CN105956379B - The determining method of the annular membrane maximum stress of center band rigid plate under uniform load - Google Patents
The determining method of the annular membrane maximum stress of center band rigid plate under uniform load Download PDFInfo
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- CN105956379B CN105956379B CN201610263954.0A CN201610263954A CN105956379B CN 105956379 B CN105956379 B CN 105956379B CN 201610263954 A CN201610263954 A CN 201610263954A CN 105956379 B CN105956379 B CN 105956379B
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- 238000000034 method Methods 0.000 title claims abstract description 9
- 239000012528 membrane Substances 0.000 title abstract description 9
- 230000015572 biosynthetic process Effects 0.000 abstract 1
- 239000000463 material Substances 0.000 description 1
- 230000002093 peripheral effect Effects 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
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- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16Z—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS, NOT OTHERWISE PROVIDED FOR
- G16Z99/00—Subject matter not provided for in other main groups of this subclass
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Abstract
The invention discloses the determining methods of the annular membrane maximum stress of center band rigid plate under uniform load：Use clamping device of the inside radius for a, it is h by thickness, the annular membrane of rigid plate that Young's modulus of elasticity E, Poisson's ratio ν, center band radius are b fixes to clamp, one outer radius of formation is a, the axial symmetry annular membrane for the center band rigid plate that the periphery that inside radius is b fixes to clamp, a uniform load q is laterally applied to it, standing balance analysis based on this On Axisymmetric Deformation of A, and using the measured value of uniform load q, then it can determine that the maximum stress σ of the annular membranem。
Description
Technical Field
The invention relates to a method for determining the maximum stress of an annular film with a rigid plate at the center under uniformly distributed load.
Background
The analytic solution of the problem of axisymmetric deformation of the annular film with the rigid plate at the center under uniformly distributed load has important significance for the development of sensors, instruments and meters. Because the film is a flexible material and usually presents larger deflection under the action of uniform load, the deformation problem of the film has stronger nonlinearity, and the nonlinearity problems are usually difficult to solve analytically. The invention is dedicated to the analytical research of the axial symmetry deformation problem of the annular film with the rigid plate at the center under the uniformly distributed load, obtains the analytical solution of the problem and provides the method for determining the maximum stress of the annular film with the rigid plate at the center under the uniformly distributed load on the basis.
Disclosure of Invention
The method for determining the maximum stress of the annular film with the rigid plate at the center under uniformly distributed load comprises the following steps: the method comprises the steps of adopting a clamping device with an inner radius of a, fixedly clamping an annular film of a rigid plate with the thickness of h, the Young modulus of elasticity of E, the Poisson ratio of v and the radius of a central belt of b to form an axisymmetric annular film of the rigid plate with the periphery fixedly clamped with the outer radius of a and the inner radius of b, transversely applying an evenly distributed load q to the axisymmetric annular film, and obtaining the maximum stress sigma of the annular film based on the static balance analysis of the axisymmetric deformation problemmThe analytic relation with the uniformly distributed load q is
Wherein,
and β ═ a + b)/2a, c1And c2Is given by the equation
And
determining, wherein,
thus, the maximum stress sigma after deformation of the annular film can be determined by accurately measuring the value of the uniformly distributed load q appliedm. Wherein, all parameters adopt international system of units.
Drawings
FIG. 1 is a schematic view of a loading configuration of a peripheral fixedly clamped annular membrane with a rigid plate in the center under a uniform load, wherein 1-the annular membrane, 2-the rigid plate, 3-the clamping means, and a denotes the inner radius of the clamping means and the outer radius of the annular membrane, b denotes the radius of the rigid plate and the inner radius of the annular membrane, r denotes the radial coordinate, w (r) denotes the transverse coordinate at point r, q denotes the transverse uniform load, wmIndicating the maximum deflection of the film.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
as shown in fig. 1, a rubber film of a rigid plate having a thickness h of 0.06mm, a young's modulus E of 7.84MPa, a poisson's ratio v of 0.47 and a center belt radius b of 5mm was fixed and clamped by a clamping device having an inner radius a of 20mm, and an axisymmetric ring-shaped film of a rigid plate having a periphery fixed and clamped with an outer radius a of 20mm and an inner radius b of 5mm was formed, and a uniform load q was applied laterally thereto and measured to be 0.01 MPa. By adopting the method provided by the invention, the equation is passed
And
then c can be obtained1＝-0.7026607165，c2-0.6927450924 wherein, in the formula,
β＝(a+b)/2a＝0.625，
finally, the equation
The maximum stress σ of the annular film can be obtainedm0.74044MPa, wherein,
Claims (1)
1. The method for determining the maximum stress of the annular film with the rigid plate at the center under uniformly distributed loads is characterized by comprising the following steps of: fixedly clamping an annular film of a rigid plate with the thickness of h, the Young's modulus of elasticity of E, the Poisson ratio of v and the radius of a central zone of b by adopting a clamping device with the inner radius of a to form an axisymmetric annular film of the rigid plate with the central zone, the periphery of which is fixedly clamped and the outer radius of a and the inner radius of b, transversely applying an evenly distributed load q to the axisymmetric annular film, measuring the value of the applied evenly distributed load q, and determining the maximum stress sigma of the annular film by the following formulam：
Wherein,
and β ═ a + b)/2a, c1And c2Is given by the equation
And
determining, wherein,
all parameters adopt an international system of units.
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| CN201610263954.0A CN105956379B (en) | 2016-04-26 | 2016-04-26 | The determining method of the annular membrane maximum stress of center band rigid plate under uniform load |
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| CN201610263954.0A CN105956379B (en) | 2016-04-26 | 2016-04-26 | The determining method of the annular membrane maximum stress of center band rigid plate under uniform load |
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| CN105956379A CN105956379A (en) | 2016-09-21 |
| CN105956379B true CN105956379B (en) | 2018-06-19 |
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Families Citing this family (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106706169B (en) * | 2017-01-16 | 2019-04-05 | 重庆大学 | The determination method of annular membrane maximum stress under combined load with hard core |
| CN106644248B (en) * | 2017-01-16 | 2019-04-05 | 重庆大学 | The determination method of circular membrane maximum stress under maximum defluxion constrained state |
| CN106769477B (en) * | 2017-01-16 | 2019-04-05 | 重庆大学 | The determination method of axis load lower prestress circular membrane maximum stress |
| CN113092040B (en) * | 2021-04-16 | 2022-10-25 | 重庆大学 | Method for determining maximum stress of annular film under transversely uniformly distributed load |
| CN113092041B (en) * | 2021-04-16 | 2022-09-27 | 重庆大学 | Method for determining maximum deflection of annular film under transversely uniformly distributed load |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104019931A (en) * | 2014-06-19 | 2014-09-03 | 重庆大学 | Method for determining maximum stress of prestressed annular thin film under transverse concentrated load |
| 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 |
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- 2016-04-26 CN CN201610263954.0A patent/CN105956379B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104019931A (en) * | 2014-06-19 | 2014-09-03 | 重庆大学 | Method for determining maximum stress of prestressed annular thin film under transverse concentrated load |
| 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 |
Non-Patent Citations (1)
| Title |
|---|
| 不同模量简支梁均布荷载下的弹性力学解;何晓婷 等;《工程力学》;20071031;第24卷(第10期);第51-56页 * |
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Effective date of registration: 20191212 Address after: 246400 Jinxi Town, Taihu County, Anqing City, Anhui Province Patentee after: Taihu County market supervision and Inspection Institute (Taihu County functional membrane Testing Institute) Address before: 400044 Shapingba District Sha Street, No. 174, Chongqing Patentee before: Chongqing University |
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