CN109323924B - Method for determining maximum stress of circular film under limitation of elasticity on maximum deflection - Google Patents

Method for determining maximum stress of circular film under limitation of elasticity on maximum deflection Download PDF

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CN109323924B
CN109323924B CN201811566941.6A CN201811566941A CN109323924B CN 109323924 B CN109323924 B CN 109323924B CN 201811566941 A CN201811566941 A CN 201811566941A CN 109323924 B CN109323924 B CN 109323924B
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CN109323924A (en
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何晓婷
李雪
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Chongqing University
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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
    • 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
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    • G01N2203/067—Parameter measured for estimating the property
    • G01N2203/0676—Force, weight, load, energy, speed or acceleration
    • 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
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Abstract

The invention discloses a method for determining the maximum stress of a circular film under the limitation of elasticity on the maximum deflection, which comprises the following steps: e for Young's modulus of elasticity, v for Poisson's ratio, h for thickness, a for radius, and q for self-weight per unit area0The initially flat round film with the fixed and clamped periphery transversely applies uniform load q to make the round film generate axisymmetric deformation so as to push a rigid round plate with radius of a, coaxial axis with the round film, parallel to the initially flat round film and smooth surface to move in parallel wmAnd the axially symmetrically deformed circular membrane and the rigid circular plate form an interaction contact area with a radius b, and the rigid circular plate moving in parallel compresses a spring with a stiffness coefficient k and an original length L by wmThen, after the dead weight of the rigid circular plate is ignored, based on the static balance analysis of the axisymmetric deformation of the circular film, the maximum stress sigma after the axisymmetric deformation of the circular film can be determined by using the measured value of the load qm。

Description

Method for determining maximum stress of circular film under limitation of elasticity on maximum deflection
Technical Field
The invention relates to a method for determining the maximum stress of a circular film under the action of transversely uniformly distributed loads, wherein the periphery of the circular film is fixedly clamped under the condition that the maximum deflection is limited by elasticity.
Background
The axisymmetric deformation of a circular film with a periphery fixedly clamped under the condition that the maximum deflection is limited by elasticity under the action of transversely uniformly distributed loads is utilized and applied in a plurality of engineering technical fields, for example, the axisymmetric deformation is used for researching the adhesion energy measurement of a film/base layer system, and researching various instruments and meters, various sensors and the like. Because the film is usually very thin, the film often generates very large deflection under the action of transversely uniformly distributed load, so that the film has strong geometric nonlinearity, which brings difficulty to analytical research, and therefore, from the new checking result of the existing literature, the axial symmetry deformation problem of the circular film with the periphery fixedly clamped under the condition that the maximum deflection is limited by elasticity under the action of transversely uniformly distributed load is not solved analytically at present. Therefore, it is necessary to perform related analytical research work, which provides convenience and a larger research and development space for the research and development of engineering technology.
Disclosure of Invention
The invention is dedicated to the analytical research of the axial symmetry deformation problem of the circular film fixedly clamped at the periphery under the condition that the maximum deflection is limited by elasticity under the action of the transversely uniformly distributed load, obtains the analytical solution of the axial symmetry deformation problem based on static balance analysis, and provides the method for determining the maximum stress of the circular film fixedly clamped at the periphery under the condition that the maximum deflection is limited by elasticity under the action of the transversely uniformly distributed load.
The method for determining the maximum stress of the circular film under the limitation of elasticity on the maximum deflection comprises the following steps: e for Young's modulus of elasticity, v for Poisson's ratio, h for thickness, a for radius, and q for self-weight per unit area0The initially flat circular film with the fixed and clamped periphery transversely applies an evenly distributed load q, so that the circular film generates axisymmetric deformation to push a rigid circular plate with the radius of a, the circle center of the rigid circular plate is on the same axis with the circle center of the circular film, the rigid circular plate is always parallel to the initially flat circular film, the surface of the rigid circular plate is smooth, and the rigid circular plate moves in parallel wmAnd the axisymmetrically deformed circular membrane forms an interaction contact area with a radius b with the rigid circular plate, and the parallel moving rigid circular plate compresses a spring with a stiffness coefficient k from an original length L by wmThen, after neglecting the dead weight of the rigid circular plate, based on the static balance analysis of the axisymmetric deformation of the circular film, the applied load q and the maximum stress sigma of the axisymmetric deformation of the circular film can be obtainedmAnalytic relationship between
Figure BDA0001913051010000011
Wherein the content of the first and second substances,
Figure BDA0001913051010000021
Figure BDA0001913051010000022
Figure BDA0001913051010000023
Figure BDA0001913051010000024
Figure BDA0001913051010000031
and b, c0、c1Is given by the equation
Figure BDA0001913051010000032
Figure BDA0001913051010000033
And
Figure BDA0001913051010000034
determining, wherein,
Figure BDA0001913051010000035
Figure BDA0001913051010000041
Figure BDA0001913051010000042
Figure BDA0001913051010000043
Figure BDA0001913051010000044
Figure BDA0001913051010000051
thus, the maximum stress sigma after the axial symmetric deformation of the circular film can be obtained by accurately measuring the value of the load qmDetermined, wherein the parameters a, b, h, L, wmAll units of (A) are millimeters (mm), reference E, q0、q、σmAll units of (2) are Newton per square millimeter (N/mm)2) The unit of the parameter k is Newton per millimeter (N/mm), while the parameters v, c0、c1、c2、c3、c4、c5、c6、d1、d2、d3、d4、d5、d6All are dimensionless quantities.
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FIG. 1 is a schematic diagram showing the problem of axisymmetric deformation of a circular film fixedly clamped at its periphery under elastic limit of maximum deflection under a laterally uniform load, wherein 1 is the circular film after axisymmetric deformation, 2 is a rigid circular plate, 3 is a spring, 4 is a clamping device, 5 is a support, 6 is a geometric middle plane of the initially flat circular film, a represents the radii of the circular film and the rigid circular plate and the inner radius of the clamping device, b represents the contact radius of the circular film with the rigid circular plate after axisymmetric deformation, L represents the original length of the spring, q represents the laterally uniform load, o represents the origin of coordinates, r represents a radial coordinate, w represents a lateral coordinate, and w represents a lateral coordinatemShowing the maximum deflection after axisymmetric deformation of the circular film and the distance that the rigid circular plate is moved in parallel and the length that the spring is compressed.
Detailed Description
The technical solution of the present invention is further described with reference to fig. 1 below:
as shown in FIG. 1, the Young's modulus E is 7.84N/mm using a clamp with an inner radius a of 20mm2Poisson's ratio v is 0.47, thickness h is 1mm, unit area dead weight q0＝7.64×10-7N/mm2Clamping the initially flat film and then fixing the clamping device on the support, toForming a circular film structure with a radius a of 20mm and fixedly clamped on the periphery, transversely applying a uniformly distributed load q to the circular film, and enabling the circular film to generate axisymmetric deformation so as to push a round plate with a smooth surface, a radius a of 20mm, a circle center of the round plate and the circle center of the circular film on the same axis, and a round plate parallel to the original flat circular film all the time to move in parallelmAnd an interaction contact area with radius b is formed between the circular film after the axisymmetric deformation and the rigid circular plate, and the rigid circular plate moving in parallel compresses a spring with stiffness coefficient k of 1.5N/mm from the original length L of 50mm by wmThe measured load q is 0.01N/mm2The method provided by the invention is adopted and is represented by the following equation
Figure BDA0001913051010000061
Figure BDA0001913051010000062
Figure BDA0001913051010000063
Figure BDA0001913051010000064
Figure BDA0001913051010000065
Figure BDA0001913051010000066
Figure BDA0001913051010000071
Figure BDA0001913051010000072
Figure BDA0001913051010000081
Figure BDA0001913051010000082
Figure BDA0001913051010000083
Figure BDA0001913051010000091
Figure BDA0001913051010000092
Figure BDA0001913051010000101
B is 4.018560m, mc0＝0.401570、c1＝-0.073751、c2＝-0.121406、c3＝-0.023084、c4＝-0.008135、c5＝-0.064018、c60.100262. Finally, the equation
Figure BDA0001913051010000102
Obtaining the maximum stress sigma after the axisymmetric deformation of the circular filmm＝0.281402N/mm2。

Claims (1)

1. Maximum stress of circular film under limitation of maximum deflection by elasticityThe determination method is characterized in that: e for Young's modulus of elasticity, v for Poisson's ratio, h for thickness, a for radius, and q for self-weight per unit area0The initially flat circular film with the fixed and clamped periphery transversely applies an evenly distributed load q, so that the circular film generates axisymmetric deformation to push a rigid circular plate with the radius of a, the circle center of the rigid circular plate is on the same axis with the circle center of the circular film, the rigid circular plate is always parallel to the initially flat circular film, the surface of the rigid circular plate is smooth, and the rigid circular plate moves in parallel wmAnd the axisymmetrically deformed circular membrane forms an interaction contact area with a radius b with the rigid circular plate, and the parallel moving rigid circular plate compresses a spring with a stiffness coefficient k from an original length L by wmThen, after neglecting the dead weight of the rigid circular plate, based on the static equilibrium analysis of the axisymmetric deformation of the circular film, using the measured value of the load q, from the following equation
Figure FDA0001913050000000011
Figure FDA0001913050000000012
Figure FDA0001913050000000013
Figure FDA0001913050000000014
Figure FDA0001913050000000015
Figure FDA0001913050000000016
Figure FDA0001913050000000017
Figure FDA0001913050000000021
Figure FDA0001913050000000031
Figure FDA0001913050000000032
Figure FDA0001913050000000033
Figure FDA0001913050000000041
Figure FDA0001913050000000042
Figure FDA0001913050000000051
Determining the variables b, c0、c1、c2、c3、c4、c5、c6And finally, from the equation
Figure FDA0001913050000000052
Determining the maximum stress sigma after axisymmetric deformation of a circular filmmWherein the parameters a, b, h, L, wmAll units of (A) are millimeters (mm), reference E, q0、q、σmAll units of (2) are Newton per square millimeter (N/mm)2) The unit of the parameter k is Newton per millimeter (N/mm), while the parameters v, c0、c1、c2、c3、c4、c5、c6、d1、d2、d3、d4、d5、d6All are dimensionless quantities.
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CN110044538B (en) * 2019-04-09 2020-10-09 重庆大学 Method for determining maximum stress of circular film under action of liquid
CN109991083B (en) * 2019-04-12 2021-02-19 重庆大学 Method for determining maximum stress under condition of large rotation angle of circular film limited by elasticity
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
CN111474042A (en) * 2020-04-22 2020-07-31 重庆大学 Method for determining maximum stress of prestressed circular thin film under uniformly distributed load
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
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

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
SU1753340A1 (en) * 1989-08-07 1992-08-07 Электростальское научно-производственное объединение "Неорганика" Method for determining mechanical properties of sheet materials
RU2296976C2 (en) * 2004-05-31 2007-04-10 Институт механики и машиностроения Казанского научного центра РАН Method for testing samples of metallic membranes under voltage and device for realization of said method
JP2014126358A (en) * 2012-12-25 2014-07-07 Nagoya Institute Of Technology Biaxial tensile testing method and device used for the same
CN105675484A (en) * 2016-04-26 2016-06-15 重庆大学 Method for determining elastic energy of circular membrane with rigid slab in center and under uniformly distributed load
CN106596267A (en) * 2017-01-16 2017-04-26 重庆大学 Method for determining elastic energy of circular film under condition of restricted maximal deflection

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
SU1753340A1 (en) * 1989-08-07 1992-08-07 Электростальское научно-производственное объединение "Неорганика" Method for determining mechanical properties of sheet materials
RU2296976C2 (en) * 2004-05-31 2007-04-10 Институт механики и машиностроения Казанского научного центра РАН Method for testing samples of metallic membranes under voltage and device for realization of said method
JP2014126358A (en) * 2012-12-25 2014-07-07 Nagoya Institute Of Technology Biaxial tensile testing method and device used for the same
CN105675484A (en) * 2016-04-26 2016-06-15 重庆大学 Method for determining elastic energy of circular membrane with rigid slab in center and under uniformly distributed load
CN106596267A (en) * 2017-01-16 2017-04-26 重庆大学 Method for determining elastic energy of circular film under condition of restricted maximal deflection

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
《Theoretical study on shaft-loaded blister test technique: Synchronous characterization of surface and interfacial mechanical properties》;Junyi Sun et al.;《International Journal of Adhesion & Adhesives》;20140318;第51卷;第128-139页 *
《均布荷载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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