CN110231215A - The determination method of the maximum defluxion for the prestressing force circular membrane that amount of deflection is limited by elasticity - Google Patents
The determination method of the maximum defluxion for the prestressing force circular membrane that amount of deflection is limited by elasticity Download PDFInfo
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- CN110231215A CN110231215A CN201910488159.5A CN201910488159A CN110231215A CN 110231215 A CN110231215 A CN 110231215A CN 201910488159 A CN201910488159 A CN 201910488159A CN 110231215 A CN110231215 A CN 110231215A
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- 239000012528 membrane Substances 0.000 title claims abstract description 49
- 238000000034 method Methods 0.000 title claims abstract description 9
- 230000003993 interaction Effects 0.000 claims abstract description 3
- 240000007594 Oryza sativa Species 0.000 claims 1
- 235000007164 Oryza sativa Nutrition 0.000 claims 1
- VIKNJXKGJWUCNN-XGXHKTLJSA-N norethisterone Chemical compound O=C1CC[C@@H]2[C@H]3CC[C@](C)([C@](CC4)(O)C#C)[C@@H]4[C@@H]3CCC2=C1 VIKNJXKGJWUCNN-XGXHKTLJSA-N 0.000 claims 1
- 235000009566 rice Nutrition 0.000 claims 1
- 230000002093 peripheral effect Effects 0.000 description 8
- 239000010408 film Substances 0.000 description 7
- 238000011160 research Methods 0.000 description 4
- 230000006835 compression Effects 0.000 description 3
- 238000007906 compression Methods 0.000 description 3
- 238000011161 development Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 239000004744 fabric Substances 0.000 description 1
- 238000011835 investigation Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012827 research and development Methods 0.000 description 1
- 239000000758 substrate Substances 0.000 description 1
- 239000010409 thin film Substances 0.000 description 1
Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/02—Details
- G01N3/04—Chucks
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/0202—Control of the test
- G01N2203/0212—Theories, calculations
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/026—Specifications of the specimen
- G01N2203/0262—Shape of the specimen
- G01N2203/0278—Thin specimens
- G01N2203/0282—Two dimensional, e.g. tapes, webs, sheets, strips, disks or membranes
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- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- General Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
- Immunology (AREA)
- Pathology (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
A kind of determination method of the maximum defluxion of the prestressing force circular membrane limited by elasticity the invention discloses amount of deflection: being E to Young's modulus of elasticity, Poisson's ratio ν, prestressing force σ0, radius a, with a thickness of h, unit area self weight be q0The prestressing force circular membrane that fixes to clamp of periphery apply a lateral uniform load q, allow prestressing force circular membrane to generate axisymmetric deformation so push one piece of radius be a, always perpendicular to lateral uniform load q's and with circular membrane coaxial line, rigid circular plate that surface is smooth move in parallel so that the maximum defluxion of the prestressing force circular membrane after axisymmetric deformation reaches wmWhile rigid circular plate also moved in parallel wmDistance, and the rigid circular plate moved in parallel an original length is L, the spring-compressed that stiffness coefficient is k wmAnd the prestressing force circular membrane after axisymmetric deformation and the rounded contact region that the interaction that a radius is b is ultimately formed between rigid circular plate, so after having ignored the self weight of rigid circular plate, standing balance analysis based on prestressing force circular membrane axisymmetric deformation, utilize the measured value of load q, so that it may the maximum defluxion w after determining prestressing force circular membrane axisymmetric deformationm。
Description
Technical field
The present invention relates to a kind of prestressing force circular membrane that lateral Uniform Loads following peripheral fixes to clamp amount of deflection by
The determination method of maximum defluxion under conditions of elasticity limitation.
Background technique
Axis of the circular membrane that lateral Uniform Loads following peripheral fixes to clamp under conditions of amount of deflection is limited by elasticity
Symmetric deformation has utilization, application in many field of engineering technology, for example, being used to study film/substrate system adhesion energy
Measurement and the various instrument and meters of development and various kinds of sensors etc..However, in terms of the result of document Investigation, at present only laterally
The axis pair without prestressed circular membrane under conditions of amount of deflection is limited by elasticity that Uniform Loads following peripheral fixes to clamp
The analysis research achievement for claiming problem on deformation, without the prestressing force circle fixed to clamp about lateral Uniform Loads following peripheral
The analysis research achievement of On Axisymmetric Deformation of A of shape film under conditions of amount of deflection is limited by elasticity.But in fact, to circle
Shape film carries out periphery when fix to clamp, it is easy to which the circular membrane after causing periphery to fix to clamp is stretched (or pressure
Contracting), so that the circular membrane after fixing to clamp periphery is before applying lateral uniform load just already provided with initial drawing
Stretch (or compression) stress (that is, becoming a kind of prestressing force circular membrane that periphery fixes to clamp).In addition, even existing
When fixing to clamp to circular membrane progress periphery, the circular membrane after periphery not being caused to fix to clamp is with initial
(or compression) stress is stretched, but since thin-film material generally all has the property expanded with heat and contract with cold, thus if applied laterally equal
Temperature when cloth load with circular membrane is carried out temperature difference when periphery fixes to clamp it is larger if, then in this feelings
It, will be thin as a kind of prestressing force circle that periphery fixes to clamp without prestressed circular membrane when periphery fixes to clamp under shape
Film.Therefore, the prestressing force circular membrane that further development lateral Uniform Loads following peripheral fixes to clamp is in amount of deflection by elasticity
The analysis research of On Axisymmetric Deformation of A under conditions of limitation can provide bigger research and development space for field of engineering technology.
Summary of the invention
This invention address that the prestressing force circular membrane that fixes to clamp of lateral Uniform Loads following peripheral is in amount of deflection by bullet
Property limitation under conditions of On Axisymmetric Deformation of A analysis research, based on standing balance analyze, obtained the axisymmetric deformation
The analytic solutions of problem, and it is thin to give the prestressing force circle that lateral Uniform Loads following peripheral fixes to clamp on this basis
The determination method of maximum defluxion of film under conditions of amount of deflection is limited by elasticity.
The determination method of the maximum defluxion for the prestressing force circular membrane that amount of deflection is limited by elasticity: be E to Young's modulus of elasticity,
Poisson's ratio is ν, prestressing force σ0, radius a, with a thickness of h, unit area self weight be q0Periphery fix to clamp prestressing force circle
Shape film applies a lateral uniform load q, allows prestressing force circular membrane to generate one piece of radius of axisymmetric deformation and then promotion and is
A, always perpendicular to lateral uniform load q's and with circular membrane coaxial line, rigid circular plate that surface is smooth is parallel moves
It is dynamic, so that the maximum defluxion of the prestressing force circular membrane after axisymmetric deformation reaches wmWhile rigid circular plate also move in parallel
W is movedmDistance, and the rigid circular plate moved in parallel an original length is L, the spring-compressed that stiffness coefficient is k
wm, and the prestressing force circular membrane after axisymmetric deformation and ultimately formed between rigid circular plate a radius be b it is mutual
The rounded contact region of effect, then being based on prestressing force circular membrane axisymmetric deformation after having ignored the self weight of rigid circular plate
Standing balance analysis, so that it may the maximum defluxion after obtaining applied load q and prestressing force circular membrane axisymmetric deformation
wmBetween 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 which the maximum after prestressing force circular membrane axisymmetric deformation is scratched
Spend wmIt decides, wherein parameter a, b, h, L, wmUnit be millimeter (mm), parameters E, q0、q、σ0Unit be ox
Pause every square millimeter of (N/mm2), the unit of parameter k is Newton per millimeter (N/mm), and parameter ν, c0、c1、c2、c3、 c4、c5、c6、
d0、d1、d2、d3、d4、d5、d6It is characteristic.
Detailed description of the invention
Fig. 1 is that the prestressing force circular membrane that lateral Uniform Loads following peripheral fixes to clamp is limited in amount of deflection by elasticity
Under the conditions of axisymmetric deformation schematic diagram, wherein 1 is the prestressing force circular membrane after axisymmetric deformation, and 2 be rigid circular plate,
3 be spring, and 4 be clamping device, and 5 be support, and 6 indicate the prestressing force circular membrane that peripheries fix to clamp, and a indicates prestressing force
The inside radius of the radius and clamping device of circular membrane and rigid circular plate, after b indicates prestressing force circular membrane axisymmetric deformation
The radius of the rounded contact region formed with rigid circular plate, L indicate that the original length of spring, q indicate lateral uniform load, wm
The distance and spring quilt that maximum defluxion and rigid circular plate after indicating prestressing force circular membrane axisymmetric deformation are moved in parallel
The length of compression.
Specific embodiment
Below with reference to Fig. 1, further description of the technical solution of the present invention:
As shown in Figure 1, to Young's modulus of lasticity E=7.84N/mm2, Poisson's ratio ν=0.47, prestressing force σ0=1N/mm2, half
Diameter a=20mm, thickness h=1mm, unit area self weight q0=7.64 × 10-7N/mm2Periphery fix to clamp prestressing force circle
Shape film applies a lateral uniform load q, allows prestressing force circular membrane to generate axisymmetric deformation and then pushes one piece of radius a
=20mm, always perpendicular to lateral uniform load q's and with circular membrane coaxial line, rigid circular plate that surface is smooth it is flat
Row movement, so that the maximum defluxion of the prestressing force circular membrane after axisymmetric deformation reaches wmWhile rigid circular plate it is also parallel
Move wmDistance, and the rigid circular plate moved in parallel is an original length L=50mm, stiffness coefficient k=1.5N/
The spring-compressed of mm wm, and the prestressing force circular membrane after axisymmetric deformation and one is ultimately formed between rigid circular plate
A radius is the rounded contact region of the interaction of b, measures load q=0.01N/mm2, using side given by the present invention
Method, by equation
Obtain b=3.8796mm, c0=0.4461, c1=-0.0613 and c2=-0.0972, c3=-0.0126, c4=-
0.0015、 c5=0.0450, c6=0.0827, d0=0.3552, d1=-0.5985, d2=-0.6608, d3=-0.0380, d4
=-0.1631, d5=0.0805, d6=-0.1811.Finally, by equation
Maximum defluxion w after obtaining prestressing force circular membrane axisymmetric deformationm=2.8595mm.
Claims (1)
1. the determination method of the maximum defluxion for the prestressing force circular membrane that amount of deflection is limited by elasticity, it is characterised in that: to Young bullet
Property modulus is E, Poisson's ratio ν, prestressing force σ0, radius a, with a thickness of h, unit area self weight be q0Periphery fix to clamp
Prestressing force circular membrane apply a lateral uniform load q, allow prestressing force circular membrane to generate axisymmetric deformation and then push
One piece of radius be a, always perpendicular to lateral uniform load q's and with circular membrane coaxial line, rigidity circle that surface is smooth
Plate moves in parallel, so that the maximum defluxion of the prestressing force circular membrane after axisymmetric deformation reaches wmWhile rigid circular plate
W is moved in parallelmDistance, and the rigid circular plate moved in parallel an original length is L, the spring that stiffness coefficient is k
Have compressed wm, and the prestressing force circular membrane after axisymmetric deformation and ultimately formed between rigid circular plate a radius be b
The rounded contact region of interaction be based on prestressing force circular membrane axis pair then after having ignored the self weight of rigid circular plate
The standing balance analysis for claiming deformation, using the measured value of load q, by equation
Determine parameter b, c0、c1And c2、c3、c4、c5、c6、d0、d1、d2、d3、d4、d5、d6Value, finally, by equation
Maximum defluxion w after determining prestressing force circular membrane axisymmetric deformationm, wherein parameter a, b, h, L, wmUnit be milli
Rice (mm), parameters E, q0、q、σ0Unit be Newton per square millimetre (N/mm2), the unit of parameter k is Newton per millimeter (N/
Mm), parameter ν, c0、c1、c2、c3、c4、c5、c6、d0、d1、d2、d3、d4、d5、d6It is characteristic.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111426568A (en) * | 2020-03-20 | 2020-07-17 | 重庆大学 | Method for determining deflection of circular film with limited maximum deflection under gas pressure |
| CN111426567A (en) * | 2020-03-20 | 2020-07-17 | 重庆大学 | Method for determining maximum stress of circular film with limited maximum deflection under air pressure |
| CN111474038A (en) * | 2020-04-22 | 2020-07-31 | 重庆大学 | Method for determining maximum deflection of prestressed circular film under uniformly distributed load |
| CN112880950A (en) * | 2021-01-18 | 2021-06-01 | 重庆大学 | Method for determining deflection of circular prestressed film with limited maximum deflection under air pressure |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111426568A (en) * | 2020-03-20 | 2020-07-17 | 重庆大学 | Method for determining deflection of circular film with limited maximum deflection under gas pressure |
| CN111426567A (en) * | 2020-03-20 | 2020-07-17 | 重庆大学 | Method for determining maximum stress of circular film with limited maximum deflection under air pressure |
| CN111474038A (en) * | 2020-04-22 | 2020-07-31 | 重庆大学 | Method for determining maximum deflection of prestressed circular film under uniformly distributed load |
| CN112880950A (en) * | 2021-01-18 | 2021-06-01 | 重庆大学 | Method for determining deflection of circular prestressed film with limited maximum deflection under air pressure |
| CN112880950B (en) * | 2021-01-18 | 2023-05-02 | 重庆大学 | Deflection determination method for circular prestress film with limited maximum deflection under air pressure |
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| CN110231215B (en) | 2021-06-08 |
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