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CN105956379A - Method for determining maximum stress of annular thin film with rigid plate in center under uniformly distributed load - Google Patents

Method for determining maximum stress of annular thin film with rigid plate in center under uniformly distributed load Download PDF

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CN105956379A
CN105956379A CN201610263954.0A CN201610263954A CN105956379A CN 105956379 A CN105956379 A CN 105956379A CN 201610263954 A CN201610263954 A CN 201610263954A CN 105956379 A CN105956379 A CN 105956379A
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rigid plate
sigma
maximum stress
radius
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CN105956379B (en
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孙俊贻
练永盛
杨志欣
何晓婷
蔡珍红
郑周练
杨鹏
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Taihu County Market Supervision And Inspection Institute Taihu County Functional Membrane Testing Institute
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Chongqing University
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Abstract

本发明公开了均布载荷下中心带刚性板的环形薄膜最大应力的确定方法：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，并利用均布载荷q的测量值，则可确定出该环形薄膜的最大应力σm。

The invention discloses a method for determining the maximum stress of an annular film with a rigid plate in the center under a uniformly distributed load: a clamping device with an inner radius of a is used, and the thickness is h, Young's modulus of elasticity is E, Poisson's ratio is ν, The annular membrane with a rigid plate with a radius b in the center is fixed and clamped to form an axisymmetric annular membrane with a rigid plate in the center with an outer radius a and an inner radius b fixed and clamped, and a uniform load is applied to it in the transverse direction q, based on the static equilibrium analysis of this axisymmetric deformation problem, and using the measured value of the uniformly distributed load q, the maximum stress σ m of the annular membrane can be determined.

Description

均布载荷下中心带刚性板的环形薄膜最大应力的确定方法Method for Determination of Maximum Stress of Annular Membrane with Rigid Plate in the Center under Uniform Load

技术领域technical field

本发明涉及均布载荷下中心带刚性板的环形薄膜最大应力的确定方法。The invention relates to a method for determining the maximum stress of an annular film with a rigid plate in the center under a uniformly distributed load.

背景技术Background technique

均布载荷下中心带刚性板的环形薄膜轴对称变形问题的解析解，对传感器以及仪器、仪表的研制具有重要意义。由于薄膜是柔性材料，在均布载荷作用下通常呈现出较大的挠度，因而其变形问题具有较强的非线性，这些非线性问题通常难以解析求解。本发明致力于均布载荷下中心带刚性板的环形薄膜轴对称变形问题的解析研究，获得了该问题的解析解，并在此基础上给出了均布载荷下中心带刚性板的环形薄膜最大应力的确定方法。The analytical solution to the axisymmetric deformation problem of the annular membrane with a rigid plate in the center under a uniform load is of great significance to the development of sensors, instruments and meters. Since the film is a flexible material, it usually exhibits a large deflection under a uniform load, so its deformation problem has a strong nonlinearity, and these nonlinear problems are usually difficult to solve analytically. The present invention is devoted to the analytical research on the axisymmetric deformation problem of the annular film with the rigid plate in the center under uniform load, and obtains the analytical solution of the problem, and on this basis, provides the annular film with the rigid plate in the center under uniform load Determination of maximum stress.

发明内容Contents of the invention

均布载荷下中心带刚性板的环形薄膜最大应力的确定方法：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，就可以得到该环形薄膜的最大应力σm与均布载荷q的解析关系为The determination method of the maximum stress of the annular membrane with a rigid plate in the center under a uniform load: using a clamping device with an inner radius of a, the thickness is h, Young’s modulus of elasticity is E, Poisson’s ratio is ν, and the radius of the central band is The annular membrane of the rigid plate of b is fixed and clamped to form an axisymmetric annular membrane with a rigid plate in the center fixed and clamped around the outer radius a and inner radius b, and a uniform load q is applied to it in the transverse direction, based on this Static force balance analysis of the axisymmetric deformation problem, the analytical relationship between the maximum stress σ m of the annular film and the uniformly distributed load q can be obtained as

σσ mm == -- 11 22 (( EaEa 22 qq 22 hh 22 )) 11 // 33 ΣΣ nno == 00 1010 dd nno (( bb -- aa 22 aa )) nno ,,

其中，in,

dd 00 == ββ cc 11 ,,

dd 11 == 11 cc 11 22 (( -- 22 βcβc 22 ++ cc 11 )) ,,

dd 22 == 11 22 ββ 22 cc 11 22 (( 66 ββ 22 cc 22 -- 33 βcβc 11 ++ cc 11 44 )) ,,

dd 33 == 11 66 ββ 33 cc 11 22 (( -- 24twenty four ββ 22 cc 22 ++ 44 βcβc 11 33 cc 22 ++ 1212 βcβc 11 -- 55 cc 11 44 )) ,,

dd 44 == 11 24twenty four ββ 55 cc 11 22 (( 24twenty four ββ 33 cc 11 22 cc 22 22 ++ 120120 ββ 33 cc 22 -- 4848 ββ 22 cc 11 33 cc 22 -- 6060 ββ 22 cc 11 ++ 3333 βcβc 11 44 -- 22 cc 11 77 )) ,,

dd 55 == 11 6060 ββ 66 cc 11 22 (( 9696 ββ 44 cc 11 cc 22 33 -- 288288 ββ 33 cc 11 22 cc 22 22 -- 360360 ββ 33 cc 22 ++ 180180 ββ 22 cc 11 ++ 294294 ββ 22 cc 11 33 cc 22 -- 22twenty two βcβc 11 66 cc 22 -- 132132 βcβc 11 44 ++ 1717 cc 11 77 )) ,,

dd 66 == 11 360360 ββ 88 cc 11 22 (( 960960 ββ 66 cc 22 44 -- 39363936 ββ 55 cc 11 cc 22 33 ++ 59405940 ββ 44 cc 11 22 cc 22 22 ++ 25202520 ββ 44 cc 22 -- 408408 ββ 33 cc 11 55 cc 22 22 -- 40384038 ββ 33 cc 11 33 cc 22 -- 12601260 ββ 33 cc 11 ++ 678678 ββ 22 cc 11 66 cc 22 ++ 12811281 ββ 22 cc 11 44 -- 282282 βcβc 11 77 ++ 1111 cc 11 1010 )) ,,

dd 77 == 11 25202520 ββ 99 cc 11 33 (( 1152011520 ββ 77 cc 22 55 -- 6048060480 ββ 66 cc 11 cc 22 44 ++ 124128124128 ββ 55 cc 11 22 cc 22 33 -- 76327632 ββ 44 cc 11 55 cc 22 33 -- 125100125100 ββ 44 cc 11 33 cc 22 22 -- 2016020160 ββ 44 cc 11 cc 22 ++ 2016020160 ββ 33 cc 11 66 cc 22 22 ++ 6332463324 ββ 33 cc 11 44 cc 22 ++ 1008010080 ββ 33 cc 11 22 -- 1744217442 ββ 22 cc 11 77 cc 22 -- 1500315003 ββ 22 cc 11 55 ++ 584584 βcβc 11 1010 cc 22 ++ 50105010 βcβc 11 88 -- 427427 cc 11 1111 )) ,,

dd 88 == 11 2016020160 ββ 1111 cc 11 44 (( 161280161280 ββ 99 cc 22 66 -- 10368001036800 ββ 88 cc 11 cc 22 55 ++ 27187202718720 ββ 77 cc 11 22 cc 22 44 -- 150912150912 ββ 66 cc 11 55 cc 22 44 -- 37221123722112 ββ 66 cc 11 33 cc 22 33 ++ 555840555840 ββ 55 cc 11 66 cc 22 33 ++ 28150202815020 ββ 55 cc 11 44 cc 22 22 ++ 181440181440 ββ 55 cc 11 22 cc 22 -- 752400752400 ββ 44 cc 11 77 cc 22 22 -- 11318761131876 ββ 44 cc 11 55 cc 22 -- 9072090720 ββ 44 cc 11 33 ++ 2196021960 ββ 33 cc 11 1010 cc 22 22 ++ 444984444984 ββ 33 cc 11 88 cc 22 ++ 210087210087 ββ 33 cc 11 66 -- 3458434584 ββ 22 cc 11 1111 cc 22 -- 9790597905 ββ 22 cc 11 99 ++ 1344013440 βcβc 11 1212 -- 292292 cc 11 1515 )) ,,

dd 99 == 11 181440181440 ββ 1212 cc 11 55 (( 25804802580480 ββ 1010 cc 22 77 -- 1967616019676160 ββ 99 cc 11 cc 22 66 ++ 6310656063106560 ββ 88 cc 11 22 cc 22 55 -- 32002563200256 ββ 77 cc 11 55 cc 22 55 -- 110246400110246400 ββ 77 cc 11 33 cc 22 44 ++ 1525824015258240 ββ 66 cc 11 66 cc 22 44 ++ 113274720113274720 ββ 66 cc 11 44 cc 22 33 -- 2854915228549152 ββ 55 cc 11 77 cc 22 33 -- 6858108068581080 ββ 55 cc 11 55 cc 22 22 -- 18144001814400 ββ 55 cc 11 33 cc 22 ++ 741024741024 ββ 44 cc 11 1010 cc 22 33 ++ 2621505626215056 ββ 44 cc 11 88 cc 22 22 ++ 2286792122867921 ββ 44 cc 11 66 cc 22 ++ 907200907200 ββ 44 cc 11 44 -- 18515521851552 ββ 33 cc 11 1111 cc 22 22 -- 1183606211836062 ββ 33 cc 11 99 cc 22 -- 34692303469230 ββ 33 cc 11 44 ++ 15174961517496 ββ 22 cc 11 1212 cc 22 ++ 21145592114559 ββ 22 cc 11 1010 -- 2838428384 βcβc 11 1515 cc 22 -- 408768408768 βcβc 11 1313 ++ 2050420504 cc 11 1616 )) ,,

dd 1010 == 11 18144001814400 ββ 1414 cc 11 66 (( 4644864046448640 ββ 1212 cc 22 88 -- 410296320410296320 ββ 1111 cc 11 cc 22 77 ++ 15599001601559900160 ββ 1010 cc 11 22 cc 22 66 -- 7303680073036800 ββ 99 cc 11 55 cc 22 66 -- 33301324803330132480 ββ 99 cc 11 33 cc 22 55 ++ 429684480429684480 ββ 88 cc 11 66 cc 22 55 ++ 43622064004362206400 ββ 88 cc 11 44 cc 22 44 -- 10352689921035268992 ββ 77 cc 11 77 cc 22 44 -- 35888961603588896160 ββ 77 cc 11 55 cc 22 33 ++ 2430316824303168 ββ 66 cc 11 1010 cc 22 44 ++ 1995840019958400 ββ 66 cc 11 44 cc 22 ++ 13071343681307134368 ββ 66 cc 11 88 cc 22 33 ++ 18128221201812822120 ββ 66 cc 11 66 cc 22 22 -- 8459107284591072 ββ 55 cc 11 1111 cc 22 33 -- 912287016912287016 ββ 55 cc 11 99 cc 22 22 -- 516903120516903120 ββ 55 cc 11 77 cc 22 -- 99792009979200 ββ 55 cc 11 55 ++ 108652752108652752 ββ 44 cc 11 1212 cc 22 22 ++ 334076706334076706 ββ 44 cc 11 1010 cc 22 ++ 6643215066432150 ββ 44 cc 11 88 -- 17927521792752 ββ 33 cc 11 1515 cc 22 22 -- 6107244061072440 ββ 33 cc 11 1313 cc 22 -- 5033364350333643 ββ 33 cc 11 1111 ++ 27567842756784 ββ 22 cc 11 1616 cc 22 ++ 1269072312690723 ββ 22 cc 11 1414 -- 10473721047372 βcβc 11 1717 ++ 1419214192 cc 11 2020 )) ,,

而β＝(a+b)/2a，c1和c2的值由方程While β=(a + b)/2a, the values of c1 and c2 are given by the equation

νν == 22 -- bb aa [[ ΣΣ ii == 22 1010 ii (( ii -- 11 )) cc ii (( bb aa -- ββ )) ii -- 22 ]] // [[ ΣΣ jj == 11 1010 jcjc jj (( bb aa -- ββ )) jj -- 11 ]]

和and

νν == 22 -- bb aa [[ ΣΣ ii == 22 1010 ii (( ii -- 11 )) cc ii (( 11 -- ββ )) ii -- 22 ]] // [[ ΣΣ jj == 11 1010 jcjc jj (( 11 -- ββ )) jj -- 11 ]]

确定,其中，OK, among them,

cc 33 == 11 66 11 ββ 33 cc 11 (( 88 ββ 33 cc 22 22 -- 1010 ββ 22 cc 11 cc 22 ++ 33 βcβc 11 22 -- cc 11 55 )) ,,

cc 44 == 11 24twenty four 11 ββ 44 cc 11 22 (( 4848 ββ 44 cc 22 33 -- 120120 ββ 33 cc 11 cc 22 22 ++ 9090 ββ 22 cc 11 22 cc 22 -- 1616 βcβc 11 55 cc 22 -- 21twenty one βcβc 11 33 ++ 88 cc 11 66 )) ,,

cc 55 == 11 120120 11 ββ 66 cc 11 33 (( 384384 ββ 66 cc 22 44 -- 14401440 ββ 55 cc 11 cc 22 33 ++ 18961896 ββ 44 cc 11 22 cc 22 22 -- 232232 ββ 33 cc 11 55 cc 22 22 -- 10321032 ββ 33 cc 11 33 cc 22 ++ 312312 ββ 22 cc 11 66 cc 22 ++ 198198 ββ 22 cc 11 44 -- 101101 βcβc 11 77 ++ 88 cc 11 1010 )) ,,

cc 66 == 11 720720 11 ββ 77 cc 11 44 (( 38403840 ββ 77 cc 22 55 -- 1920019200 ββ 66 cc 11 cc 22 44 ++ 3672036720 ββ 55 cc 11 22 cc 22 33 -- 35523552 ββ 44 cc 11 55 cc 22 33 -- 3336033360 ββ 44 cc 11 33 cc 22 22 ++ 82968296 ββ 33 cc 11 66 cc 22 22 ++ 1434014340 ββ 33 cc 11 44 cc 22 -- 62086208 ββ 22 cc 11 77 cc 22 -- 23402340 ββ 22 cc 11 55 ++ 344344 βcβc 11 1010 cc 22 ++ 14891489 βcβc 11 88 -- 204204 cc 11 1111 )) ,,

cc 77 == 11 25202520 11 ββ 99 cc 11 55 (( 2304023040 ββ 99 cc 22 66 -- 144000144000 ββ 88 cc 11 cc 22 55 ++ 362880362880 ββ 77 cc 11 22 cc 22 44 -- 2966429664 ββ 66 cc 11 55 cc 22 44 -- 469800469800 ββ 66 cc 11 33 cc 22 33 ++ 100944100944 ββ 55 cc 11 66 cc 22 33 ++ 328140328140 ββ 55 cc 11 44 cc 22 22 -- 124644124644 ββ 44 cc 11 77 cc 22 22 -- 116910116910 ββ 44 cc 11 55 cc 22 ++ 54165416 ββ 33 cc 11 1010 cc 22 22 ++ 6612066120 ββ 33 cc 11 88 cc 22 ++ 1660516605 ββ 33 cc 11 66 -- 74687468 ββ 22 cc 11 1111 cc 22 -- 1270812708 ββ 22 cc 11 99 ++ 25242524 βcβc 11 1212 -- 8686 cc 11 1515 )) ,,

cc 88 == 11 2016020160 11 ββ 1010 cc 11 66 (( 322560322560 ββ 1010 cc 22 77 -- 24192002419200 ββ 99 cc 11 cc 22 66 ++ 75801607580160 ββ 88 cc 11 22 cc 22 55 -- 543744543744 ββ 77 cc 11 55 cc 22 55 -- 1282176012821760 ββ 77 cc 11 33 cc 22 44 ++ 24554882455488 ββ 66 cc 11 66 cc 22 44 ++ 1260252012602520 ββ 66 cc 11 44 cc 22 33 -- 43174084317408 ββ 55 cc 11 77 cc 22 33 -- 71757007175700 ββ 55 cc 11 55 cc 22 22 ++ 156816156816 ββ 44 cc 11 1010 cc 22 33 ++ 36898083689808 ββ 44 cc 11 88 cc 22 22 ++ 21867302186730 ββ 44 cc 11 66 cc 22 -- 357560357560 ββ 33 cc 11 1111 cc 22 22 -- 15310561531056 ββ 33 cc 11 99 cc 22 -- 274995274995 ββ 33 cc 11 77 ++ 265844265844 ββ 22 cc 11 1212 cc 22 ++ 246591246591 ββ 22 cc 11 1010 -- 71367136 βcβc 11 1515 cc 22 -- 6445464454 βcβc 11 1313 ++ 45084508 cc 11 1616 )) ,,

cc 99 == 11 181440181440 11 ββ 1212 cc 11 77 (( 51609605160960 ββ 1212 cc 22 88 -- 4515840045158400 ββ 1111 cc 11 cc 22 77 ++ 169344000169344000 ββ 1010 cc 11 22 cc 22 66 -- 1091635210916352 ββ 99 cc 11 55 cc 22 66 -- 354654720354654720 ββ 99 cc 11 33 cc 22 55 ++ 6177024061770240 ββ 88 cc 11 66 cc 22 55 ++ 452571840452571840 ββ 88 cc 11 44 cc 22 44 -- 142403904142403904 ββ 77 cc 11 77 cc 22 44 -- 359432640359432640 ββ 77 cc 11 55 cc 22 33 ++ 44956804495680 ββ 66 cc 11 1010 cc 22 44 ++ 171002304171002304 ββ 66 cc 11 88 cc 22 33 ++ 173093760173093760 ββ 66 cc 11 66 cc 22 22 -- 1464019214640192 ββ 55 cc 11 1111 cc 22 33 -- 112679604112679604 ββ 55 cc 11 99 cc 22 22 -- 4613112046131120 ββ 55 cc 11 77 cc 22 ++ 1751380817513808 ββ 44 cc 11 1212 cc 22 22 ++ 3859052438590524 ββ 44 cc 11 1010 cc 22 ++ 52050605205060 ββ 44 cc 11 88 -- 392216392216 ββ 33 cc 11 1515 cc 22 22 -- 91208169120816 ββ 33 cc 11 1313 cc 22 -- 53626775362677 ββ 33 cc 11 1111 ++ 547624547624 ββ 22 cc 11 1616 cc 22 ++ 17443801744380 ββ 22 cc 11 1414 -- 188706188706 βcβc 11 1717 ++ 35683568 cc 11 2020 ))

cc 1010 == 11 181440181440 11 ββ 1313 cc 11 88 (( 9289728092897280 ββ 1313 cc 22 99 -- 9289728092897280 ββ 1212 cc 11 cc 22 88 ++ 40584499204058449920 ββ 1111 cc 11 22 cc 22 77 -- 238970880238970880 ββ 1010 cc 11 55 cc 22 77 -- 1014902784010149027840 ββ 1010 cc 11 33 cc 22 66 ++ 16301583361630158336 ββ 99 cc 11 66 cc 22 66 ++ 1598014656015980146560 ββ 99 cc 11 44 cc 22 55 -- 46760785924676078592 ββ 88 cc 11 77 cc 22 55 -- 1639709568016397095680 ββ 88 cc 11 55 cc 22 44 ++ 131654016131654016 ββ 77 cc 11 1010 cc 22 55 ++ 73040434567304043456 ββ 77 cc 11 88 cc 22 44 ++ 1094264640010942646400 ββ 77 cc 11 66 cc 22 33 -- 564117120564117120 ββ 66 cc 11 1111 cc 22 44 -- 67027707366702770736 ββ 66 cc 11 99 cc 22 33 -- 45714715204571471520 ββ 66 cc 11 77 cc 22 22 ++ 949114656949114656 ββ 55 cc 11 1212 cc 22 33 ++ 36101178363610117836 ββ 55 cc 11 1010 cc 22 22 ++ 10832648401083264840 ββ 55 cc 11 88 cc 22 -- 1840454418404544 ββ 44 cc 11 1515 cc 22 33 -- 783565920783565920 ββ 44 cc 11 1313 cc 22 22 -- 10557108001055710800 ββ 44 cc 11 1111 cc 22 -- 110837160110837160 ββ 44 cc 11 99 ++ 4146012041460120 ββ 33 cc 11 1616 cc 22 22 ++ 317333772317333772 ββ 33 cc 11 1414 cc 22 ++ 129215439129215439 ββ 33 cc 11 1212 -- 3067893630678936 ββ 22 cc 11 1717 cc 22 -- 5042028650420286 ββ 22 cc 11 1515 ++ 484984484984 βcβc 11 2020 cc 22 ++ 74576107457610 βcβc 11 1818 -- 316628316628 cc 11 21twenty one )) ..

这样，只要准确测量出所施加的均布载荷q的值，就可以确定出该环形薄膜变形后的最大应力σm。其中，所有参量皆采用国际单位制。In this way, as long as the value of the applied uniform load q is accurately measured, the maximum stress σ m after deformation of the annular membrane can be determined. Among them, all parameters are in SI units.

附图说明Description of drawings

图1为均布载荷下周边固定夹紧的中心带刚性板的环形薄膜的加载构造示意图，其中，1－环形薄膜，2－刚性板，3－夹紧装置，而a表示夹紧装置的内半径和环形薄膜的外半径，b表示刚性板的半径和环形薄膜的内半径，r表示径向坐标，w(r)表示点r处的横向坐标，q表示横向均布载荷，wm表示薄膜的最大挠度。Figure 1 is a schematic diagram of the loading structure of an annular film with a rigid plate in the center fixed and clamped around it under a uniform load, in which, 1-annular film, 2-rigid plate, 3-clamping device, and a represents the inner part of the clamping device Radius and the outer radius of the annular membrane, b indicates the radius of the rigid plate and the inner radius of the annular membrane, r indicates the radial coordinate, w(r) indicates the transverse coordinate at point r, q indicates the transverse uniform load, w m indicates the membrane maximum deflection.

具体实施方式detailed description

下面结合附图对本发明的技术方案作进一步的详细说明：Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

如图1所示，用一个内半径a＝20mm的夹紧装置，将厚度h＝0.06mm、杨氏弹性模量E＝7.84MPa、泊松比ν＝0.47、中心带半径b＝5mm的刚性板的橡胶薄膜固定夹紧，形成一个外半径a＝20mm、内半径b＝5mm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q＝0.01MPa。采用本发明所给出的方法，通过方程As shown in Figure 1, using a clamping device with an inner radius a=20mm, the thickness h=0.06mm, Young’s modulus of elasticity E=7.84MPa, Poisson’s ratio ν=0.47, and the rigidity of the central belt radius b=5mm The rubber film of the plate is fixed and clamped to form an axisymmetric annular film with a rigid plate in the center fixed and clamped around the outer radius a=20mm and inner radius b=5mm, and a uniform load q is applied to it in the transverse direction, and measured q = 0.01MPa. Adopt the method that the present invention provides, by equation

νν == 22 -- bb aa [[ ΣΣ ii == 22 1010 ii (( ii -- 11 )) cc ii (( bb aa -- ββ )) ii -- 22 ]] // [[ ΣΣ jj == 11 1010 jcjc jj (( bb aa -- ββ )) jj -- 11 ]]

和and

νν == 22 -- bb aa [[ ΣΣ ii == 22 1010 ii (( ii -- 11 )) cc ii (( 11 -- ββ )) ii -- 22 ]] // [[ ΣΣ jj == 11 1010 jcjc jj (( 11 -- ββ )) jj -- 11 ]]

则可以得到c1＝-0.7026607165，c2＝-0.6927450924，其中，Then c 1 =-0.7026607165, c 2 =-0.6927450924 can be obtained, where,

β＝(a+b)/2a＝0.625，β=(a+b)/2a=0.625,

cc 33 == 11 66 11 ββ 33 cc 11 (( 88 ββ 33 cc 22 22 -- 1010 ββ 22 cc 11 cc 22 ++ 33 βcβc 11 22 -- cc 11 55 )) ,,

cc 44 == 11 24twenty four 11 ββ 44 cc 11 22 (( 4848 ββ 44 cc 22 33 -- 120120 ββ 33 cc 11 cc 22 22 ++ 9090 ββ 22 cc 11 22 cc 22 -- 1616 βcβc 11 55 cc 22 -- 21twenty one βcβc 11 33 ++ 88 cc 11 66 )) ,,

cc 55 == 11 120120 11 ββ 66 cc 11 33 (( 384384 ββ 66 cc 22 44 -- 14401440 ββ 55 cc 11 cc 22 33 ++ 18961896 ββ 44 cc 11 22 cc 22 22 -- 232232 ββ 33 cc 11 55 cc 22 22 -- 10321032 ββ 33 cc 11 33 cc 22 ++ 312312 ββ 22 cc 11 66 cc 22 ++ 198198 ββ 22 cc 11 44 -- 101101 βcβc 11 77 ++ 88 cc 11 1010 )) ,,

cc 66 == 11 720720 11 ββ 77 cc 11 44 (( 38403840 ββ 77 cc 22 55 -- 1920019200 ββ 66 cc 11 cc 22 44 ++ 3672036720 ββ 55 cc 11 22 cc 22 33 -- 35523552 ββ 44 cc 11 55 cc 22 33 -- 3336033360 ββ 44 cc 11 33 cc 22 22 ++ 82968296 ββ 33 cc 11 66 cc 22 22 ++ 1434014340 ββ 33 cc 11 44 cc 22 -- 62086208 ββ 22 cc 11 77 cc 22 -- 23402340 ββ 22 cc 11 55 ++ 344344 βcβc 11 1010 cc 22 ++ 14891489 βcβc 11 88 -- 204204 cc 11 1111 )) ,,

cc 77 == 11 25202520 11 ββ 99 cc 11 55 (( 2304023040 ββ 99 cc 22 66 -- 144000144000 ββ 88 cc 11 cc 22 55 ++ 362880362880 ββ 77 cc 11 22 cc 22 44 -- 2966429664 ββ 66 cc 11 55 cc 22 44 -- 469800469800 ββ 66 cc 11 33 cc 22 33 ++ 100944100944 ββ 55 cc 11 66 cc 22 33 ++ 328140328140 ββ 55 cc 11 44 cc 22 22 -- 124644124644 ββ 44 cc 11 77 cc 22 22 -- 116910116910 ββ 44 cc 11 55 cc 22 ++ 54165416 ββ 33 cc 11 1010 cc 22 22 ++ 6612066120 ββ 33 cc 11 88 cc 22 ++ 1660516605 ββ 33 cc 11 66 -- 74687468 ββ 22 cc 11 1111 cc 22 -- 1270812708 ββ 22 cc 11 99 ++ 25242524 βcβc 11 1212 -- 8686 cc 11 1515 )) ,,

cc 88 == 11 2016020160 11 ββ 1010 cc 11 66 (( 322560322560 ββ 1010 cc 22 77 -- 24192002419200 ββ 99 cc 11 cc 22 66 ++ 75801607580160 ββ 88 cc 11 22 cc 22 55 -- 543744543744 ββ 77 cc 11 55 cc 22 55 -- 1282176012821760 ββ 77 cc 11 33 cc 22 44 ++ 24554882455488 ββ 66 cc 11 66 cc 22 44 ++ 1260252012602520 ββ 66 cc 11 44 cc 22 33 -- 43174084317408 ββ 55 cc 11 77 cc 22 33 -- 71757007175700 ββ 55 cc 11 55 cc 22 22 ++ 156816156816 ββ 44 cc 11 1010 cc 22 33 ++ 36898083689808 ββ 44 cc 11 88 cc 22 22 ++ 21867302186730 ββ 44 cc 11 66 cc 22 -- 357560357560 ββ 33 cc 11 1111 cc 22 22 -- 15310561531056 ββ 33 cc 11 99 cc 22 -- 274995274995 ββ 33 cc 11 77 ++ 265844265844 ββ 22 cc 11 1212 cc 22 ++ 246591246591 ββ 22 cc 11 1010 -- 71367136 βcβc 11 1515 cc 22 -- 6445464454 βcβc 11 1313 ++ 45084508 cc 11 1616 )) ,,

cc 99 == 11 181440181440 11 ββ 1212 cc 11 77 (( 51609605160960 ββ 1212 cc 22 88 -- 4515840045158400 ββ 1111 cc 11 cc 22 77 ++ 169344000169344000 ββ 1010 cc 11 22 cc 22 66 -- 1091635210916352 ββ 99 cc 11 55 cc 22 66 -- 354654720354654720 ββ 99 cc 11 33 cc 22 55 ++ 6177024061770240 ββ 88 cc 11 66 cc 22 55 ++ 452571840452571840 ββ 88 cc 11 44 cc 22 44 -- 142403904142403904 ββ 77 cc 11 77 cc 22 44 -- 359432640359432640 ββ 77 cc 11 55 cc 22 33 ++ 44956804495680 ββ 66 cc 11 1010 cc 22 44 ++ 171002304171002304 ββ 66 cc 11 88 cc 22 33 ++ 173093760173093760 ββ 66 cc 11 66 cc 22 22 -- 1464019214640192 ββ 55 cc 11 1111 cc 22 33 -- 112679604112679604 ββ 55 cc 11 99 cc 22 22 -- 4613112046131120 ββ 55 cc 11 77 cc 22 ++ 1751380817513808 ββ 44 cc 11 1212 cc 22 22 ++ 3859052438590524 ββ 44 cc 11 1010 cc 22 ++ 52050605205060 ββ 44 cc 11 88 -- 392216392216 ββ 33 cc 11 1515 cc 22 22 -- 91208169120816 ββ 33 cc 11 1313 cc 22 -- 53626775362677 ββ 33 cc 11 1111 ++ 547624547624 ββ 22 cc 11 1616 cc 22 ++ 17443801744380 ββ 22 cc 11 1414 -- 188706188706 βcβc 11 1717 ++ 35683568 cc 11 2020 )) ,,

cc 1010 == 11 181440181440 11 ββ 1313 cc 11 88 (( 9289728092897280 ββ 1313 cc 22 99 -- 9289728092897280 ββ 1212 cc 11 cc 22 88 ++ 40584499204058449920 ββ 1111 cc 11 22 cc 22 77 -- 238970880238970880 ββ 1010 cc 11 55 cc 22 77 -- 1014902784010149027840 ββ 1010 cc 11 33 cc 22 66 ++ 16301583361630158336 ββ 99 cc 11 66 cc 22 66 ++ 1598014656015980146560 ββ 99 cc 11 44 cc 22 55 -- 46760785924676078592 ββ 88 cc 11 77 cc 22 55 -- 1639709568016397095680 ββ 88 cc 11 55 cc 22 44 ++ 131654016131654016 ββ 77 cc 11 1010 cc 22 55 ++ 73040434567304043456 ββ 77 cc 11 88 cc 22 44 ++ 1094264640010942646400 ββ 77 cc 11 66 cc 22 33 -- 564117120564117120 ββ 66 cc 11 1111 cc 22 44 -- 67027707366702770736 ββ 66 cc 11 99 cc 22 33 -- 45714715204571471520 ββ 66 cc 11 77 cc 22 22 ++ 949114656949114656 ββ 55 cc 11 1212 cc 22 33 ++ 36101178363610117836 ββ 55 cc 11 1010 cc 22 22 ++ 10832648401083264840 ββ 55 cc 11 88 cc 22 -- 1840454418404544 ββ 44 cc 11 1515 cc 22 33 -- 783565920783565920 ββ 44 cc 11 1313 cc 22 22 -- 10557108001055710800 ββ 44 cc 11 1111 cc 22 -- 110837160110837160 ββ 44 cc 11 99 ++ 4146012041460120 ββ 33 cc 11 1616 cc 22 22 ++ 317333772317333772 ββ 33 cc 11 1414 cc 22 ++ 129215439129215439 ββ 33 cc 11 1212 -- 3067893630678936 ββ 22 cc 11 1717 cc 22 -- 5042028650420286 ββ 22 cc 11 1515 ++ 484984484984 βcβc 11 2020 cc 22 ++ 74576107457610 βcβc 11 1818 -- 316628316628 cc 11 21twenty one )) ..

最后，由方程Finally, by the equation

σσ mm == -- 11 22 (( EaEa 22 qq 22 hh 22 )) 11 // 33 ΣΣ nno == 00 1010 dd nno (( bb -- aa 22 aa )) nno ,,

则可以得到该环形薄膜的最大应力σm＝0.74044MPa，其中，Then the maximum stress σ m =0.74044MPa of the annular film can be obtained, where,

dd 00 == ββ cc 11 ,,

dd 11 == 11 cc 11 22 (( -- 22 βcβc 22 ++ cc 11 )) ,,

dd 22 == 11 22 ββ 22 cc 11 22 (( 66 ββ 22 cc 22 -- 33 βcβc 11 ++ cc 11 44 )) ,,

dd 33 == 11 66 ββ 33 cc 11 22 (( -- 24twenty four ββ 22 cc 22 ++ 44 βcβc 11 33 cc 22 ++ 1212 βcβc 11 -- 55 cc 11 44 )) ,,

dd 44 == 11 24twenty four ββ 55 cc 11 22 (( 24twenty four ββ 33 cc 11 22 cc 22 22 ++ 120120 ββ 33 cc 22 -- 4848 ββ 22 cc 11 33 cc 22 -- 6060 ββ 22 cc 11 ++ 3333 βcβc 11 44 -- 22 cc 11 77 )) ,,

dd 55 == 11 6060 ββ 66 cc 11 22 (( 9696 ββ 44 cc 11 cc 22 33 -- 288288 ββ 33 cc 11 22 cc 22 22 -- 360360 ββ 33 cc 22 ++ 180180 ββ 22 cc 11 ++ 294294 ββ 22 cc 11 33 cc 22 -- 22twenty two βcβc 11 66 cc 22 -- 132132 βcβc 11 44 ++ 1717 cc 11 77 )) ,,

dd 66 == 11 360360 ββ 88 cc 11 22 (( 960960 ββ 66 cc 22 44 -- 39363936 ββ 55 cc 11 cc 22 33 ++ 59405940 ββ 44 cc 11 22 cc 22 22 ++ 25202520 ββ 44 cc 22 -- 408408 ββ 33 cc 11 55 cc 22 22 -- 40384038 ββ 33 cc 11 33 cc 22 -- 12601260 ββ 33 cc 11 ++ 678678 ββ 22 cc 11 66 cc 22 ++ 12811281 ββ 22 cc 11 44 -- 282282 βcβc 11 77 ++ 1111 cc 11 1010 )) ,,

dd 77 == 11 25202520 ββ 99 cc 11 33 (( 1152011520 ββ 77 cc 22 55 -- 6048060480 ββ 66 cc 11 cc 22 44 ++ 124128124128 ββ 55 cc 11 22 cc 22 33 -- 76327632 ββ 44 cc 11 55 cc 22 33 -- 125100125100 ββ 44 cc 11 33 cc 22 22 -- 2016020160 ββ 44 cc 11 cc 22 ++ 2016020160 ββ 33 cc 11 66 cc 22 22 ++ 6332463324 ββ 33 cc 11 44 cc 22 ++ 1008010080 ββ 33 cc 11 22 -- 1744217442 ββ 22 cc 11 77 cc 22 -- 1500315003 ββ 22 cc 11 55 ++ 584584 βcβc 11 1010 cc 22 ++ 50105010 βcβc 11 88 -- 427427 cc 11 1111 )) ,,

dd 88 == 11 2016020160 ββ 1111 cc 11 44 (( 161280161280 ββ 99 cc 22 66 -- 10368001036800 ββ 88 cc 11 cc 22 55 ++ 27187202718720 ββ 77 cc 11 22 cc 22 44 -- 150912150912 ββ 66 cc 11 55 cc 22 44 -- 37221123722112 ββ 66 cc 11 33 cc 22 33 ++ 555840555840 ββ 55 cc 11 66 cc 22 33 ++ 28150202815020 ββ 55 cc 11 44 cc 22 22 ++ 181440181440 ββ 55 cc 11 22 cc 22 -- 752400752400 ββ 44 cc 11 77 cc 22 22 -- 11318761131876 ββ 44 cc 11 55 cc 22 -- 9072090720 ββ 44 cc 11 33 ++ 2196021960 ββ 33 cc 11 1010 cc 22 22 ++ 444984444984 ββ 33 cc 11 88 cc 22 ++ 210087210087 ββ 33 cc 11 66 -- 3458434584 ββ 22 cc 11 1111 cc 22 -- 9790597905 ββ 22 cc 11 99 ++ 1344013440 βcβc 11 1212 -- 292292 cc 11 1515 )) ,,

dd 99 == 11 181440181440 ββ 1212 cc 11 55 (( 25804802580480 ββ 1010 cc 22 77 -- 1967616019676160 ββ 99 cc 11 cc 22 66 ++ 6310656063106560 ββ 88 cc 11 22 cc 22 55 -- 32002563200256 ββ 77 cc 11 55 cc 22 55 -- 110246400110246400 ββ 77 cc 11 33 cc 22 44 ++ 1525824015258240 ββ 66 cc 11 66 cc 22 44 ++ 113274720113274720 ββ 66 cc 11 44 cc 22 33 -- 2854915228549152 ββ 55 cc 11 77 cc 22 33 -- 6858108068581080 ββ 55 cc 11 55 cc 22 22 -- 18144001814400 ββ 55 cc 11 33 cc 22 ++ 741024741024 ββ 44 cc 11 1010 cc 22 33 ++ 2621505626215056 ββ 44 cc 11 88 cc 22 22 ++ 2286792122867921 ββ 44 cc 11 66 cc 22 ++ 907200907200 ββ 44 cc 11 44 -- 18515521851552 ββ 33 cc 11 1111 cc 22 22 -- 1183606211836062 ββ 33 cc 11 99 cc 22 -- 34692303469230 ββ 33 cc 11 77 ++ 15174961517496 ββ 22 cc 11 1212 cc 22 ++ 21145592114559 ββ 22 cc 11 1010 -- 2838428384 βcβc 11 1515 cc 22 -- 408768408768 βcβc 11 1313 ++ 2050420504 cc 11 1616 )) ,,

dd 1010 == 11 18144001814400 ββ 1414 cc 11 66 (( 4644864046448640 ββ 1212 cc 22 88 -- 410296320410296320 ββ 1111 cc 11 cc 22 77 ++ 15599001601559900160 ββ 1010 cc 11 22 cc 22 66 -- 7303680073036800 ββ 99 cc 11 55 cc 22 66 -- 33301324803330132480 ββ 99 cc 11 33 cc 22 55 ++ 429684480429684480 ββ 88 cc 11 66 cc 22 55 ++ 43622064004362206400 ββ 88 cc 11 44 cc 22 44 -- 10352689921035268992 ββ 77 cc 11 77 cc 22 44 -- 35888961603588896160 ββ 77 cc 11 55 cc 22 33 ++ 2430316824303168 ββ 66 cc 11 1010 cc 22 44 ++ 1995840019958400 ββ 66 cc 11 44 cc 22 ++ 13071343681307134368 ββ 66 cc 11 88 cc 22 33 ++ 18128221201812822120 ββ 66 cc 11 66 cc 22 22 -- 8459107284591072 ββ 55 cc 11 1111 cc 22 33 -- 912287016912287016 ββ 55 cc 11 99 cc 22 22 -- 516903120516903120 ββ 55 cc 11 77 cc 22 -- 99792009979200 ββ 55 cc 11 55 ++ 108652752108652752 ββ 44 cc 11 1212 cc 22 22 ++ 334076706334076706 ββ 44 cc 11 1010 cc 22 ++ 6643215066432150 ββ 44 cc 11 88 -- 17927521792752 ββ 33 cc 11 1515 cc 22 22 -- 6107244061072440 ββ 33 cc 11 1313 cc 22 -- 5033364350333643 ββ 33 cc 11 1111 ++ 27567842756784 ββ 22 cc 11 1616 cc 22 ++ 1269072312690723 ββ 22 cc 11 1414 -- 10473721047372 βcβc 11 1717 ++ 1419214192 cc 11 2020 )) ,,

Claims (1)

1. The method for determining the maximum stress of the annular film with the rigid plate at the center under uniformly distributed loads is characterized by comprising the following steps of: fixedly clamping an annular film of a rigid plate with the thickness of h, the Young's modulus of elasticity of E, the Poisson ratio of v and the radius of a central zone of b by adopting a clamping device with the inner radius of a to form an axisymmetric annular film of the rigid plate with the central zone, the periphery of which is fixedly clamped and the outer radius of a and the inner radius of b, transversely applying an evenly distributed load q to the axisymmetric annular film, measuring the value of the applied evenly distributed load q, and determining the maximum stress sigma of the annular film by the following formulam：
σ m = - 1 2 ( Ea 2 q 2 h 2 ) 1 / 3 Σ n = 0 10 d n ( b - a 2 a ) n ,
Wherein,
d 0 = β c 1 ,
d 1 = 1 c 1 2 ( - 2 βc 2 + c 1 ) ,
d 2 = 1 2 β 2 c 1 2 ( 6 β 2 c 2 - 3 βc 1 + c 1 4 ) ,
d 3 = 1 6 β 3 c 1 2 ( - 24 β 2 c 2 + 4 βc 1 3 c 2 + 12 βc 1 - 5 c 1 4 ) ,
d 4 = 1 24 β 5 c 1 2 ( 24 β 3 c 1 2 c 2 2 + 120 β 3 c 2 - 48 β 2 c 1 3 c 2 - 60 β 2 c 1 + 33 βc 1 4 - 2 c 1 7 ) ,
d 5 = 1 60 β 6 c 1 2 ( 96 β 4 c 1 c 2 3 - 288 β 3 c 1 2 c 2 2 - 360 β 3 c 2 + 180 β 2 c 1 + 294 β 2 c 1 3 c 2 - 22 βc 1 6 c 2 - 132 βc 1 4 + 17 c 1 7 ) ,
d 6 = 1 360 β 8 c 1 2 ( 960 β 6 c 2 4 - 3936 β 5 c 1 c 2 3 + 5940 β 4 c 1 2 c 2 2 + 2520 β 4 c 2 - 408 β 3 c 1 5 c 2 2 - 4038 β 3 c 1 3 c 2 - 1260 β 3 c 1 + 678 β 2 c 1 6 c 2 + 1281 β 2 c 1 4 - 282 βc 1 7 + 11 c 1 10 ) ,
d 7 = 1 2520 β 9 c 1 3 ( 11520 β 7 c 2 5 - 60480 β 6 c 1 c 2 4 + 124128 β 5 c 1 2 c 2 3 - 7632 β 4 c 1 5 c 2 3 - 125100 β 4 c 1 3 c 2 2 - 20160 β 4 c 1 c 2 + 20160 β 3 c 1 6 c 2 2 + 63324 β 3 c 1 4 c 2 + 10080 β 3 c 1 2 - 17442 β 2 c 1 7 c 2 - 15003 β 2 c 1 5 + 584 βc 1 10 c 2 + 5010 βc 1 8 - 427 c 1 11 ) ,
d 8 = 1 20160 β 11 c 1 4 ( 161280 β 9 c 2 6 - 1036800 β 8 c 1 c 2 5 + 2718720 β 7 c 1 2 c 2 4 - 150912 β 6 c 1 5 c 2 4 - 3722112 β 6 c 1 3 c 2 3 + 555840 β 5 c 1 6 c 2 3 + 2815020 β 5 c 1 4 c 2 2 + 181440 β 5 c 1 2 c 2 - 752400 β 4 c 1 7 c 2 2 - 1131876 β 4 c 1 5 c 2 - 90720 β 4 c 1 3 + 21960 β 3 c 1 10 c 2 2 + 444984 β 3 c 1 8 c 2 + 210087 β 3 c 1 6 - 34584 β 2 c 1 11 c 2 - 97905 β 2 c 1 9 + 13440 βc 1 12 - 292 c 1 15 ) ,
d 9 = 1 181440 β 12 c 1 5 ( 2580480 β 10 c 2 7 - 19676160 β 9 c 1 c 2 6 + 63106560 β 8 c 1 2 c 2 5 - 3200256 β 7 c 1 5 c 2 5 - 110246400 β 7 c 1 3 c 2 4 + 15258240 β 6 c 1 6 c 2 4 + 113274720 β 6 c 1 4 c 2 3 - 28549152 β 5 c 1 7 c 2 3 - 68581080 β 5 c 1 5 c 2 2 - 1814400 β 5 c 1 3 c 2 + 741024 β 4 c 1 10 c 2 3 + 26215056 β 4 c 1 8 c 2 2 + 22867921 β 4 c 1 6 c 2 + 907200 β 4 c 1 4 - 1851552 β 3 c 1 11 c 2 2 - 11836062 β 3 c 1 9 c 2 - 3469230 β 3 c 1 4 + 1517496 β 2 c 1 12 c 2 + 2114559 β 2 c 1 10 - 28384 βc 1 15 c 2 - 408768 βc 1 13 + 20504 c 1 16 ) ,
d 10 = 1 1814400 β 14 c 1 6 ( 46448640 β 12 c 2 8 - 410296320 β 11 c 1 c 2 7 + 1559900160 β 10 c 1 2 c 2 6 - 73036800 β 9 c 1 5 c 2 6 - 3330132480 β 9 c 1 3 c 2 5 + 429684480 β 8 c 1 6 c 2 5 + 4362206400 β 8 c 1 4 c 2 4 - 1035268992 β 7 c 1 7 c 2 4 - 3588896160 β 7 c 1 5 c 2 3 + 24303168 β 6 c 1 10 c 2 4 + 19958400 β 6 c 1 4 c 2 + 1307134368 β 6 c 1 8 c 2 3 + 1812822120 β 6 c 1 6 c 2 2 - 84591072 β 5 c 1 11 c 2 3 - 912287016 β 5 c 1 9 c 2 2 - 516903120 β 5 c 1 7 c 2 - 9979200 β 5 c 1 5 + 108652752 β 4 c 1 12 c 2 2 + 334076706 β 4 c 1 10 c 2 + 66432150 β 4 c 1 8 - 1792752 β 3 c 1 15 c 2 2 - 61072440 β 3 c 1 13 c 2 - 50333643 β 3 c 1 11 + 2756784 β 2 c 1 16 c 2 + 12690723 β 2 c 1 14 - 1047372 βc 1 17 + 14192 c 1 20 ) ,
and β ═ a + b)/2a, c1And c2Is given by the equation
ν = 2 - b a [ Σ i = 2 10 i ( i - 1 ) c i ( b a - β ) i - 2 ] / [ Σ j = 1 10 jc j ( b a - β ) j - 1 ]
And
ν = 2 - 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 ]
determining, wherein,
c 3 = 1 6 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 = 1 24 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 ) ,
c 5 = 1 120 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 ) ,
c 6 = 1 720 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 ) ,
c 7 = 1 2520 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 ) ,
c 8 = 1 20160 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 ) ,
c 9 = 1 181440 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 ) ,
c 10 = 1 181440 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 ) .
all parameters adopt an international system of units.
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106644248A (en) * 2017-01-16 2017-05-10 重庆大学 Method for determining maximum stress of circular membrane under limited maximum deflection
CN106706169A (en) * 2017-01-16 2017-05-24 重庆大学 Method for confirming maximum stress of annular film with hard core under combined load
CN106769477A (en) * 2017-01-16 2017-05-31 重庆大学 Axle loads the determination method of lower prestress circular membrane maximum stress
CN113092041A (en) * 2021-04-16 2021-07-09 重庆大学 Method for determining maximum deflection of annular film under transversely uniformly distributed load
CN113092040A (en) * 2021-04-16 2021-07-09 重庆大学 Method for determining maximum stress of annular film under transversely uniformly distributed load

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104019931A (en) * 2014-06-19 2014-09-03 重庆大学 Method for determining maximum stress of prestressed annular thin film under transverse concentrated load
CN104749033A (en) * 2015-04-22 2015-07-01 重庆大学 Determination method for maximum stress of large-turning angle circular membrane under uniformly distributed load

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104019931A (en) * 2014-06-19 2014-09-03 重庆大学 Method for determining maximum stress of prestressed annular thin film under transverse concentrated load
CN104749033A (en) * 2015-04-22 2015-07-01 重庆大学 Determination method for maximum stress of large-turning angle circular membrane under uniformly distributed load

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
何晓婷 等: "不同模量简支梁均布荷载下的弹性力学解", 《工程力学》 *

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CN106644248B (en) * 2017-01-16 2019-04-05 重庆大学 The determination method of circular membrane maximum stress under maximum defluxion constrained state
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