横向均布载荷下预应力圆薄膜弹性能的确定方法

专利类型：发明专利 

语 言：中文 

申 请 号：CN201610802144.8 

申 请 日：20160905 

发 明 人：孙俊贻杨志欣王腾飞练永盛郭莹蔡珍红何晓婷 

申 请 人：重庆大学 

申请人地址：400044 重庆市沙坪坝区沙正街174号 

公 开 日：20170222 

公 开 号：CN106442129A 

代 理 人：黄河 

代理机构：重庆博凯知识产权代理有限公司 50212 

摘　　要：本发明公开了横向均布载荷下预应力圆薄膜弹性能的确定方法：对周边固定夹紧的预应力圆形薄膜横向施加一个均布载荷q，其中圆形薄膜的厚度为h、杨氏弹性模量为E、泊松比为ν、预应力为σ0、半径为a，基于这个轴对称变形问题的静力平衡分析，利用均布载荷q的测量值，则可以确定出薄膜变形后的弹性能U。 

主 权 项：横向均布载荷下预应力圆薄膜弹性能的确定方法，其特征在于：对周边固定夹紧的预应力圆形薄膜横向施加一个均布载荷q，其中圆形薄膜的厚度为h、半径为a、杨氏弹性模量为E、泊松比为ν、预应力为σ₀，测得所施加的均布载荷q的值，由以下公式确定该圆形薄膜变形后的弹性能U：$U=\frac{{\mathrm{\pi a}}^{10/3}{c}^{1/3}{q}^{4/3}}{2^{1/3}{E}^{1/3}{h}^{1/3}}[g\left(c\right)-h\left(c\right)],$其中，π是圆周率，$\begin{array}{c}g\left(c\right)=1+\left(\frac{1}{4}+\frac{1}{2}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}\right)c+\left(\frac{5}{36}+\frac{11}{18}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}+\frac{1}{2}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}\right)c^2\\ +\left(\frac{55}{576}+\frac{49}{72}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}+\frac{61}{48}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{5}{8}\frac{2a^2{q}^2}{h^2{E}^{2}c}\right)c^3+(\frac{7}{96}+\frac{2647}{3600}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}\\ +\frac{4051}{1800}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{253}{100}\frac{2a^2{q}^2}{h^2{E}^{2}c}+\frac{7}{8}\frac{2^{4/3}{a}^{8/3}{q}^{8/3}}{h^{8/3}{E}^{8/3}{c}^{4/3}})c^4+(\frac{205}{3456}+\frac{101639}{129600}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}\\ +\frac{443119}{129600}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{8521}{1350}\frac{2a^2{q}^2}{h^2{E}^{2}c}+\frac{7141}{1440}\frac{2^{4/3}{a}^{8/3}{q}^{8/3}}{h^{8/3}{E}^{8/3}{c}^{4/3}}+\frac{21}{16}\frac{2^{5/3}{a}^{10/3}{q}^{10/3}}{h^{10/3}{E}^{10/3}{c}^{5/3}})c^5\\ +(\frac{17051}{338688}+\frac{2639243}{3175200}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}+\frac{866077}{181440}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{13308283}{1058400}\frac{2a^2{q}^2}{h^2{E}^{2}c}\\ +\frac{1904549}{117600}\frac{2^{4/3}{a}^{8/3}{q}^{8/3}}{h^{8/3}{E}^{8/3}{c}^{4/3}}+\frac{113623}{11760}\frac{2^{5/3}{a}^{10/3}{q}^{10/3}}{h^{10/3}{E}^{10/3}{c}^{5/3}}+\frac{33}{16}\frac{4a^4{q}^4}{h^4{E}^4{c}^2})c^6+(\frac{2864485}{65028096}\\ +\frac{5947093}{6773760}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}+\frac{91705651}{14515200}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{1115512751}{50803200}\frac{2a^2{q}^2}{h^2{E}^{2}c}\\ +\frac{1366411591}{33868800}\frac{2^{4/3}{a}^{8/3}{q}^{8/3}}{h^{8/3}{E}^{8/3}{c}^{4/3}}+\frac{740195}{18816}\frac{2^{5/3}{a}^{10/3}{q}^{10/3}}{h^{10/3}{E}^{10/3}{c}^{5/3}}+\frac{33661}{1792}\frac{4a^4{q}^4}{h^4{E}^4{c}^2}\\ +\frac{429}{128}\frac{2^{7/3}{a}^{14/3}{q}^{14/3}}{h^{14/3}{E}^{14/3}{c}^{7/3}})c^7\end{array},$$\begin{array}{c}h\left(c\right)=\frac{1}{2}+\frac{1}{3}\left(\frac{1}{4}+\frac{1}{2}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}\right)c+\frac{1}{4}\left(\frac{5}{36}+\frac{11}{18}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}+\frac{1}{2}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}\right)c^2\\ +\frac{1}{5}\left(\frac{55}{576}+\frac{49}{72}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}+\frac{61}{48}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{5}{8}\frac{2a^2{q}^2}{h^2{E}^{2}c}\right)c^3+\frac{1}{6}(\frac{7}{96}+\frac{2647}{3600}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}\\ +\frac{4051}{1800}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{253}{100}\frac{2a^2{q}^2}{h^2{E}^{2}c}+\frac{7}{8}\frac{2^{4/3}{a}^{8/3}{q}^{8/3}}{h^{8/3}{E}^{8/3}{c}^{4/3}})c^4+\frac{1}{7}(\frac{205}{3456}+\frac{101639}{129600}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}\\ +\frac{443119}{129600}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{8521}{1350}\frac{2a^2{q}^2}{h^2{E}^{2}c}+\frac{7141}{1440}\frac{2^{4/3}{a}^{8/3}{q}^{8/3}}{h^{8/3}{E}^{8/3}{c}^{4/3}}+\frac{21}{16}\frac{2^{5/3}{a}^{10/3}{q}^{10/3}}{h^{10/3}{E}^{10/3}{c}^{5/3}})c^5\\ +\frac{1}{8}(\frac{17051}{338688}+\frac{2639243}{3175200}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}+\frac{866077}{181440}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{13308283}{1058400}\frac{2a^2{q}^2}{h^2{E}^{2}c}\\ +\frac{1904549}{117600}\frac{2^{4/3}{a}^{8/3}{q}^{8/3}}{h^{8/3}{E}^{8/3}{c}^{4/3}}+\frac{113623}{11760}\frac{2^{5/3}{a}^{10/3}{q}^{10/3}}{h^{10/3}{E}^{10/3}{c}^{5/3}}+\frac{33}{16}\frac{4a^4{q}^4}{h^4{E}^4{c}^2})c^6+\frac{1}{9}(\frac{2864485}{65028096}\\ +\frac{5947093}{6773760}\frac{2^{1/3}{a}^{2/3}{q}^{2/3}}{h^{2/3}{E}^{2/3}{c}^{1/3}}+\frac{91705651}{14515200}\frac{2^{2/3}{a}^{4/3}{q}^{4/3}}{h^{4/3}{E}^{4/3}{c}^{2/3}}+\frac{1115512751}{50803200}\frac{2a^2{q}^2}{h^2{E}^{2}c}\\ +\frac{1366411591}{33868800}\frac{2^{4/3}{a}^{8/3}{q}^{8/3}}{h^{8/3}{E}^{8/3}{c}^{4/3}}+\frac{740195}{18816}\frac{2^{5/3}{a}^{10/3}{q}^{10/3}}{h^{10/3}{E}^{10/3}{c}^{5/3}}+\frac{33661}{1792}\frac{4a^4{q}^4}{h^4{E}^4{c}^2}\\ +\frac{429}{128}\frac{2^{7/3}{a}^{14/3}{q}^{14/3}}{h^{14/3}{E}^{14/3}{c}^{7/3}})c^7\end{array},$而中间参量c的值由方程$[2{\mathrm{cf}}^{\prime }\left(c\right)+(1-\nu )f\left(c\right)]-(1-\nu )\frac{2^{5/3}{h}^{2/3}{c}^{1/3}}{a^{2/3}{q}^{2/3}{E}^{1/3}}{\sigma }_0=0$确定，其中，

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法律状态：生效 

IPC专利分类号：G01N3/08