ANSYS中粘彈材質(zhì)屬性參數(shù)輸入和分析

1、 TOC o 1-3 h z u HYPERLINK l _Toc167097319 ANSYS中粘彈材質(zhì)屬性參數(shù)輸入和分析 )要注意的是，ANSYS中對Prony級數(shù)的支持項數(shù)不能超過6項，即。這確實是一個遺憾。另外，The viscoelasticity input for HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_E_SHELL181.html o SHELL181 description SHELL181, HYPERLINK mk:MSITStore:G:ANSYS%209

2、0v90commonfileshelpen-usansyshelp.chm:/Hlp_E_PLANE182.html o PLANE182 description PLANE182, HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_E_PLANE183.html o PLANE183 description PLANE183, HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_E_SOL

3、ID185.html o SOLID185 description SOLID185, HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_E_SOLID186.html o SOLID186 description SOLID186, HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_E_SOLID187.html o SOLID187 description SOLID187, HYPE

4、RLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_E_SOLSH190.html o SOLSH190 description SOLSH190, HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_E_SHELL208.html o SHELL208 description SHELL208, and HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfile

5、shelpen-usansyshelp.chm:/Hlp_E_SHELL209.html o SHELL209 description SHELL209 consists of elasticity properties and relaxation properties. The underlying elasticity is specified by either the HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_C_MP.html o MP description MP co

6、mmand (for hypoelasticity) or by the HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_C_TB.html o TB description TB,HYPER command (for hyperelasticity). Use the HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_C_TB.html o TB description TB,PRON

7、Y or HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_C_TB.html o TB description TB,SHIFT commands to input the relaxation properties.可見，此時除了由Prony級數(shù)形式附加粘彈性，還需輸入“彈性”屬性。這里我對hypoelasticity不了解，具體也說不上來。在ANSYS幫助文檔里有這樣一段：!Small Strain Viscoelasticitymp,ex,1,20.0E5!elastic prope

8、rtiesmp,nuxy,1,0.3tb,prony,1,2,shear!define viscosity parameters (shear)tbdata,1,0.5,2.0,0.25,4.0tb,prony,1,2,bulk!define viscosity parameters (bulk)tbdata,1,0.5,2.0,0.25,4.0!Large Strain Viscoelasticitytb,hyper,1,moon!elastic propertiestbdata,1,38.462E4,1.2E-6tb,prony,1,1,shear!define viscosity par

9、ameterstbdata,1,0.5,2.0tb,prony,1,1,bulk!define viscosity parameterstbdata,1,0.5,2.01.3 Maxwell形式For the viscoelastic elements HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_E_VISCO88.html o VISCO88 description VISCO88 and HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfil

10、eshelpen-usansyshelp.chm:/Hlp_E_VISCO89.html o VISCO89 description VISCO89 the material properties are expressed in integral form using the kernel function of the generalized Maxwell elements as: MACROBUTTON MTPlaceRef * MERGEFORMAT SEQ MTEqn h * MERGEFORMAT ( SEQ MTSec c * Arabic * MERGEFORMAT 0. S

11、EQ MTEqn c * Arabic * MERGEFORMAT 12) MACROBUTTON MTPlaceRef * MERGEFORMAT SEQ MTEqn h * MERGEFORMAT ( SEQ MTSec c * Arabic * MERGEFORMAT 0. SEQ MTEqn c * Arabic * MERGEFORMAT 13)其中為折算時間，由于不考慮溫度載荷，方程中的折算時間就是實際時間，即，類同Prony級數(shù)情形的。 = reduced or pseudo timeG() = shear relaxation kernel functionK() = bulk

12、 relaxation kernel functionnG = number of Maxwell elements used to approximate the shear relaxation kernel (input constant 50)nK = number of Maxwell elements used to approximate the bulk relaxation kernel (input constant 71)Ci = constants associated with the instantaneous response for shear behavior

13、 (input constants 5160)Di = constants associated with the instantaneous response for bulk behavior (input constants 7685)G0 = initial shear modulus (input constant 46)= final shear modulus (input constant 47)K0 = initial bulk modulus (input constant 48) = final bulk modulus (input constant 49) = con

14、stants associated with a discrete relaxation spectrum in shear (input constant 61-70)= constants associated with a discrete relaxation spectrum in bulk (input constant 86-95)同Prony技術(shù)情形一樣的：由試驗數(shù)據(jù)擬合得到 GOTOBUTTON ZEqnNum455541 * MERGEFORMAT REF ZEqnNum455541 ! * MERGEFORMAT (0.12)；由 GOTOBUTTON ZEqnNum45

15、5541 * MERGEFORMAT REF ZEqnNum455541 ! * MERGEFORMAT (0.12)即可確定：級數(shù)項數(shù)；K和G的初始值和穩(wěn)態(tài)值：和；時間松弛系數(shù)、；再分別根據(jù) GOTOBUTTON ZEqnNum503369 * MERGEFORMAT REF ZEqnNum503369 ! * MERGEFORMAT (0.13)計算得到參數(shù)。將上面計算所得值分別填入Maxwell材質(zhì)屬性表即可。Here, G0 and K0 are, respectively, the shear and bulk moduli at the fast load limit (i.e.

16、the instantaneous moduli), and and are the moduli at the slow limit. The elasticity parameters input correspond to those of the fast load limit.Initialize the constant table with HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_C_TB.html o TB description TB,EVISC. You can

17、 define up to 95 constants (C1-C95) with HYPERLINK mk:MSITStore:G:ANSYS%2090v90commonfileshelpen-usansyshelp.chm:/Hlp_C_TBDATA.html o TBDATA description TBDATA commands (6 per command):1.3 建模與載荷條件1.3.1 模型設(shè)計如圖3.1-1所示，一個圓孔形的藥柱，內(nèi)徑為a，外徑為b，彈性鋼殼體厚度為h。藥柱內(nèi)表面受均布壓強載荷作用。另外，我們假設(shè)：a、藥柱外表面與殼體是直接粘接在一起的，忽略絕熱層等材料的厚度；

18、b、該圓孔型藥柱足夠長，可以簡化為平面應變問題來處理；c、推進劑泊松比為常數(shù)。其中，相關(guān)物性參數(shù)如下：1、殼體： E=196.5 Gpa， =0.29，并認為v為常數(shù)處理；2、推進劑：=0.495，松弛模量E(t)用Prony級數(shù)表示為： MACROBUTTON MTPlaceRef * MERGEFORMAT SEQ MTEqn h * MERGEFORMAT ( SEQ MTSec c * Arabic * MERGEFORMAT 0. SEQ MTEqn c * Arabic * MERGEFORMAT 14)3、幾何參數(shù)： a=100mm, b=177mm, h=3mm。圖3.1-14

19、、階躍壓力載荷： MACROBUTTON MTPlaceRef * MERGEFORMAT SEQ MTEqn h * MERGEFORMAT ( SEQ MTSec c * Arabic * MERGEFORMAT 0. SEQ MTEqn c * Arabic * MERGEFORMAT 15)其中，為穩(wěn)態(tài)壓強值，取，。我們還可以將所得結(jié)果于其加以對比。1.3.2 有限元建模圖3.1-1所示的模型的幾何形狀以及所受載荷條件和邊界條件具有明顯的對稱性，出于方便建模和適當計算量的考慮，我們?nèi)∑?/4來建模分析。根據(jù)前面藥柱外表面與殼體內(nèi)表面是直接粘接在一起的假設(shè)，可以將這兩個面位移耦合。其有限

20、元模型和網(wǎng)格劃分如圖3.1-2所示。圖中還標出模型位移邊界約束，內(nèi)表面壓強載荷以及藥柱與殼體粘結(jié)面上節(jié)點耦合約束。這里我們統(tǒng)一選用Plane183單元來劃分網(wǎng)格的，共200個單元，718個節(jié)點：其中，殼體部分有單元50個，節(jié)點205個；藥柱部分有單元150個，節(jié)點513個。圖3.1-2求解時間定為1s。下面就不同加載方式，分別計算分析。我們將就節(jié)點A（如圖3.1-2中所示）取其徑向應力/應變和周向應力/應變加以比較。1.3.3 理論解析解計算式 限于篇幅，這里不準備列寫出理論解析解的詳細公式推導過程，根據(jù)文獻，這里直接給出最終計算表達式。(1) 徑向應力：(3) 徑向應變：(2) 周向應力：(

21、4) 周向應變：其中， a、b為藥柱的內(nèi)徑和外徑，h為殼體厚度， 為殼體的彈性模量，是推進劑蠕變?nèi)崃浚c松弛模量有如下關(guān)系：。即可由作一定變換得到。1.4 有限元數(shù)值解與結(jié)果比較1.4.1 Plane183、Prony級數(shù)方式參數(shù)變換另外，根據(jù)前面Prony級數(shù)表示方式，經(jīng)換算得到相關(guān)各系數(shù)為：， 常數(shù)；根據(jù) GOTOBUTTON ZEqnNum532648 * MERGEFORMAT REF ZEqnNum532648 ! * MERGEFORMAT (0.8)式， 參數(shù)輸入情況分別如下圖所示：計算結(jié)果比較以圓通內(nèi)表面點A的應力應變?yōu)閰⒖紒砜疾欤瑢NSYS計算值與理論值比較，結(jié)果如下面幾個

22、圖中所示的： 1.4.2 Maxwell形式參數(shù)變換與輸入根據(jù)前面Prony級數(shù)表示方式，由 GOTOBUTTON ZEqnNum455541 * MERGEFORMAT REF ZEqnNum455541 ! * MERGEFORMAT (0.12)即可確定：級數(shù)項數(shù)；和；時間松弛系數(shù)；再分別根據(jù) GOTOBUTTON ZEqnNum503369 * MERGEFORMAT REF ZEqnNum503369 ! * MERGEFORMAT (0.13)計算得到參數(shù)。因為我們這里是假設(shè)泊松比是常數(shù)的；否則，擬合所得和形式就沒有 GOTOBUTTON ZEqnNum532648 * MERGEFORMAT REF ZEqnNum532648 ! * MERGEFORMAT (0.8)那樣簡潔的關(guān)系，當然的相應系數(shù)比也就不相同了。而且亦可以取為不同，這都不影響上面參數(shù)的換算的。參數(shù)輸入情況分別如下圖所示。其中無需對EX等參數(shù)輸入。計算結(jié)果比較同樣以圓通內(nèi)表面點A的應力應變?yōu)閰⒖紒砜疾欤瑢NSYS計算值與理論值比較，結(jié)果如下面幾個圖中所