CN110231214A - The determination method of the elasticity energy for the prestressing force circular membrane that amount of deflection is limited by elasticity - Google Patents
The determination method of the elasticity energy for the prestressing force circular membrane that amount of deflection is limited by elasticity Download PDFInfo
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- CN110231214A CN110231214A CN201910488158.0A CN201910488158A CN110231214A CN 110231214 A CN110231214 A CN 110231214A CN 201910488158 A CN201910488158 A CN 201910488158A CN 110231214 A CN110231214 A CN 110231214A
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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 4
- 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
- 238000005516 engineering process Methods 0.000 description 2
- 240000002853 Nelumbo nucifera Species 0.000 description 1
- 235000006508 Nelumbo nucifera Nutrition 0.000 description 1
- 235000006510 Nelumbo pentapetala Nutrition 0.000 description 1
- 235000008331 Pinus X rigitaeda Nutrition 0.000 description 1
- 235000011613 Pinus brutia Nutrition 0.000 description 1
- 241000018646 Pinus brutia Species 0.000 description 1
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- 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
- 238000012827 research and development Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 239000000758 substrate Substances 0.000 description 1
- 239000010409 thin film Substances 0.000 description 1
- 238000005303 weighing Methods 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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- General Health & Medical Sciences (AREA)
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- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
A kind of elasticity of the prestressing force circular membrane limited by elasticity the invention discloses amount of deflection can determination method: be 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 which the elasticity after determining prestressing force circular membrane axisymmetric deformation can U.
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 elasticity energy 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 the survey of film/substrate system adhesion energy
Amount and the various instrument and meters of development and various kinds of sensors etc..However, in terms of the result of document Investigation, it is only laterally equal at present
The axial symmetry without prestressed circular membrane under conditions of amount of deflection is limited by elasticity that cloth load effect following peripheral fixes to clamp
The analysis research achievement of problem on deformation, the prestressing force circle without fixing to clamp about lateral Uniform Loads following peripheral are thin
The analysis research achievement of On Axisymmetric Deformation of A of film under conditions of amount of deflection is limited by elasticity.But in fact, to round thin
When film progress periphery fixes to clamp, it is easy to which the circular membrane after causing periphery to fix to clamp is stretched (or compression)
, so that the circular membrane after fixing to clamp periphery is before applying lateral uniform load just already provided with initial tensile
(or compression) stress (that is, becoming a kind of prestressing force circular membrane that periphery fixes to clamp).In addition, even to circle
When shape film progress periphery fixes to clamp, the circular membrane after periphery not being caused to fix to clamp has initial tensile
(or compression) stress, but since thin-film material generally all has the property expanded with heat and contract with cold, thus if applying laterally uniformly distributed carry
Temperature when lotus with circular membrane is carried out temperature difference when periphery fixes to clamp it is larger if, then in this case,
A kind of prestressing force circular membrane that periphery fixes to clamp will be become without prestressed circular membrane when periphery fixes to clamp.Cause
This, further carries out what the prestressing force circular membrane that lateral Uniform Loads following peripheral fixes to clamp was limited in amount of deflection by elasticity
Under the conditions of On Axisymmetric Deformation of A analysis research, bigger research and development space can be provided 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 the prestressing force circular membrane that lateral Uniform Loads following peripheral fixes to clamp is given on this basis
The determination method of elasticity energy under conditions of amount of deflection is limited by elasticity.
The determination method of the elasticity energy for the prestressing force circular membrane that amount of deflection is limited by elasticity: being E to Young's modulus of elasticity, pool
Pine is than being ν, prestressing force σ0, radius a, with a thickness of h, unit area self weight be q0The prestressing force that fixes to clamp of periphery it is round
Film applies a lateral uniform load q, and allowing prestressing force circular membrane to generate axisymmetric deformation and then pushing one piece of radius is 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 wm
Distance, and the rigid circular plate moved in parallel an original length is L, the spring-compressed that stiffness coefficient is k wm, and
Prestressing force circular membrane after axisymmetric deformation and the circle that the interaction that a radius is b is ultimately formed between rigid circular plate
Shape contact area, then the static(al) based on prestressing force circular membrane axisymmetric deformation is flat after having ignored the self weight of rigid circular plate
Weighing apparatus analysis, so that it may the parsing between elasticity energy U after obtaining applied load q and prestressing force circular membrane axisymmetric deformation
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 elastic energy after prestressing force circular membrane axisymmetric deformation
U is decided, wherein the unit of parameter U is ox millimeter (Nmm), parameter a, b, h, L, wmUnit be millimeter (mm),
Parameters E, q0、q、σ0Unit be Newton per square millimetre (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
It is spring, 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 circle
The inside radius of the radius and clamping device of shape film and rigid circular plate, b indicate prestressing force circular membrane axisymmetric deformation after with
The radius for the rounded contact region that rigid circular plate is formed, L indicate that the original length of spring, q indicate lateral uniform load, wmIt indicates
The distance and spring that maximum defluxion and rigid circular plate after prestressing force circular membrane axisymmetric deformation are moved in parallel are compressed
Length.
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/mm2The prestressing force that fixes to clamp of periphery it is round
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 parallel
It is mobile, 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 is an original length L=50mm, stiffness coefficient k=1.5N/mm
Spring-compressed wm, and the prestressing force circular membrane after axisymmetric deformation and one and half are ultimately formed between rigid circular plate
Diameter is the rounded contact region of the interaction of b, measures load q=0.01N/mm2, using method given by the present invention, 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
Elasticity after obtaining prestressing force circular membrane axisymmetric deformation can U=14.0159Nmm.
Claims (1)
1. the determination method of the elasticity energy for the prestressing force circular membrane that amount of deflection is limited by elasticity, it is characterised in that: to Young elasticity
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 applies a lateral uniform load q, allows prestressing force circular membrane to generate axisymmetric deformation and then pushes one
Block radius be a, always perpendicular to lateral uniform load q's and with circular membrane coaxial line, rigid circular plate that surface is smooth
It moves in parallel, so that the maximum defluxion of the prestressing force circular membrane after axisymmetric deformation reaches wmWhile rigid circular plate also put down
Row moves wmDistance, and the rigid circular plate moved in parallel an original length is L, the spring pressure that stiffness coefficient is k
Contracted wm, and the prestressing force circular membrane after axisymmetric deformation and radius is ultimately formed between rigid circular plate is b
The rounded contact region of interaction, then being based on prestressing force circular membrane axial symmetry after having ignored the self weight of rigid circular plate
The standing balance of deformation is analyzed, 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
Elasticity energy U after determining prestressing force circular membrane axisymmetric deformation, wherein the unit of parameter U is ox millimeter (N
Mm), parameter a, b, h, L, wmUnit be millimeter (mm), parameters E, q0、q、σ0Unit be Newton per square millimetre (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.
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| CN201910488158.0A CN110231214B (en) | 2019-06-05 | 2019-06-05 | Method for determining elastic energy of prestressed circular film with deflection limited by elasticity |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111426566A (en) * | 2020-03-20 | 2020-07-17 | 重庆大学 | Method for determining elastic energy of circular film with limited maximum deflection under gas 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 |
| CN112903216A (en) * | 2021-01-18 | 2021-06-04 | 重庆大学 | Method for determining elastic energy of circular prestressed film with limited maximum deflection under air pressure |
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|---|---|---|---|---|
| US4899581A (en) * | 1988-02-19 | 1990-02-13 | Massachusetts Institute Of Technology | Method and apparatus for the quantitative measurement of adhesion of thin films |
| RU2184361C1 (en) * | 2000-10-24 | 2002-06-27 | ООО "Издательство "SOS" | Method of determination of strength properties of film materials |
| CN102072875A (en) * | 2010-10-26 | 2011-05-25 | 重庆大学 | Geometric measurement method of elastic strain energy in coating films in pressurized blister test |
| CN103822822A (en) * | 2014-03-24 | 2014-05-28 | 重庆大学 | Method for measuring elastic energy of bubbled film in bubbling test on flat-bottom cylinder |
| JP2014126358A (en) * | 2012-12-25 | 2014-07-07 | Nagoya Institute Of Technology | Biaxial tensile testing method and device used for the same |
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2019
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| US4899581A (en) * | 1988-02-19 | 1990-02-13 | Massachusetts Institute Of Technology | Method and apparatus for the quantitative measurement of adhesion of thin films |
| RU2184361C1 (en) * | 2000-10-24 | 2002-06-27 | ООО "Издательство "SOS" | Method of determination of strength properties of film materials |
| CN102072875A (en) * | 2010-10-26 | 2011-05-25 | 重庆大学 | Geometric measurement method of elastic strain energy in coating films in pressurized blister test |
| JP2014126358A (en) * | 2012-12-25 | 2014-07-07 | Nagoya Institute Of Technology | Biaxial tensile testing method and device used for the same |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111426566A (en) * | 2020-03-20 | 2020-07-17 | 重庆大学 | Method for determining elastic energy of circular film with limited maximum deflection under gas 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 |
| CN112903216A (en) * | 2021-01-18 | 2021-06-04 | 重庆大学 | Method for determining elastic energy of circular prestressed film with limited maximum deflection under air pressure |
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