CN110286040A - A kind of determination method of the maximum stress of liquid effects lower prestress circular membrane - Google Patents
A kind of determination method of the maximum stress of liquid effects lower prestress circular membrane Download PDFInfo
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- CN110286040A CN110286040A CN201910488164.6A CN201910488164A CN110286040A CN 110286040 A CN110286040 A CN 110286040A CN 201910488164 A CN201910488164 A CN 201910488164A CN 110286040 A CN110286040 A CN 110286040A
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- circular pipe
- prestressing force
- rigid circular
- circular membrane
- rigid
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- 239000012528 membrane Substances 0.000 title claims abstract description 39
- 239000007788 liquid Substances 0.000 title claims abstract description 34
- 230000000694 effects Effects 0.000 title claims abstract description 17
- 238000000034 method Methods 0.000 title claims abstract description 9
- 230000005484 gravity Effects 0.000 claims abstract description 7
- 230000001133 acceleration Effects 0.000 claims description 3
- 230000003068 static effect Effects 0.000 claims description 2
- 238000005303 weighing Methods 0.000 claims description 2
- 241000219000 Populus Species 0.000 claims 1
- 238000002347 injection Methods 0.000 claims 1
- 239000007924 injection Substances 0.000 claims 1
- 238000007789 sealing Methods 0.000 abstract 1
- 230000002093 peripheral effect Effects 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
- 239000010408 film Substances 0.000 description 3
- 239000010409 thin film Substances 0.000 description 2
- 238000010586 diagram Methods 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
- 239000007787 solid 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
-
- 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
- G01N3/10—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces generated by pneumatic or hydraulic pressure
- G01N3/12—Pressure testing
-
- 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
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
- G01N2203/0075—Strain-stress relations or elastic constants
-
- 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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- Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Chemical & Material Sciences (AREA)
- 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)
- Separation Using Semi-Permeable Membranes (AREA)
Abstract
The invention discloses a kind of determination methods of the maximum stress of liquid effects lower prestress circular membrane: fixed to clamp on the lower edge for the rigid circular pipe that a height is H, wall thickness t, inside radius a, axial line are parallel with gravity direction one piece of Young's modulus of elasticity be E, Poisson's ratio ν, with a thickness of h, prestressing force σ0Film, to enable rigid circular pipe lower end to form the prestressing force circular membrane structure that the periphery that a radius is a fixes to clamp while sealing, and it is suitable to injecting inside rigid circular pipe, density is the liquid of ρ, prestressing force circular membrane is set to generate axisymmetric deformation under liquid effects, and the liquid level after reaching standing balance inside rigid circular pipe can exceed the plane where the lower edge of rigid circular pipe, standing balance analysis so based on prestressing force circular membrane axisymmetric deformation, utilize the difference in height h where rigid circular pipe internal liquid level and rigid circular pipe lower edge between plane0Measured value, so that it may the maximum stress σ after determining prestressing force circular membrane axisymmetric deformationm。
Description
Technical field
The present invention relates to a kind of determinations of the maximum stress of prestressing force circular membrane that liquid effects following peripheral fixes to clamp
Method.
Background technique
The axisymmetric deformation for the circular membrane that liquid effects following peripheral fixes to clamp can be used to develop rainfall measurement system
System and various sensors, instrument and meter etc..However, only liquid effects following peripheral is solid at present in terms of the result of document Investigation
The analysis research achievement of the tight On Axisymmetric Deformation of A without prestressing force circular membrane of clamp, without about liquid effects next week
While the analysis research achievement of the On Axisymmetric Deformation of A of the prestressing force circular membrane fixed to clamp.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)
, thus the circular membrane after fixing to clamp periphery before applying transverse load just already provided with initial tensile (or
Compression) stress (that is, become a kind of prestressing force circular membrane that periphery fixes to clamp).In addition, even to round thin
Film carries out periphery when fix to clamp, the circular membrane after periphery not being caused to fix to clamp with initial tensile (or
Compression) stress, but since thin-film material generally all has the property expanded with heat and contract with cold, thus if temperature when applying transverse load
With circular membrane is carried out temperature difference when periphery fixes to clamp it is larger if, then in this case, periphery fixing clamp
A kind of prestressing force circular membrane that periphery fixes to clamp will be become without prestressed circular membrane when tight.Therefore, it further opens
The analysis research of the On Axisymmetric Deformation of A for the prestressing force circular membrane that exhibition liquid effects following peripheral fixes to clamp, can be engineering
Technical field provides bigger research and development space.
Summary of the invention
This invention address that the On Axisymmetric Deformation of A for the prestressing force circular membrane that liquid effects following peripheral fixes to clamp
Analysis research is analyzed based on standing balance, has obtained the analytic solutions of the On Axisymmetric Deformation of A, and give liquid on this basis
The determination method of the maximum stress for the prestressing force circular membrane that body effect following peripheral fixes to clamp.
A kind of determination method of the maximum stress of liquid effects lower prestress circular membrane: a height is H, wall thickness is
T, one piece of Young's modulus of elasticity is fixed to clamp on the lower edge for the rigid circular pipe that inside radius is a, axial line is parallel with gravity direction
For E, Poisson's ratio ν, with a thickness of h, prestressing force σ0Film, so as to enable rigid circular pipe lower end seal while form one
The prestressing force circular membrane structure that fixes to clamp of periphery that radius is a, and to injecting suitable, density ρ inside rigid circular pipe
Liquid, so that prestressing force circular membrane is generated axisymmetric deformation under liquid effects and rigidly justify after reaching standing balance
Liquid level inside pipe can exceed the plane where the lower edge of rigid circular pipe, then being based on prestressing force circular membrane axisymmetric deformation
Standing balance analysis, so that it may the difference in height where obtaining rigid circular pipe internal liquid level and rigid circular pipe lower edge between plane
h0With the maximum stress σ after prestressing force circular membrane axisymmetric deformationmParsing relationship
Wherein,
And d0、c0Value by equation
With
It determines, wherein
As long as in this way, the difference in height where accurately measuring rigid circular pipe internal liquid level and rigid circular pipe lower edge between plane
h0Value, so that it may the maximum stress σ after prestressing force circular membrane axisymmetric deformationmIt decides, wherein gravity acceleration g
Unit be the every quadratic power second (mm/s of millimeter2), the unit of the density p of liquid is gram every cubic millimeter of (g/mm3), parameters E, σ0
And σmUnit be Newton per square millimetre (N/mm2), parameter a, h, wm、h0, H, t unit be millimeter (mm), and parameter
ν、c0、c2、c4、c6、c8、c10、c12、d0、d2、d4、d6、d8、d10、d12It is characteristic.
Detailed description of the invention
Fig. 1 is the schematic diagram of the axisymmetric deformation for the prestressing force circular membrane that liquid effects following peripheral fixes to clamp, wherein
1 is the prestressing force circular membrane after axisymmetric deformation, and 2 be rigid circular pipe, and 3 be clamping device, and 4 indicate the liquid inside rigid circular pipe
Face, 5 indicate the plane where rigid circular pipe lower edges, and a indicate the inside radius of rigid circular pipe, clamping device inside radius with
And the radius of prestressing force circular membrane, H indicate the height of rigid circular pipe, h0It indicates under rigid circular pipe internal liquid level and rigid circular pipe
Difference in height where edge between plane, t indicate the wall thickness of rigid circular pipe, wmAfter indicating prestressing force circular membrane axisymmetric deformation
Maximum defluxion.
Specific embodiment
Below with reference to Fig. 1, further description of the technical solution of the present invention:
As shown in Figure 1, in a height H=50mm, wall thickness t=5mm, inside radius a=50mm, axial line and gravity direction
A Young's modulus of lasticity E=7.84N/mm is fixed to clamp on the lower edge of parallel rigid circular pipe2, it is Poisson's ratio ν=0.47, thick
Spend h=1mm, prestressing force σ0=1N/mm2Film, enable rigid circular pipe lower end seal while formed a radius be a=
The prestressing force circular membrane structure that the periphery of 50mm fixes to clamp, and be ρ=1 to suitable, density is injected inside rigid circular pipe
×10-3g/mm3Liquid, so that prestressing force circular membrane is generated axisymmetric deformation and flat reaching static(al) under liquid effects
Liquid level after weighing apparatus inside rigid circular pipe can exceed the plane where the lower edge of rigid circular pipe, measure rigid circular pipe internal liquid level with
Difference in height h where rigid circular pipe lower edge between plane0=200mm, and acceleration of gravity takes g=1 × 10-3mm/s2, use
Method given by the present invention, by equation
Obtain c0=0.128296, d0=0.024987 and c2=-1.563762 × 10-4、c4=1.968238 × 10-7、
c6=5.101696 × 10-12、c8=-1.591351 × 10-13、c10=-9.298577 × 10-17、c12=1.742449 × 10-19、 d2=-0.025010, d4=2.360932 × 10-5、d6=1.567395 × 10-8、d8=-9.620052 × 10-12、 d10
=-2.799694 × 10-14、d12=-7.337128 × 10-18,
Finally, by equation
Maximum stress σ after obtaining prestressing force circular membrane axisymmetric deformationm=1.005841N/mm2。
Claims (1)
1. a kind of determination method of the maximum stress of liquid effects lower prestress circular membrane, it is characterised in that: in a height
One piece of poplar is fixed to clamp on lower edge for H, wall thickness t, inside radius a, the axial line rigid circular pipe parallel with gravity direction
Family name's elasticity modulus is E, Poisson's ratio ν, with a thickness of h, prestressing force σ0Film, so as to make rigid circular pipe lower end seal while
The prestressing force circular membrane structure that the periphery that a radius is a fixes to clamp can be formed, and appropriate to injection inside rigid circular pipe
, density be ρ liquid, make prestressing force circular membrane is generated under liquid effects axisymmetric deformation and reach static(al) put down
Liquid level after weighing apparatus inside rigid circular pipe can exceed the plane where the lower edge of rigid circular pipe, then being based on prestressing force circular membrane
The standing balance of axisymmetric deformation is analyzed, and the height where rigid circular pipe internal liquid level and rigid circular pipe lower edge between plane is utilized
Spend difference h0Measured value, by equation
Determine parameter c0、d0And c2、c4、c6、c8、c10、c12、d2、d4、d6、d8、d10、d12Value, finally, by equation
Maximum stress σ after determining prestressing force circular membrane axisymmetric deformationm, wherein the unit of gravity acceleration g is that millimeter is every
Quadratic power second (mm/s2), the unit of the density p of liquid is gram every cubic millimeter of (g/mm3), parameters E, σ0And σmUnit be
Newton per square millimetre (N/mm2), parameter a, h, wm、h0, H, t unit be millimeter (mm), and parameter ν, c0、c2、c4、c6、
c8、c10、c12、d0、d2、d4、d6、d8、d10、d12It is characteristic.
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| CN201910488164.6A CN110286040B (en) | 2019-06-05 | 2019-06-05 | Method for determining maximum stress of prestressed circular thin film under action of liquid |
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| CN201910488164.6A CN110286040B (en) | 2019-06-05 | 2019-06-05 | Method for determining maximum stress of prestressed circular thin film under action of liquid |
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| CN110286040B CN110286040B (en) | 2021-06-25 |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111442982A (en) * | 2020-03-18 | 2020-07-24 | 重庆大学 | Method for determining maximum stress of circular film under uniformly distributed load |
| CN111442984A (en) * | 2020-03-25 | 2020-07-24 | 重庆大学 | Method for determining maximum stress of circular film under transversely uniformly distributed load |
| CN112903218A (en) * | 2021-01-18 | 2021-06-04 | 重庆大学 | Method for determining maximum stress of prestressed circular film with limited maximum deflection under air pressure |
| CN113720689A (en) * | 2021-08-17 | 2021-11-30 | 重庆大学 | Method for determining the maximum stress of a circular membrane in contact with a rigid plate under gas pressure |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111442982A (en) * | 2020-03-18 | 2020-07-24 | 重庆大学 | Method for determining maximum stress of circular film under uniformly distributed load |
| CN111442984A (en) * | 2020-03-25 | 2020-07-24 | 重庆大学 | Method for determining maximum stress of circular film under transversely uniformly distributed load |
| CN112903218A (en) * | 2021-01-18 | 2021-06-04 | 重庆大学 | Method for determining maximum stress of prestressed circular film with limited maximum deflection under air pressure |
| CN113720689A (en) * | 2021-08-17 | 2021-11-30 | 重庆大学 | Method for determining the maximum stress of a circular membrane in contact with a rigid plate under gas pressure |
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