CN110018050A - Method for obtaining the elasticity modulus of tabular component - Google Patents

Method for obtaining the elasticity modulus of tabular component Download PDF

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Publication number
CN110018050A
CN110018050A CN201910339395.0A CN201910339395A CN110018050A CN 110018050 A CN110018050 A CN 110018050A CN 201910339395 A CN201910339395 A CN 201910339395A CN 110018050 A CN110018050 A CN 110018050A
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tabular component
formula
pressure
elasticity modulus
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CN110018050B (en
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林韦廷
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Hefei Lianbao Information Technology Co Ltd
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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
    • G01N2203/0014—Type of force applied
    • G01N2203/0016—Tensile or compressive
    • G01N2203/0019—Compressive
    • 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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  • General Health & Medical Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
  • Developing Agents For Electrophotography (AREA)
  • Compositions Of Macromolecular Compounds (AREA)

Abstract

The invention discloses a kind of methods for obtaining the elasticity modulus of tabular component, comprising the following steps: S10: 3 stress test conditions is established, to obtain to the pressure P of tabular component and based on amount of deflection Umax caused by pressure P；S20: based on Plate Theory acquisition about the elastic modulus E of tabular component, the relational expression of pressure P and amount of deflection Umax；S30: the elastic modulus E of tabular component is calculated based on pressure P and amount of deflection Umax.The present invention obtains the elasticity modulus of tabular component by introducing the calculation formula of Plate Theory, so that specimen size is not by limiting width in the test specifications such as ASTM and GB, scalable body size range to be measured is wider, so that influence of the tabular component width to elasticity modulus is contemplated in the calculating process of elasticity modulus, so that the calculated elasticity modulus of institute is closer to true elasticity modulus.

Description

Method for obtaining the elasticity modulus of tabular component
Technical field
The present invention relates to field of engineering technology more particularly to a kind of methods for obtaining the elasticity modulus of tabular component.
Background technique
Be readily appreciated that ground, using tabular component on an electronic device because electronic equipment using when be often subject to outer masterpiece With or impact, need to know the mechanical property of its (tabular component), it is especially desirable to obtain the elasticity modulus of tabular component.
In the prior art, the elasticity modulus of tabular component is obtained by the mode that 3 stress tests are combined with theoretical formula , wherein applied theoretical formula is mostly the various beam theory formula by transformation, this leads to the bullet of obtained tabular component Property modulus because do not consider the width of tabular component to deformation influence (in the test specifications such as ASTM and GB, the width of tabular component Degree is limited in the range of very little, so that the elasticity modulus acquisition of tabular component is considered not considering width parameters) and It differs greatly with actual elastic modulus, that is, the accuracy of the elasticity modulus of tabular component obtained is very poor.
Summary of the invention
For the above-mentioned technical problems in the prior art, the embodiment provides one kind for obtaining plate The method of the elasticity modulus of component.
In order to solve the above technical problems, the embodiment of the present invention the technical solution adopted is that:
A method of for obtaining the elasticity modulus of tabular component, comprising the following steps:
S10: establishing 3 stress test conditions, to obtain to the pressure P of tabular component and based on produced by pressure P Amount of deflection Umax；
S20: based on Plate Theory acquisition about the elastic modulus E of tabular component, the relationship of pressure P and amount of deflection Umax Formula；
S30: the elastic modulus E of tabular component is calculated based on pressure P and amount of deflection Umax.
Preferably, S10 the following steps are included:
S11: being spaced and two support bars are arranged in parallel；
S12: tabular component is placed on two support bars, the extending direction of support bar and the width direction of tabular component Unanimously, the arranged direction of two support bars and the length direction of tabular component are consistent；
S13: applying downward pressure P to the upper face of the tabular component for the medium position being located between two support bars, The produced amount of deflection Umax of the tabular component at pressure P is obtained by the displacement sensor being located at below tabular component.
Preferably, S20 the following steps are included:
S21: by the strain field formula (1) in Plate Theory:
And the stress field formula (2) in Plate Theory:
Substitute into the strain energy formulation (3) in Plate Theory:
Vs=1/2 ∫ ∫ ∫ (σxεx+σyεy+σzεz+τxyεxy+τxzεxz+τyzεyz)dxdydz
S22: by the displacement field formula (4) in Plate Theory:
Substitute into the acting formula (5) in Plate Theory:
Wload=∫ ∫ (- p (x, y) Uz) dxdy=∫ ∫ (- p (x, y) w) dxdy
S23: formula (4) and formula (5) are substituted into Chinese John Milton principle formula (6):
δ(1)=∫ (- Vs+Wload) dt=0
The deformation equation (7) for deriving You La-Lagrange equation to obtain rectangular specimen is handled through variation:
Wherein, D=(E h3)/(12(1-v2))
Wherein: p (x, y) is pressure function；P (x, y)=(P/b) δ (x-L/2)
S24: Lay is tieed up into formula (8):
W=Σ { [Am e(-mπy)/L+y Bm e(-mπy)/L+Cm e(mπy)/L+y Dm e(mπy)/L+(2L3P Sin(mπ/2))/(b D m4π4)]Sin((mπx)/L)}
The boundary condition for first substituting into 3 stress tests parses Am, Bm, Cm, Dm, then by Am to Dm together with formula (8) generation Enter in formula (7), to parse:
Wherein:
L are as follows: the tested length of span of tabular component.
B are as follows: the width of tabular component；
H are as follows: the thickness of tabular component；
X are as follows: with tabular component coordinate consistent in length；
Y are as follows: the coordinate with tabular component equivalent width；
Z are as follows: the coordinate with tabular component consistency of thickness；
V are as follows: Poisson's ratio, access value are 0.35.
Compared with prior art, the beneficial effect of the method for the elasticity modulus for obtaining tabular component of the invention is:
1, the present invention obtains the elasticity modulus of tabular component by introducing the calculation formula of Plate Theory, so that springform Influence of the tabular component width to elasticity modulus is contemplated in the calculating process of amount, so that specimen size is not tested by ASTM and GB etc. To the limitation of width in specification, scalable body size range to be measured is wider, so that the calculated elasticity modulus of institute is closer to very Real elasticity modulus.
2, the present invention obtains boundary condition ginseng using Chinese John Milton principle and You La-glug Lang variation equation formula The relation formula between P and Umax and elasticity modulus is measured, so that can by obtaining that elasticity modulus becomes according to Plate Theory Energy.
3, the present invention parses elasticity modulus using Lay dimension method, and then keeps the process for parsing elasticity modulus simpler.
Detailed description of the invention
Fig. 1 is the experimental rig for establishing three point test condition.
Specific embodiment
Technical solution in order to enable those skilled in the art to better understand the present invention, with reference to the accompanying drawing and specific embodiment party Formula elaborates to the present invention.
Embodiment of the invention discloses a kind of methods for obtaining the elasticity modulus of tabular component 10, including following step It is rapid:
S10: establishing 3 stress test conditions, to obtain to the pressure P of tabular component 10 and be produced based on pressure P Raw amount of deflection Umax；
S20: based on Plate Theory acquisition about the elastic modulus E of tabular component 10, the relationship of pressure P and amount of deflection Umax Formula；
S30: the elastic modulus E of tabular component 10 is calculated based on pressure P and amount of deflection Umax.
Preferably, such as Fig. 1, S10 the following steps are included:
S11: being spaced and two support bars are arranged in parallel；
S12: tabular component 10 is placed on two support bars, the extending direction of support bar and the width of tabular component 10 Direction is consistent, and the arranged direction of two support bars is consistent with the length direction of tabular component 10；
S13: apply downward pressure to the upper face of the tabular component 10 for the medium position being located between two support bars P obtains the produced amount of deflection of the tabular component 10 at pressure P by the displacement sensor for being located at 10 lower section of tabular component Umax。
Preferably, S20 the following steps are included:
S21: by the strain field formula (1) in Plate Theory:
And the stress field formula (2) in Plate Theory:
Substitute into the strain energy formulation (3) in Plate Theory:
Vs=1/2 ∫ ∫ ∫ (σxεx+σyεy+σzεz+τxyεxy+τxzεxz+τyzεyz)dxdydz
S22: by the displacement field formula (4) in Plate Theory:
Substitute into the acting formula (5) in Plate Theory:
Wload=∫ ∫ (- p (x, y) Uz) dxdy=∫ ∫ (- p (x, y) w) dxdy
S23: formula (4) and formula (5) are substituted into Chinese John Milton principle formula (6):
δ(1)=∫ (- Vs+Wload) dt=0
The deformation equation (7) for deriving You La-Lagrange equation to obtain rectangular specimen is handled through variation:
Wherein, D=(E h3)/(12(1-v2))
Wherein: p (x, y) is pressure function；P (x, y)=(P/b) δ (x-L/2)
S24: Lay is tieed up into formula (8):
W=Σ { [Am e(-mπy)/L+y Bm e(-mπy)/L+Cm e(mπy)/L+y Dm e(mπy)/L+(2L3P Sin(mπ/2))/(b D m4π4)]Sin((mπx)/L)}
The boundary condition for first substituting into 3 stress tests parses Am, Bm, Cm, Dm, then by Am to Dm together with formula (8) generation Enter in formula (7), to parse:
Wherein:
L are as follows: the tested length of span of tabular component 10.
B are as follows: the width of tabular component 10；
H are as follows: the thickness of tabular component 10；
X are as follows: with the coordinate consistent in length of tabular component 10；
Y are as follows: the coordinate with 10 equivalent width of tabular component；
Z are as follows: the coordinate with 10 consistency of thickness of tabular component；
V are as follows: Poisson's ratio, access value are 0.35.
Advantage provided by the present invention for obtaining the method for the elasticity modulus of tabular component 10 is:
1, the present invention obtains the elasticity modulus of tabular component 10 by introducing the calculation formula of Plate Theory, so that elastic Influence of 10 width of tabular component to elasticity modulus is contemplated in the calculating process of modulus, so that specimen size is not (international by ASTM Test specification) and the test specifications such as GB in limitation to width, scalable body size range to be measured is wider, so that being calculated Elasticity modulus closer to true elasticity modulus.
2, the present invention obtains boundary condition ginseng using Chinese John Milton principle and You La-glug Lang variation equation formula The relation formula between P and Umax and elasticity modulus is measured, so that can by obtaining that elasticity modulus becomes according to Plate Theory Energy.
3, the present invention parses elasticity modulus using Lay dimension method, and then keeps the process for parsing elasticity modulus simpler.
Above embodiments are only exemplary embodiment of the present invention, are not used in the limitation present invention, protection scope of the present invention It is defined by the claims.Those skilled in the art can within the spirit and scope of the present invention make respectively the present invention Kind modification or equivalent replacement, this modification or equivalent replacement also should be regarded as being within the scope of the present invention.

Claims (3)

1. a kind of method for obtaining the elasticity modulus of tabular component, which comprises the following steps:
S10: establishing 3 stress test conditions, to obtain to the pressure P of tabular component and based on scratching caused by pressure P Spend Umax；
S20: based on Plate Theory acquisition about the elastic modulus E of tabular component, the relational expression of pressure P and amount of deflection Umax；
S30: the elastic modulus E of tabular component is calculated based on pressure P and amount of deflection Umax.
2. the method according to claim 1 for obtaining the elasticity modulus of tabular component, which is characterized in that S10 includes Following steps:
S11: being spaced and two support bars are arranged in parallel；
S12: tabular component is placed on two support bars, the extending direction of support bar and the width direction one of tabular component It causes, the arranged direction of two support bars and the length direction of tabular component are consistent；
S13: applying downward pressure P to the upper face of the tabular component for the medium position being located between two support bars, by Displacement sensor below tabular component obtains the produced amount of deflection Umax of the tabular component at pressure P.
3. the method according to claim 1 for obtaining the elasticity modulus of tabular component, which is characterized in that S20 includes Following steps:
S21: by the strain field formula (1) in Plate Theory:
And the stress field formula (2) in Plate Theory:
Substitute into the strain energy formulation (3) in Plate Theory:
Vs=1/2 ∫ ∫ ∫ (σxεx+σyεy+σzεz+τxyεxy+τxzεxz+τyzεyz)dxdydz
S22: by the displacement field formula (4) in Plate Theory:
Substitute into the acting formula (5) in Plate Theory:
Wload=∫ ∫ (- p (x, y) Uz) dxdy=∫ ∫ (- p (x, y) w) dxdy
S23: formula (4) and formula (5) are substituted into Chinese John Milton principle formula (6):
δ(1)=∫ (- Vs+Wload) dt=0
The deformation equation (7) for deriving You La-Lagrange equation to obtain rectangular specimen is handled through variation:
Wherein, D=(E h3)/(12(1-v2))
Wherein: p (x, y) is pressure function；P (x, y)=(P/b) δ (x-L/2)
S24: Lay is tieed up into formula (8):
W=Σ { [Ame(-mπy)/L+y Bme(-mπy)/L+Cme(mπy)/L+y Dme(mπy)/L+(2L3P Sin(mπ/2))/(b D m4π4)] Sin((mπx)/L)}
The boundary condition for first substituting into 3 stress tests parses Am, Bm, Cm, Dm, then Am to Dm is substituted into public affairs together with formula (8) In formula (7), to parse:
Wherein:
L are as follows: the tested length of span of tabular component.
B are as follows: the width of tabular component；
H are as follows: the thickness of tabular component；
X are as follows: with tabular component coordinate consistent in length；
Y are as follows: the coordinate with tabular component equivalent width；
Z are as follows: the coordinate with tabular component consistency of thickness；
V are as follows: Poisson's ratio, access value are 0.35.
CN201910339395.0A 2019-04-25 2019-04-25 Method for obtaining the modulus of elasticity of a plate-shaped component Active CN110018050B (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111177944A (en) * 2020-01-09 2020-05-19 暨南大学 Deep-sea pipeline buckling propagation pressure calculation method based on plate-shell theory

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CN101788427A (en) * 2010-01-29 2010-07-28 湘潭大学 Device for detecting mechanical property of multifunctional film
CN103245437A (en) * 2012-02-13 2013-08-14 付康 System and method for determining nonlinear membrane stress
CN105547861A (en) * 2016-02-06 2016-05-04 南京林业大学 Method for enhancing capability of testing modulus of elasticity and precision of Poisson's ratio of wood by four-point bent beam
CN106596256A (en) * 2016-12-13 2017-04-26 西安科技大学 Apparatus suitable for measuring bending rigidity, elasticity modulus, shear modulus and bulk modulus
CN107729605A (en) * 2017-09-06 2018-02-23 北京航空航天大学 A kind of modification method of the layer stripping residual stress measurement value based on Plate Theory
CN109342225A (en) * 2018-12-05 2019-02-15 郑州大学 Elasticity modulus test method is drawn in Polypropylene Fiber Reinforced Cement Stabilized Macadam bending resistance

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111177944A (en) * 2020-01-09 2020-05-19 暨南大学 Deep-sea pipeline buckling propagation pressure calculation method based on plate-shell theory
CN111177944B (en) * 2020-01-09 2022-04-08 暨南大学 Deep-sea pipeline buckling propagation pressure calculation method based on plate-shell theory

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