CN109342192A - Maximum defluxion is limited down the determination method of circular membrane maximum defluxion by elasticity - Google Patents
Maximum defluxion is limited down the determination method of circular membrane maximum defluxion by elasticity Download PDFInfo
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- CN109342192A CN109342192A CN201811540012.8A CN201811540012A CN109342192A CN 109342192 A CN109342192 A CN 109342192A CN 201811540012 A CN201811540012 A CN 201811540012A CN 109342192 A CN109342192 A CN 109342192A
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- 239000012528 membrane Substances 0.000 title claims abstract description 41
- 238000000034 method Methods 0.000 title claims abstract description 9
- 230000003993 interaction Effects 0.000 claims abstract description 4
- 238000011160 research Methods 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 2
- 238000012827 research and development Methods 0.000 description 2
- 240000007594 Oryza sativa Species 0.000 description 1
- 235000007164 Oryza sativa 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
- 238000010586 diagram Methods 0.000 description 1
- 239000004744 fabric Substances 0.000 description 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 description 1
- 235000009566 rice Nutrition 0.000 description 1
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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
- G01N3/08—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
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
- G01N2203/0075—Strain-stress relations or elastic constants
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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
- G01N2203/06—Indicating or recording means; Sensing means
- G01N2203/067—Parameter measured for estimating the property
- G01N2203/0676—Force, weight, load, energy, speed or acceleration
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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
- G01N2203/06—Indicating or recording means; Sensing means
- G01N2203/067—Parameter measured for estimating the property
- G01N2203/0682—Spatial dimension, e.g. length, area, angle
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- General Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
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- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
The invention discloses a kind of maximum defluxions to be limited down the determination method of circular membrane maximum defluxion 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 wmDistance, 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 parallelm, 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 defluxion w after determining circular membrane axisymmetric deformationm。
Description
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 defluxion 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 defluxion under lateral Uniform Loads.
Maximum defluxion is limited down the determination method of circular membrane maximum defluxion 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 wmDistance, 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 wm, 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 defluxion w after applied load q and circular membrane axisymmetric deformationmBetween 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 defluxion w after circular membrane axisymmetric deformationmReally
It decides, wherein parameter a, b, h, L, wmUnit be millimeter (mm), parameters E, q0, q unit be every square of milli of newton
Rice (N/mm2), the unit of parameter k is Newton per millimeter (N/mm), and parameter v, 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 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, wmThe 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 wmDistance, 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=50mmm, measure load q=0.01N/mm2, using given by the present invention
Method, by following equation
Obtain b=4.018560mm, c0=0.401570, c1=-0.073751 and d0=0.396980, d1=-
0.663931、d2=-0.753233, d3=-0.081738, d4=-0.231329, d5=0.059966, d6=-0.241261.
Finally, by equation
Maximum defluxion w after obtaining circular membrane axisymmetric deformationm=3.178515mm.
Claims (1)
1. the determination method that maximum defluxion is limited down circular membrane maximum defluxion 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 wmDistance, 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 wm, 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、c1And d0、d1、d2、d3、d4、d5、d6Value, finally, by equation
Maximum defluxion w after determining circular membrane axisymmetric deformationm, wherein parameter a, b, h, L, wmUnit be millimeter
(mm), parameters E, q0, q unit be Newton per square millimetre (N/mm2), the unit of parameter k is Newton per millimeter (N/mm),
And parameter v, c0、c1、c2、c3、c4、c5、c6、d0、d1、d2、d3、d4、d5、d6It is characteristic.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811540012.8A CN109342192B (en) | 2018-12-17 | 2018-12-17 | Method for determining maximum deflection of circular film under limitation of elasticity of maximum deflection |
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|---|---|---|---|
| CN201811540012.8A CN109342192B (en) | 2018-12-17 | 2018-12-17 | Method for determining maximum deflection of circular film under limitation of elasticity of maximum deflection |
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| CN109342192A true CN109342192A (en) | 2019-02-15 |
| CN109342192B CN109342192B (en) | 2020-11-13 |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110044538A (en) * | 2019-04-09 | 2019-07-23 | 重庆大学 | A kind of determination method of circular membrane maximum stress under liquid effects |
| CN110231215A (en) * | 2019-06-05 | 2019-09-13 | 重庆大学 | The determination method of the maximum defluxion for the prestressing force circular membrane that amount of deflection is limited by elasticity |
| CN110320101A (en) * | 2019-06-05 | 2019-10-11 | 重庆大学 | A kind of determination method of the maximum defluxion of liquid effects lower prestress circular membrane |
| CN113434986A (en) * | 2021-07-14 | 2021-09-24 | 重庆大学 | Method for determining deflection of annular thin film with rigid connection between inner edge and circular thin plate |
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| CN103968801A (en) * | 2014-05-30 | 2014-08-06 | 重庆大学 | Method for determining maximum deflection value of pre-stressed circular thin film under uniformly distributed load |
| CN105890970A (en) * | 2016-04-26 | 2016-08-24 | 重庆大学 | Method for determining maximum deflection of annular films of central zone rigid plates under uniformly distributed load |
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2018
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110044538A (en) * | 2019-04-09 | 2019-07-23 | 重庆大学 | A kind of determination method of circular membrane maximum stress under liquid effects |
| CN110231215A (en) * | 2019-06-05 | 2019-09-13 | 重庆大学 | The determination method of the maximum defluxion for the prestressing force circular membrane that amount of deflection is limited by elasticity |
| CN110320101A (en) * | 2019-06-05 | 2019-10-11 | 重庆大学 | A kind of determination method of the maximum defluxion of liquid effects lower prestress circular membrane |
| CN110231215B (en) * | 2019-06-05 | 2021-06-08 | 重庆大学 | Method for determining maximum deflection of prestressed circular film with deflection limited by elasticity |
| CN110320101B (en) * | 2019-06-05 | 2021-06-29 | 重庆大学 | Method for determining maximum deflection of prestressed circular film under action of liquid |
| CN113434986A (en) * | 2021-07-14 | 2021-09-24 | 重庆大学 | Method for determining deflection of annular thin film with rigid connection between inner edge and circular thin plate |
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| CN109342192B (en) | 2020-11-13 |
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