均布载荷下中心带刚性板的环形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：CN201610266626.6

申请日：20160426

发明人：何晓婷练永盛杨志欣郭莹孙俊贻郑周练蔡珍红

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：20160615

公开号：CN105675484A

代理人：张先芸

代理机构：重庆博凯知识产权代理有限公司 50212

摘　　要：本发明公开了均布载荷下中心带刚性板的环形薄膜弹性能的确定方法：采用内半径为a的夹紧装置，将厚度为h、杨氏弹性模量为E、泊松比为ν、中心带半径为b的刚性板的环形薄膜固定夹紧，形成一个外半径为a、内半径为b的周边固定夹紧的中心带刚性板的轴对称环形薄膜，对其横向施加一个均布载荷q，基于这个轴对称变形问题的静力平衡分析和能量平衡分析，并利用均布载荷q的测量值，则可确定出该环形薄膜的弹性能U。

主权项：均布载荷下中心带刚性板的环形薄膜弹性能的确定方法，其特征在于：采用内半径为a的夹紧装置，将厚度为h、杨氏弹性模量为E、泊松比为ν、中心带半径为b的刚性板的环形薄膜固定夹紧，形成一个外半径为a、内半径为b的周边固定夹紧的中心带刚性板的轴对称环形薄膜，对其横向施加一个均布载荷q，并测得所施加的均布载荷q的值，由以下公式确定该环形薄膜的弹性能U： $U = π {(\frac{a^{4} q^{4}}{h E})}^{1 / 3} Σ_{n = 0}^{10} [\frac{4 a^{2} c_{n}}{n + 2} {(\frac{a - b}{2 a})}^{n + 2} + \frac{2 a (a + b) c_{n}}{n + 1} {(\frac{a - b}{2 a})}^{n + 1} + b^{2} c_{n} {(\frac{b - a}{2 a})}^{n}],$ 其中， $c_{3} = \frac{1}{6} \frac{1}{β^{3} c_{1}} (8 β^{3} c_{2}^{2} - 10 β^{2} c_{1} c_{2} + 3 {βc}_{1}^{2} - c_{1}^{5}),$ $c_{4} = \frac{1}{24} \frac{1}{β^{4} c_{1}^{2}} (48 β^{4} c_{2}^{3} - 120 β^{3} c_{1} c_{2}^{2} + 90 β^{2} c_{1}^{2} c_{2} - 16 {βc}_{1}^{5} c_{2} - 21 {βc}_{1}^{3} + 8 c_{1}^{6}),$ $\begin{matrix} c_{5} = \frac{1}{120} \frac{1}{β^{6} c_{1}^{3}} (384 β^{6} c_{2}^{4} - 1440 β^{5} c_{1} c_{2}^{3} + 1896 β^{4} c_{1}^{2} c_{2}^{2} - 232 β^{3} c_{1}^{5} c_{2}^{2} - 1032 β^{3} c_{1}^{3} c_{2} \\ + 312 β^{2} c_{1}^{6} c_{2} + 198 β^{2} c_{1}^{4} - 101 {βc}_{1}^{7} + 8 c_{1}^{10}) \end{matrix},$ $\begin{matrix} c_{6} = \frac{1}{720} \frac{1}{β^{7} c_{1}^{4}} (3840 β^{7} c_{2}^{5} - 19200 β^{6} c_{1} c_{2}^{4} + 36720 β^{5} c_{1}^{2} c_{2}^{3} - 3552 β^{4} c_{1}^{5} c_{2}^{3} \\ - 33360 β^{4} c_{1}^{3} c_{2}^{2} + 8296 β^{3} c_{1}^{6} c_{2}^{2} + 14340 β^{3} c_{1}^{4} c_{2} - 6208 β^{2} c_{1}^{7} c_{2} \\ - 2340 β^{2} c_{1}^{5} + 344 {βc}_{1}^{10} c_{2} + 1489 {βc}_{1}^{8} - 204 c_{1}^{11}) \end{matrix},$ $\begin{matrix} c_{7} = \frac{1}{2520} \frac{1}{β^{9} c_{1}^{5}} (23040 β^{9} c_{2}^{6} - 144000 β^{8} c_{1} c_{2}^{5} + 362880 β^{7} c_{1}^{2} c_{2}^{4} - 39664 β^{6} c_{1}^{5} c_{2}^{4} \\ - 469800 β^{6} c_{1}^{3} c_{2}^{3} + 100944 β^{5} c_{1}^{6} c_{2}^{3} + 328140 β^{5} c_{1}^{4} c_{2}^{2} - 124644 β^{4} c_{1}^{7} c_{2}^{2} \\ - 116910 β^{4} c_{1}^{5} c_{2} + 5416 β^{3} c_{1}^{10} c_{2}^{2} + 66120 β^{3} c_{1}^{8} c_{2} + 16605 β^{3} c_{1}^{6} \\ - 7468 β^{2} c_{1}^{11} c_{2} - 12708 β^{2} c_{1}^{9} + 2524 {βc}_{1}^{12} - 86 c_{1}^{15}) \end{matrix},$ $\begin{matrix} c_{8} = \frac{1}{20160} \frac{1}{β^{10} c_{1}^{6}} (322560 β^{10} c_{2}^{7} - 2419200 β^{9} c_{1} c_{2}^{6} + 7580160 β^{8} c_{1}^{2} c_{2}^{5} - 543744 β^{7} c_{1}^{5} c_{2}^{5} \\ - 12821760 β^{7} c_{1}^{3} c_{2}^{4} + 2455488 β^{6} c_{1}^{6} c_{2}^{4} + 12602520 β^{6} c_{1}^{4} c_{2}^{3} - 4317408 β^{5} c_{1}^{7} c_{2}^{3} \\ - 7175700 β^{5} c_{1}^{5} c_{2}^{2} + 156816 β^{4} c_{1}^{10} c_{2}^{3} + 3689808 β^{4} c_{1}^{8} c_{2}^{2} + 2186730 β^{4} c_{1}^{6} c_{2} \\ - 357560 β^{3} c_{1}^{11} c_{2}^{2} - 1531056 β^{3} c_{1}^{9} c_{2} - 274995 β^{3} c_{1}^{7} + 265844 β^{2} c_{1}^{12} c_{2} \\ + 246591 β^{2} c_{1}^{10} - 7136 {βc}_{1}^{15} c_{2} - 64454 {βc}_{1}^{13} + 4508 c_{1}^{16}) \end{matrix},$ $\begin{matrix} c_{9} = \frac{1}{181440} \frac{1}{β^{12} c_{1}^{7}} (5160960 β^{12} c_{2}^{8} - 45158400 β^{11} c_{1} c_{2}^{7} + 169344000 β^{10} c_{1}^{2} c_{2}^{6} \\ - 10916352 β^{9} c_{1}^{5} c_{2}^{6} - 354654720 β^{9} c_{1}^{3} c_{2}^{5} + 61770240 β^{8} c_{1}^{6} c_{2}^{5} + 452571840 β^{8} c_{1}^{4} c_{2}^{4} \\ - 142403904 β^{7} c_{1}^{7} c_{2}^{4} - 359432640 β^{7} c_{1}^{5} c_{2}^{3} + 4495680 β^{6} c_{1}^{10} c_{2}^{4} + 171002304 β^{6} c_{1}^{8} c_{2}^{3} \\ + 173093760 β^{6} c_{1}^{6} c_{2}^{2} - 14640192 β^{5} c_{1}^{11} c_{2}^{3} - 112679604 β^{5} c_{1}^{9} c_{2}^{2} - 46131120 β^{5} c_{1}^{7} c_{2} \\ + 17513808 β^{4} c_{1}^{12} c_{2}^{2} + 38590524 β^{4} c_{1}^{10} c_{2} + 5205060 β^{4} c_{1}^{8} - 392216 β^{3} c_{1}^{15} c_{2}^{2} \\ - 9120816 β^{3} c_{1}^{13} c_{2} - 5362677 β^{3} c_{1}^{11} + 547624 β^{2} c_{1}^{16} c_{2} + 1744380 β^{2} c_{1}^{14} \\ - 188706 {βc}_{1}^{17} + 3568 c_{1}^{20}) \end{matrix},$ $\begin{matrix} c_{10} = \frac{1}{181440} \frac{1}{β^{13} c_{1}^{8}} (92897280 β^{13} c_{2}^{9} - 92897280 β^{12} c_{1} c_{2}^{8} + 4058449920 β^{11} c_{1}^{2} c_{2}^{7} \\ - 238970880 β^{10} c_{1}^{5} c_{2}^{7} - 10149027840 β^{10} c_{1}^{3} c_{2}^{6} + 1630158336 β^{9} c_{1}^{6} c_{2}^{6} \\ + 15980146560 β^{9} c_{1}^{4} c_{2}^{5} - 4676078592 β^{8} c_{1}^{7} c_{2}^{5} - 16397095680 β^{8} c_{1}^{5} c_{2}^{4} \\ + 131654016 β^{7} c_{1}^{10} c_{2}^{5} + 7304043456 β^{7} c_{1}^{8} c_{2}^{4} + 10942646400 β^{7} c_{1}^{6} c_{2}^{3} \\ - 564117120 β^{6} c_{1}^{11} c_{2}^{4} - 6702770736 β^{6} c_{1}^{9} c_{2}^{3} - 4571471520 β^{6} c_{1}^{7} c_{2}^{2} \\ + 949114656 β^{5} c_{1}^{12} c_{2}^{3} + 3610117836 β^{5} c_{1}^{10} c_{2}^{2} + 1083264840 β^{5} c_{1}^{8} c_{2} \\ - 18404544 β^{4} c_{1}^{15} c_{2}^{3} - 783565920 β^{4} c_{1}^{13} c_{2}^{2} - 1055710800 β^{4} c_{1}^{11} c_{2} \\ - 110837160 β^{4} c_{1}^{9} + 41460120 β^{3} c_{1}^{16} c_{2}^{2} + 317333772 β^{3} c_{1}^{14} c_{2} \\ + 129215439 β^{3} c_{1}^{12} - 30678936 β^{2} c_{1}^{17} c_{2} - 50420286 β^{2} c_{1}^{15} \\ + 484984 {βc}_{1}^{20} c_{2} + 7457610 {βc}_{1}^{18} - 316628 c_{1}^{21}) \end{matrix},$ 而β＝(a+b)/2a，c₁和c₂的值由方程 $ν = 2 - \frac{b}{a} [Σ_{i = 2}^{10} i (i - 1) c_{i} {(\frac{b}{a} - β)}^{i - 2}] / [Σ_{j = 1}^{10} {jc}_{j} {(\frac{b}{a} - β)}^{j - 1}]$ 和 $ν = 2 - \frac{b}{a} [Σ_{i = 2}^{10} i (i - 1) c_{i} {(1 - β)}^{i - 2}] / [Σ_{j = 1}^{10} {jc}_{j} {(1 - β)}^{j - 1}]$ 确定,c₀的值由方程 $c_{0} = - Σ_{j = 1}^{10} c_{j} {(1 - β)}^{j}$ 确定，所有参量皆采用国际单位制。

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法律状态：公开

IPC专利分类号：G01N19/00(2006.01)I