CN106644248B - The determination method of circular membrane maximum stress under maximum defluxion constrained state - Google Patents
The determination method of circular membrane maximum stress under maximum defluxion constrained state Download PDFInfo
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- CN106644248B CN106644248B CN201710030473.XA CN201710030473A CN106644248B CN 106644248 B CN106644248 B CN 106644248B CN 201710030473 A CN201710030473 A CN 201710030473A CN 106644248 B CN106644248 B CN 106644248B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L9/00—Measuring steady of quasi-steady pressure of fluid or fluent solid material by electric or magnetic pressure-sensitive elements; Transmitting or indicating the displacement of mechanical pressure-sensitive elements, used to measure the steady or quasi-steady pressure of a fluid or fluent solid material, by electric or magnetic means
- G01L9/12—Measuring steady of quasi-steady pressure of fluid or fluent solid material by electric or magnetic pressure-sensitive elements; Transmitting or indicating the displacement of mechanical pressure-sensitive elements, used to measure the steady or quasi-steady pressure of a fluid or fluent solid material, by electric or magnetic means by making use of variations in capacitance, i.e. electric circuits therefor
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- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
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Abstract
The determination method of circular membrane maximum stress under maximum defluxion constrained state: to a thickness of h, radius is a, Young's modulus of elasticity is E, Poisson's ratio is that the circular membrane that the periphery of ν fixes to clamp is laterally applied to a uniform load q, deformed film is set to be in contact with a smooth plates, and make smooth plates parallel with the film before deformation, and keep distance H between the two constant, to limit the maximum defluxion of circular membrane after deformation, based on the standing balance analysis to this On Axisymmetric Deformation of A, utilize the measured value of film and the radius b of smooth plates contact area, it then can determine that maximum stress σ of the circular membrane after contacting smooth platesm。
Description
Technical field
The circular membrane fixed to clamp the present invention relates to uniform load following peripheral film under maximum defluxion constrained state
The determination method of maximum stress.
Background technique
Circular membrane structure has a wide range of applications in fields such as machinery, electronics, bioengineering.Capacitance pressure transducer,
Development in, needing to allow circular membrane arrangement works, noncontact mode: film is not generated with smooth electrodes plate in both modes
Contact；Contact mode: film is contacted with smooth electrodes plate.Under contact mode, periphery fixing clamp (under uniform load) under pressure
The maximum defluxion of tight circular membrane is limited by the smooth electrodes plate parallel with the film before deformation always.And from text
It offers and looks into new result and see, maximum defluxion is limited the axial symmetry of circular membrane that rear perimeter edge fixes to clamp under Uniform Loads and becomes
Shape problem, there are no resolved solutions, thus influence the development work of capacitance pressure transducer,.
Summary of the invention
Analytical Solution of the present invention maximum defluxion is limited circular membrane that rear perimeter edge fixes to clamp under the Uniform Loads
On Axisymmetric Deformation of A, and give circular membrane that uniform load following peripheral fixes to clamp on this basis in maximum defluxion
The determination method of film maximum stress under constrained state.
The determination method of circular membrane maximum stress under maximum defluxion constrained state: to a thickness of h, radius a, Young
The circular membrane that the periphery that elasticity modulus is E, Poisson's ratio is ν fixes to clamp is laterally applied to a uniform load q, makes deformed
Film is in contact with a smooth plates, and makes smooth plates parallel with the film before deformation, and keeps smooth plates and become
The distance between film before shape H is constant, so that the maximum defluxion of circular membrane after deformation is limited, then based on to this axis
The standing balance of symmetric deformation problem is analyzed, maximum stress σ of the circular membrane after contacting smooth platesmWith contact area
The parsing relationship of radius b can be expressed as
Wherein,
β=(a+b)/(2a),
α=(a2+2ab-3b2)/(4a2), c0And c1Value by equation
With
It determines, and d0Value by equation
It determines, all parameters all use the International System of Units.
As long as in this way, measuring the value of the radius b of circular membrane and smooth plates contact area, so that it may determine the circle
Maximum stress σ of the film after contacting smooth platesm。
Detailed description of the invention
Fig. 1 is that the circular membrane that the restricted periphery of maximum defluxion fixes to clamp loads organigram, wherein 1- becomes
Circular membrane after shape, 2- smooth plates, 3- clamping device, the circular membrane before 4- deformation, and a indicates circular membrane
Radius, b indicate that the radius of film and smooth plates contact area, r indicate that radial coordinate, w (r) indicate the lateral coordinates at point r,
Q indicates lateral uniform load, and H indicates the distance between circular membrane and smooth plates.
Specific embodiment
Technical solution of the present invention is described in further detail below with reference to Fig. 1:
One uniform load q is laterally applied to the round rubber film that periphery fixes to clamp, makes deformed rubber film
It is in contact with a smooth plates, and makes smooth plates parallel with the film before deformation, and before holding smooth plates and deformation
The distance between film H it is constant, to limit the maximum defluxion of round rubber film after deformation, wherein smooth plates with
The distance between film before deformation H=10mm, thickness h=1mm of round rubber film, radius a=50mm, Young springform
Measure E=7.84MPa, Poisson's ratio ν=0.47.Measure the radius b=10mm of round rubber film Yu smooth plates contact area.It adopts
The method given by the present invention, then α=(a2+2ab-3b2)/(4a2)=0.32, β=(a+b)/(2a)=0.6, passes through equation
With
That is, equation
With
Wherein,
Available c0=0.401817101, c1=-0.07385364133.Then, by equation
That is, equation
Wherein,
d1=-0.6636518605,
d2=-0.7522933448,
d3=-0.08210724161,
d4=-0.2302974328,
d5=0.0593281574,
d6=-0.2400642425,
d7=0.2102577768,
Available d0=0.3970094535.Finally, by formula
That is, formula
It is then available, when the radius b of deformed film and smooth plates contact area reaches 10mm, the circle rubber
The maximum stress σ of glue filmm=0.446MPa.
Claims (1)
1. the determination method of circular membrane maximum stress under maximum defluxion constrained state, it is characterised in that: to a thickness of h, half
The circular membrane that the periphery that diameter is a, Young's modulus of elasticity E, Poisson's ratio are ν fixes to clamp is laterally applied to a uniform load q,
So that deformed film is in contact with a smooth plates, and makes smooth plates parallel with the film before deformation, and keep light
The distance between film before sliding plate and deforming H is constant, to limit the maximum defluxion of circular membrane after deformation, measures thin
The value of the radius b of film and smooth plates contact area, maximum stress σ of the circular membrane after contacting smooth platesmBy following
Formula is determining,
Wherein,
β=(a+b)/(2a),
α=(a2+2ab-3b2)/(4a2), c0And c1Value by equation
With
It determines, and d0Value by equation
It determines, all parameters all use the International System of Units.
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| CN201710030473.XA CN106644248B (en) | 2017-01-16 | 2017-01-16 | The determination method of circular membrane maximum stress under maximum defluxion constrained state |
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| CN106644248B true CN106644248B (en) | 2019-04-05 |
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Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108096664B (en) * | 2017-12-25 | 2024-01-26 | 浙江师范大学 | Novel separable piezoelectric medical infusion pump |
| CN110286031B (en) * | 2019-06-05 | 2021-06-29 | 重庆大学 | Method for determining maximum stress of prestressed circular thin film with flexibility limited by elasticity |
| CN110286040B (en) * | 2019-06-05 | 2021-06-25 | 重庆大学 | Method for determining maximum stress of prestressed circular thin film under action of liquid |
| CN112903218B (en) * | 2021-01-18 | 2023-01-20 | 重庆大学 | Method for determining maximum stress of prestressed circular film with limited maximum deflection under air pressure |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103983380A (en) * | 2014-05-30 | 2014-08-13 | 重庆大学 | Method for determining maximum stress value of prestress circular thin film under uniformly-distributed loads |
| CN104749033A (en) * | 2015-04-22 | 2015-07-01 | 重庆大学 | Determination method for maximum stress of large-turning angle circular membrane under uniformly distributed load |
| CN105956379A (en) * | 2016-04-26 | 2016-09-21 | 重庆大学 | Method for determining maximum stress of annular thin film with rigid plate in center under uniformly distributed load |
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2017
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103983380A (en) * | 2014-05-30 | 2014-08-13 | 重庆大学 | Method for determining maximum stress value of prestress circular thin film under uniformly-distributed loads |
| CN104749033A (en) * | 2015-04-22 | 2015-07-01 | 重庆大学 | Determination method for maximum stress of large-turning angle circular membrane under uniformly distributed load |
| CN105956379A (en) * | 2016-04-26 | 2016-09-21 | 重庆大学 | Method for determining maximum stress of annular thin film with rigid plate in center under uniformly distributed load |
Non-Patent Citations (3)
| Title |
|---|
| Nonlinear bending analysis of thin circular plates by differential quadrature;Alfred G.Striz etc.;《Thin-Walled Structures》;20030218;第6卷(第1期);第51-62页 |
| 均变载荷下固定边圆薄板大挠度问题;潘立宙;《力学学报》;19570531;第1卷(第2期);第205-232页 |
| 均布载荷下受有预加张力圆薄膜的轴对称变形;何晓婷 等;《重庆大学学报》;20100131;第33卷(第1期);第109-112页 |
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