CN112730071A - 气体压力下圆形预应力薄膜弹性能的确定方法 - Google Patents

气体压力下圆形预应力薄膜弹性能的确定方法 Download PDF

Info

Publication number
CN112730071A
CN112730071A CN202011432266.5A CN202011432266A CN112730071A CN 112730071 A CN112730071 A CN 112730071A CN 202011432266 A CN202011432266 A CN 202011432266A CN 112730071 A CN112730071 A CN 112730071A
Authority
CN
China
Prior art keywords
gas pressure
circular prestressed
circular
prestressed film
elastic energy
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202011432266.5A
Other languages
English (en)
Inventor
孙俊贻
吴际
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Chongqing University
Original Assignee
Chongqing University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Chongqing University filed Critical Chongqing University
Priority to CN202011432266.5A priority Critical patent/CN112730071A/zh
Publication of CN112730071A publication Critical patent/CN112730071A/zh
Pending legal-status Critical Current

Links

Images

Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • G01N3/10Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces generated by pneumatic or hydraulic pressure
    • G01N3/12Pressure testing
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014Type of force applied
    • G01N2203/0016Tensile or compressive
    • G01N2203/0019Compressive
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/003Generation of the force
    • G01N2203/0042Pneumatic or hydraulic means
    • G01N2203/0044Pneumatic means
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058Kind of property studied
    • G01N2203/0069Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0075Strain-stress relations or elastic constants
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02Details not specific for a particular testing method
    • G01N2203/026Specifications of the specimen
    • G01N2203/0262Shape of the specimen
    • G01N2203/0278Thin specimens
    • G01N2203/0282Two dimensional, e.g. tapes, webs, sheets, strips, disks or membranes

Landscapes

  • Physics & Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)

Abstract

本发明公开了一种气体压力下圆形预应力薄膜弹性能的确定方法,其特征在于:对杨氏弹性模量为E、泊松比为v、半径为a、厚度为h、预应力为σ0、最初平坦且周边固定夹紧的圆形预应力薄膜施加气体压力q,让该圆形预应力薄膜在气体压力作用下产生轴对称变形,那么基于该圆形预应力薄膜轴对称变形的静力平衡分析,利用气体压力q的测量值,就可以确定出该圆形预应力薄膜轴对称变形后的弹性能U。

Description

气体压力下圆形预应力薄膜弹性能的确定方法
技术领域
本发明涉及一种气体压力作用下周边固定夹紧的圆形预应力薄膜的弹性能的确定方法。
背景技术
气体压力作用下周边固定夹紧的圆形预应力薄膜的轴对称变形问题的解析解,在许多技术、以及工程领域都有应用,例如,用来研制各种仪器仪表和各类传感器、以及研究薄膜/基层系统的粘附能测量等。从文献查新的结果来看,目前仅有横向均布载荷作用下周边固定夹紧的圆形预应力薄膜轴对称变形问题的解析研究成果,例如发明专利“一种确定均布载荷下预应力圆薄膜弹性能的方法”(专利号:ZL201410238597.3)就是在这个解析研究成果的基础上提出的,还没有气体压力作用下周边固定夹紧的圆形预应力薄膜的轴对称变形问题的解析研究成果。众所周知,横向均布载荷作用下圆形预应力薄膜的轴对称变形问题与气体压力作用下圆形预应力薄膜的轴对称变形问题是两个不同的力学问题,因为横向均布载荷与气体压力的作用方向是不同的。在圆形薄膜轴对称变形的过程中,横向均布载荷作用在薄膜上的方向是保持不变的,而气体压力作用在薄膜上的方向是随着圆形薄膜的轴对称变形而变化的,即,横向均布载荷始终垂直于最初平坦的圆形薄膜的几何中面,而气体压力则始终垂直于轴对称变形的圆形薄膜的表面。显而易见,如果能够获得气体压力作用下圆形预应力薄膜的轴对称变形问题的解析解,这无疑是一项非常有价值的工作,可以为工程技术领域提供更大的研发空间。
发明内容
本发明致力于气体压力作用下周边固定夹紧的圆形预应力薄膜的轴对称变形问题的解析研究,基于气体压力作用下周边固定夹紧的圆形预应力薄膜轴对称变形的静力平衡分析,得到了该轴对称变形问题的解析解,并在此基础上给出了气体压力下圆形预应力薄膜弹性能的确定方法。
气体压力下圆形预应力薄膜弹性能的确定方法:对杨氏弹性模量为E、泊松比为v、半径为a、厚度为h、预应力为σ0、最初平坦且周边固定夹紧的圆形预应力薄膜施加气体压力q,让该圆形预应力薄膜在气体压力作用下产生轴对称变形,那么基于该圆形预应力薄膜轴对称变形的静力平衡分析,就可以得到所施加的气体压力q与该圆形预应力薄膜轴对称变形后的弹性能U之间的解析关系
Figure BDA0002825918230000011
其中,
Figure BDA0002825918230000021
Figure BDA0002825918230000022
Figure BDA0002825918230000023
Figure BDA0002825918230000024
Figure BDA0002825918230000025
Figure BDA0002825918230000026
Figure BDA0002825918230000027
而b0的值由方程
Figure BDA0002825918230000028
Figure BDA0002825918230000029
Figure BDA00028259182300000210
Figure BDA0002825918230000031
Figure BDA0002825918230000032
Figure BDA0002825918230000033
Figure BDA0002825918230000034
d0=b0
Figure BDA0002825918230000035
Figure BDA0002825918230000036
Figure BDA0002825918230000037
Figure BDA0002825918230000038
Figure BDA0002825918230000041
Figure BDA0002825918230000042
确定。
这样,只要准确测得气体压力q的值,就可以把该圆形预应力薄膜轴对称变形后的弹性能U确定下来,其中,a、h的单位均为毫米(mm),σ0、E、q的单位均为牛顿每平方毫米(N/mm2),U的单位为牛顿·毫米(N·mm),而v、b0、b2、b4、b6、b8、b10、b12、c0、c2、c4、c6、c8、c10、c12、d0、d2、d4、d6、d8、d10、d12均为无量纲的量。
附图说明
图1为气体压力作用下周边固定夹紧的圆形预应力薄膜轴对称变形的示意图,其中,1是轴对称变形后的圆形预应力薄膜,2是夹紧装置,3是最初平坦的圆形预应力薄膜的几何中面,4是支座,而a表示圆形预应力薄膜的半径和夹紧装置的内半径,o表示坐标系的原点,r表示径向坐标,w表示横向坐标(也表示轴对称变形后的圆形预应力薄膜上任一点的挠度),q表示作用在圆形预应力薄膜表面上的气体压力,wm表示圆形预应力薄膜轴对称变形后的最大挠度。
具体实施方式
下面结合具体案例对本发明的技术方案作进一步的说明:
如图1所示,对杨氏弹性模量E=7.84N/mm2、泊松比v=0.47、半径a=20mm、厚度h=0.2mm、预应力σ0=3N/mm2、最初平坦且周边固定夹紧的圆形预应力薄膜施加气体压力q,让该圆形预应力薄膜在气体压力作用下产生轴对称变形,测得气体压力q=0.05N/mm2,那么采用本发明所给出的方法,由方程
Figure BDA0002825918230000051
Figure BDA0002825918230000052
Figure BDA0002825918230000053
Figure BDA0002825918230000054
Figure BDA0002825918230000055
Figure BDA0002825918230000056
Figure BDA0002825918230000057
d0=b0
Figure BDA0002825918230000058
Figure BDA0002825918230000061
Figure BDA0002825918230000062
Figure BDA0002825918230000063
Figure BDA0002825918230000064
Figure BDA0002825918230000065
得到b0=0.5920715以及b2=-0.1671145、b4=-0.0255077、b6=-0.0075440、b8=-0.0027627、b10=-0.0011289、b12=-0.0004934、d0=0.5920715、d2=-0.1581024、d4=-0.0307167、d6=-0.0107168、d8=-0.0044513、d10=-0.0020137、d12=-0.0009585,再由方程
Figure BDA0002825918230000066
Figure BDA0002825918230000067
Figure BDA0002825918230000071
Figure BDA0002825918230000072
Figure BDA0002825918230000073
Figure BDA0002825918230000074
Figure BDA0002825918230000075
得到c0=0.3252652、c2=-0.2692897、c4=-0.0380040、c6=-0.0110184、c8=-0.0040089、c10=-0.0016350、c12=-0.0007146,最后由方程
Figure BDA0002825918230000076
确定出该圆形预应力薄膜在气体压力q=0.05N/mm2作用下的弹性能为U=4371.9010N·mm。

Claims (1)

1.气体压力下圆形预应力薄膜弹性能的确定方法,其特征在于:对杨氏弹性模量为E、泊松比为v、半径为a、厚度为h、预应力为σ0、最初平坦且周边固定夹紧的圆形预应力薄膜施加气体压力q,让该圆形预应力薄膜在气体压力作用下产生轴对称变形,那么基于该圆形预应力薄膜轴对称变形的静力平衡分析,利用气体压力q的测量值,由方程
Figure FDA0002825918220000011
Figure FDA0002825918220000012
Figure FDA0002825918220000013
Figure FDA0002825918220000014
Figure FDA0002825918220000015
Figure FDA0002825918220000016
Figure FDA0002825918220000017
d0=b0
Figure FDA0002825918220000021
Figure FDA0002825918220000022
Figure FDA0002825918220000023
Figure FDA0002825918220000024
Figure FDA0002825918220000025
Figure FDA0002825918220000026
确定b0以及b2、b4、b6、b8、b10、b12、d0、d2、d4、d6、d8、d10、d12的值,然后由方程
Figure FDA0002825918220000027
Figure FDA0002825918220000028
Figure FDA0002825918220000029
Figure FDA0002825918220000031
Figure FDA0002825918220000032
Figure FDA0002825918220000033
Figure FDA0002825918220000034
确定c0、c2、c4、c6、c8、c10、c12的值,最后由方程
Figure FDA0002825918220000035
确定该圆形预应力薄膜轴对称变形后的弹性能U,其中,a、h的单位均为毫米(mm),σ0、E、q的单位均为牛顿每平方毫米(N/mm2),U的单位为牛顿·毫米(N·mm),而v、b0、b2、b4、b6、b8、b10、b12、c0、c2、c4、c6、c8、c10、c12、d0、d2、d4、d6、d8、d10、d12均为无量纲的量。
CN202011432266.5A 2020-12-09 2020-12-09 气体压力下圆形预应力薄膜弹性能的确定方法 Pending CN112730071A (zh)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011432266.5A CN112730071A (zh) 2020-12-09 2020-12-09 气体压力下圆形预应力薄膜弹性能的确定方法

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011432266.5A CN112730071A (zh) 2020-12-09 2020-12-09 气体压力下圆形预应力薄膜弹性能的确定方法

Publications (1)

Publication Number Publication Date
CN112730071A true CN112730071A (zh) 2021-04-30

Family

ID=75598737

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011432266.5A Pending CN112730071A (zh) 2020-12-09 2020-12-09 气体压力下圆形预应力薄膜弹性能的确定方法

Country Status (1)

Country Link
CN (1) CN112730071A (zh)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113720689A (zh) * 2021-08-17 2021-11-30 重庆大学 气体压力下与刚性板接触的圆薄膜的最大应力的确定方法
CN113720688A (zh) * 2021-08-17 2021-11-30 重庆大学 气体压力下与刚性板接触的圆薄膜的弹性能的确定方法
CN115307788A (zh) * 2022-07-08 2022-11-08 重庆大学 一种非接触式圆形导电薄膜可变电容器电容量的确定方法
CN115307789A (zh) * 2022-07-08 2022-11-08 重庆大学 一种接触式圆形导电薄膜可变电容器电容量的确定方法

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
BIN-BIN SHI ET AL: "Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading", 《MATHEMATICS》 *
JUN-YI SUN ET AL: "Theoretical study of adhesion energy measurement for film/substrate interface using pressurized blister test: Energy release rate", 《MEASUREMENT》 *
W.B.FICHTER: "Some Solutions for the Large Deflections of Uniformly Loaded Circular Membranes", 《NASA TECHNICAL PAPER》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113720689A (zh) * 2021-08-17 2021-11-30 重庆大学 气体压力下与刚性板接触的圆薄膜的最大应力的确定方法
CN113720688A (zh) * 2021-08-17 2021-11-30 重庆大学 气体压力下与刚性板接触的圆薄膜的弹性能的确定方法
CN115307788A (zh) * 2022-07-08 2022-11-08 重庆大学 一种非接触式圆形导电薄膜可变电容器电容量的确定方法
CN115307789A (zh) * 2022-07-08 2022-11-08 重庆大学 一种接触式圆形导电薄膜可变电容器电容量的确定方法

Similar Documents

Publication Publication Date Title
CN112730071A (zh) 气体压力下圆形预应力薄膜弹性能的确定方法
CN111426567A (zh) 气压下最大挠度受限的圆形薄膜的最大应力的确定方法
CN111426566A (zh) 气体压力下最大挠度受限的圆薄膜的弹性能的确定方法
CN111426568A (zh) 气体压力下最大挠度受限的圆形薄膜的挠度的确定方法
CN111442977B (zh) 横向均布载荷作用下圆形薄膜最大应力的确定方法
CN109323924B (zh) 最大挠度受弹性限制下圆形薄膜最大应力的确定方法
CN109323923B (zh) 最大挠度受弹性限制下圆形薄膜弹性能的确定方法
CN111442976B (zh) 横向均布载荷作用下圆形薄膜最大挠度的确定方法
CN113092041B (zh) 横向均布载荷下环形薄膜最大挠度的确定方法
CN111442985A (zh) 一种确定横向均布载荷下圆形薄膜最大挠度的方法
CN111442982A (zh) 均布载荷下圆形薄膜最大应力的确定方法
CN111442984A (zh) 一种确定横向均布载荷下圆形薄膜最大应力的方法
CN113092039B (zh) 横向均布载荷下环形薄膜弹性能的确定方法
CN109342192B (zh) 最大挠度受弹性限制下圆形薄膜最大挠度的确定方法
CN111474040A (zh) 预应力圆薄膜在均布载荷作用下的弹性能的确定方法
CN111474038A (zh) 均布载荷下预应力圆形薄膜最大挠度的确定方法
CN113092040B (zh) 横向均布载荷下环形薄膜最大应力的确定方法
CN111442981A (zh) 均布载荷下圆形薄膜弹性应变能的确定方法
CN112903218B (zh) 气压下最大挠度受限的预应力圆薄膜最大应力的确定方法
CN113075048A (zh) 气体压力下圆形薄膜最大挠度的确定方法
CN111442978B (zh) 横向均布载荷作用下圆形薄膜弹性应变能的确定方法
CN112858001A (zh) 一种确定均布载荷下圆形预应力薄膜最大应力的方法
CN112730072A (zh) 气体压力下圆形预应力薄膜最大挠度的确定方法
CN106644248A (zh) 最大挠度受限制状态下圆形薄膜最大应力的确定方法
CN112880950A (zh) 气压下最大挠度受限的圆形预应力薄膜的挠度确定方法

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20210430