、d₂、d₃、 d₄、d₅、d₆It is characteristic.

Detailed description of the invention

Fig. 1 is that the circular membrane that periphery fixes to clamp under conditions of maximum defluxion is limited by elasticity is made in lateral uniform load The schematic diagram of On Axisymmetric Deformation of A under, wherein 1 is the circular membrane after axisymmetric deformation, and 2 be rigid circular plate, and 3 be bullet Spring, 4 be clamping device, and 5 be support, and 6 be face in the geometry of the circular membrane of original flat, and a indicates circular membrane and rigidity The radius of plectane and the inside radius of clamping device, b indicate contact radius with rigid circular plate after circular membrane axisymmetric deformation, L indicates that the original length of spring, q indicate lateral uniform load, o indicates coordinate origin, and r indicates that radial coordinate, w indicate laterally to sit Mark, w_mThe distance and spring that maximum defluxion and rigid circular plate after indicating circular membrane axisymmetric deformation are moved in parallel are pressed The length of contracting.

Specific embodiment

Below with reference to Fig. 1, further description of the technical solution of the present invention:

As shown in Figure 1, with the clamping device of an inside radius a=20mm by Young's modulus of lasticity E=7.84N/mm², pool Pine ratio ν=0.47, thickness h=1mm, unit area self weight q₀=7.64 × 10^-7N/mm²Original flat film clamp, so It is afterwards that clamping device is fixed on the support, to form the circular membrane structure that the periphery of a radius a=20mm fixes to clamp, and One uniform load q is laterally applied to circular membrane, circular membrane is allowed to generate axisymmetric deformation and then pushes one piece of radius a= 20mm, its center of circle and circular membrane center of circle on the same axis and the circular membrane that is parallel to original flat always, The smooth rigid circular plate in surface moves in parallel w_mDistance, and shape between the circular membrane and rigid circular plate after axisymmetric deformation At the contact area for the interaction that a radius is b, and the rigid circular plate moved in parallel is a stiffness coefficient k= The spring of 1.5N/mm has compressed w from original length L=50mm_m, measure load q=0.01N/mm², using given by the present invention Method, by following equation

Obtain b=4.018560m, mc₀=0.401570, c₁=-0.073751, c₂=-0.121406, c₃=- 0.023084、c₄=-0.008135, c₅=-0.064018, c₆=0.100262.Finally, by equation

Maximum stress σ after obtaining circular membrane axisymmetric deformation_m=0.281402N/mm²。

Claims

1. the determination method that maximum defluxion is limited down circular membrane maximum stress by elasticity, it is characterised in that: to Young springform Amount be E, Poisson's ratio v, with a thickness of h, radius a, unit area be self-possessed be q₀Original flat and the circle that fixes to clamp of periphery Shape film is laterally applied to a uniform load q, allow circular membrane to generate axisymmetric deformation so that push one piece of radius be a, its The center of circle and the center of circle of circular membrane on the same axis and the circular membrane that is parallel to original flat always, surface it is smooth Rigid circular plate move in parallel w_mDistance, and form one between the circular membrane and rigid circular plate after axisymmetric deformation Radius is the contact area of the interaction of b, and the rigid circular plate moved in parallel a stiffness coefficient for k spring from original Beginning, length L had compressed w_m, then after having ignored the self weight of rigid circular plate, the standing balance based on circular membrane axisymmetric deformation Analysis, using the measured value of load q, by following equation

Determine parameter b, c₀、c₁、c₂、c₃、c₄、c₅、c₆Value, finally, by equation

Maximum stress σ after determining circular membrane axisymmetric deformation_m, wherein parameter a, b, h, L, w_mUnit be millimeter (mm), parameters E, q₀、q、σ_mUnit be Newton per square millimetre (N/mm²), the unit of parameter k is Newton per millimeter (N/ Mm), parameter v, c₀、c₁、c₂、c₃、c₄、c₅、c₆、d₁、d₂、d₃、d₄、d₅、d₆It is characteristic.