均布载荷下带硬芯的预应力环膜弹性能的确定方法

专利类型：发明专利

语言：中文

申请号：CN201610802707.3

申请日：20160905

发明人：何晓婷杨志欣练永盛肖涛葛晓明蔡珍红孙俊贻

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：20170118

公开号：CN106338437A

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：本发明公开了均布载荷下带硬芯的预应力环膜弹性能的确定方法：对中心区域带有硬芯的周边固定夹紧的预应力环形薄膜构造横向施加一个均布载荷q，其中，环形薄膜的厚度为h、杨氏弹性模量为E、泊松比为ν、预应力为σ0、外半径为a、内半径为b，环形薄膜中心区域所带硬芯的半径也为b，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，则可确定出该环形薄膜变形后的弹性能U。

主权项：均布载荷下带硬芯的预应力环膜弹性能的确定方法，其特征在于：对中心区域带有硬芯的周边固定夹紧的预应力环形薄膜构造横向施加一个均布载荷q，其中环形薄膜的厚度为h、杨氏弹性模量为E、泊松比为ν、预应力为σ₀、外半径为a、内半径为b，环形薄膜中心区域所带硬芯的半径也为b，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变形后的弹性能U： $\begin{matrix} U = π {(\frac{a^{4} q^{4}}{h E})}^{1 / 3} Σ_{i = 0}^{10} [\frac{2 a^{2} c_{i}}{i + 2} {(1 - β)}^{i + 2} + \frac{a (a + b) c_{i}}{i + 1} {(1 - β)}^{i + 1} - \frac{2 a^{2} c_{i}}{i + 2} {(\frac{b}{a} - β)}^{i + 2} \\ - \frac{a (a + b) c_{i}}{i + 1} {(\frac{b}{a} - β)}^{i + 1} + b^{2} c_{i} {(\frac{b}{a} - β)}^{i}] \end{matrix},$ 其中，π是圆周率，?β＝(a+b)/2a， $c_{3} = \frac{1}{6} \frac{1}{β^{3} c_{1}} (8 β^{3} c_{2}^{2} - 10 β^{2} c_{1} c_{2} + 3 {βc}_{1}^{2} - c_{1}^{5}),$ $c_{4} = \frac{1}{24} \frac{1}{β^{4} c_{1}^{2}} (48 β^{4} c_{2}^{3} - 120 β^{3} c_{1} c_{2}^{2} + 90 β^{2} c_{1}^{2} c_{2} - 16 {βc}_{1}^{5} c_{2} - 21 {βc}_{1}^{3} + 8 c_{1}^{6}),$ $\begin{matrix} c_{5} = \frac{1}{120} \frac{1}{β^{6} c_{1}^{3}} (384 β^{6} c_{2}^{4} - 1440 β^{5} c_{1} c_{2}^{3} + 1896 β^{4} c_{1}^{2} c_{2}^{2} - 232 β^{3} c_{1}^{5} c_{2}^{2} - 1032 β^{3} c_{1}^{3} c_{2} \\ + 312 β^{2} c_{1}^{6} c_{2} + 198 β^{2} c_{1}^{4} - 101 {βc}_{1}^{7} + 8 c_{1}^{10}) \end{matrix},$ $\begin{matrix} c_{6} = \frac{1}{720} \frac{1}{β^{7} c_{1}^{4}} (3840 β^{7} c_{2}^{5} - 19200 β^{6} c_{1} c_{2}^{4} + 36720 β^{5} c_{1}^{2} c_{2}^{3} - 3552 β^{4} c_{1}^{5} c_{2}^{3} \\ - 33360 β^{4} c_{1}^{3} c_{2}^{2} + 8296 β^{3} c_{1}^{6} c_{2}^{2} + 14340 β^{3} c_{1}^{4} c_{2} - 6208 β^{2} c_{1}^{7} c_{2} \\ - 2340 β^{2} c_{1}^{5} + 344 {βc}_{1}^{10} c_{2} + 1489 {βc}_{1}^{8} - 204 c_{1}^{11}) \end{matrix},$ $\begin{matrix} c_{7} = \frac{1}{2520} \frac{1}{β^{9} c_{1}^{5}} (23040 β^{9} c_{2}^{6} - 144000 β^{8} c_{1} c_{2}^{5} + 362880 β^{7} c_{1}^{2} c_{2}^{4} - 29664 β^{6} c_{1}^{5} c_{2}^{4} \\ - 469800 β^{6} c_{1}^{3} c_{2}^{3} + 100944 β^{5} c_{1}^{6} c_{2}^{3} + 328140 β^{5} c_{1}^{4} c_{2}^{2} - 124644 β^{4} c_{1}^{7} c_{2}^{2} \\ - 116910 β^{4} c_{1}^{5} c_{2} + 5416 β^{3} c_{1}^{10} c_{2}^{2} + 66120 β^{3} c_{1}^{8} c_{2} + 16605 β^{3} c_{1}^{6} \\ - 7468 β^{2} c_{1}^{11} c_{2} - 12708 β^{2} c_{1}^{9} + 2524 {βc}_{1}^{12} - 86 c_{1}^{15}) \end{matrix},$ $\begin{matrix} c_{8} = \frac{1}{20160} \frac{1}{β^{10} c_{1}^{6}} (322560 β^{10} c_{2}^{7} - 2419200 β^{9} c_{1} c_{2}^{6} + 7580160 β^{8} c_{1}^{2} c_{2}^{5} - 543744 β^{7} c_{1}^{5} c_{2}^{5} \\ - 12821760 β^{7} c_{1}^{3} c_{2}^{4} + 2455488 β^{6} c_{1}^{6} c_{2}^{4} + 12602520 β^{6} c_{1}^{4} c_{2}^{3} - 4317408 β^{5} c_{1}^{7} c_{2}^{3} \\ - 7175700 β^{5} c_{1}^{5} c_{2}^{5} + 156816 β^{4} c_{1}^{10} c_{2}^{3} + 3689808 β^{4} c_{1}^{8} c_{2}^{2} + 2186730 β^{4} c_{1}^{6} c_{2} \\ - 357560 β^{3} c_{1}^{11} c_{2}^{2} - 1531056 β^{3} c_{1}^{9} c_{2} - 274995 β^{5} c_{1}^{7} + 265844 β^{2} c_{1}^{12} c_{2} \\ + 246591 β^{2} c_{1}^{10} - 7136 {βc}_{1}^{15} c_{2} - 64454 {βc}_{1}^{13} + 4508 c_{1}^{16}) \end{matrix},$ $\begin{matrix} c_{9} = \frac{1}{181440} \frac{1}{β^{12} c_{1}^{7}} (5160960 β^{12} c_{2}^{8} - 45158400 β^{11} c_{1} c_{2}^{7} + 169344000 β^{10} c_{1}^{2} c_{2}^{6} \\ - 10916352 β^{9} c_{1}^{5} c_{2}^{6} - 354654720 β^{9} c_{1}^{3} c_{2}^{5} + 61770240 β^{8} c_{1}^{6} c_{2}^{5} + 452571840 β^{8} c_{1}^{4} c_{2}^{4} \\ - 142403904 β^{7} c_{1}^{7} c_{2}^{4} - 359432640 β^{7} c_{1}^{5} c_{2}^{3} + 4495680 β^{6} c_{1}^{10} c_{2}^{4} + 171002304 β^{6} c_{1}^{8} c_{2}^{3} \\ + 173093760 β^{6} c_{1}^{6} c_{2}^{2} - 14640192 β^{5} c_{1}^{11} c_{2}^{3} - 112679604 β^{5} c_{1}^{9} c_{2}^{2} - 46131120 β^{5} c_{1}^{7} c_{2} \\ + 17513808 β^{4} c_{1}^{12} c_{2}^{2} + 38590524 β^{4} c_{1}^{10} c_{2} + 5205060 β^{4} c_{1}^{8} - 392216 β^{3} c_{1}^{15} c_{2}^{2} \\ - 9120816 β^{3} c_{1}^{13} c_{2} - 5362677 β^{3} c_{1}^{11} + 547624 β^{2} c_{1}^{16} c_{2} + 1744380 β^{2} c_{1}^{14} \\ - 188706 {βc}_{1}^{17} + 3568 c_{1}^{20}) \end{matrix},$ $\begin{matrix} c_{10} = \frac{1}{181440} \frac{1}{β^{13} c_{1}^{8}} (92897280 β^{13} c_{2}^{9} - 92897280 β^{12} c_{1} c_{2}^{8} + 4058449920 β^{11} c_{1}^{2} c_{2}^{7} \\ - 238970880 β^{10} c_{1}^{5} c_{2}^{7} - 10149027840 β^{10} c_{1}^{3} c_{2}^{6} + 1630158336 β^{9} c_{1}^{6} c_{2}^{6} \\ + 15980146560 β^{9} c_{1}^{4} c_{2}^{5} - 4676078592 β^{8} c_{1}^{7} c_{2}^{5} - 16397095680 β^{8} c_{1}^{5} c_{2}^{4} \\ + 131654016 β^{7} c_{1}^{10} c_{2}^{5} + 7304043456 β^{7} c_{1}^{8} c_{2}^{4} + 10942646400 β^{7} c_{1}^{6} c_{2}^{3} \\ - 564117120 β^{6} c_{1}^{11} c_{2}^{4} - 6702770736 β^{6} c_{1}^{9} c_{2}^{3} - 4571471520 β^{6} c_{1}^{7} c_{2}^{2} \\ + 949114656 β^{5} c_{1}^{12} c_{2}^{3} + 3610117836 β^{5} c_{1}^{10} c_{2}^{2} + 1083264840 β^{5} c_{1}^{8} c_{2} \\ - 18404544 β^{4} c_{1}^{15} c_{2}^{3} - 783565920 β^{4} c_{1}^{13} c_{2}^{2} - 1055710800 β^{4} c_{1}^{11} c_{2} \\ - 110837160 β^{4} c_{1}^{9} + 41460120 β^{3} c_{1}^{16} c_{2}^{2} + 317333772 β^{3} c_{1}^{14} c_{2} \\ + 129215439 β^{3} c_{1}^{12} - 30678936 β^{2} c_{1}^{17} c_{2} - 50420286 β^{2} c_{1}^{15} \\ + 484984 {βc}_{1}^{20} c_{2} + 7457610 {βc}_{1}^{18} - 316628 c_{1}^{21}) \end{matrix},$ 而中间参量c₁和c₂的值由方程 $Σ_{i = 2}^{10} i (i - 1) c_{i} {(1 - β)}^{i - 2} - (2 - ν) Σ_{i = 1}^{10} {ic}_{i} {(1 - β)}^{i - 1} = \frac{2 h^{2 / 3} (1 - ν)}{q^{2 / 3} a^{2 / 3} E^{1 / 3}} σ_{0} {[Σ_{i = 1}^{10} {ic}_{i} {(1 - β)}^{i - 1}]}^{2}$ ?和 ${(\frac{b}{a})}^{2} Σ_{i = 2}^{10} i (i - 1) c_{i} {(\frac{b}{a} - β)}^{i - 2} - \frac{b}{a} (2 - ν) Σ_{i = 1}^{10} {ic}_{i} {(\frac{b}{a} - β)}^{i - 1} = \frac{2 h^{2 / 3} (1 - ν)}{q^{2 / 3} a^{2 / 3} E^{1 / 3}} σ_{0} {[Σ_{i = 1}^{10} {ic}_{i} {(\frac{b}{a} - β)}^{i - 1}]}^{2}$ 确定，中间参量c₀的值由公式 $c_{0} = - Σ_{i = 1}^{10} c_{i} {(1 - β)}^{i}$ 确定，中间参量c₀、c₁、c₂没有单位，其它所有参量皆采用国际单位制。

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法律状态：生效

IPC专利分类号：G01N3/08