彈性力學(xué)基礎(chǔ)及有限元法-12

1、內(nèi)蒙古科技大學(xué)內(nèi)蒙古科技大學(xué) 機(jī)械工程學(xué)院機(jī)械工程學(xué)院 劉學(xué)杰劉學(xué)杰 2015-052015-05動(dòng)力學(xué)問題的有限元法，動(dòng)態(tài)分析動(dòng)力學(xué)問題的有限元法，動(dòng)態(tài)分析FEM & ANSYS-12有限元法及實(shí)踐有限元法及實(shí)踐-12Finite Element Method (FEM) & the PracticeOutline 概要概要n1. Review 回顧回顧n2. 有限元法有限元法:動(dòng)力學(xué)問題動(dòng)力學(xué)問題n3.動(dòng)態(tài)分析實(shí)例動(dòng)態(tài)分析實(shí)例 模態(tài)分析模態(tài)分析Review 回顧：回顧：n1 1 學(xué)習(xí)報(bào)告：學(xué)習(xí)報(bào)告：1313組組- -王炎王炎n2 2 靜態(tài)分析小結(jié)靜態(tài)分析小結(jié)n1 1）平面問

2、題：三節(jié)點(diǎn)單元、四節(jié)點(diǎn)單元）平面問題：三節(jié)點(diǎn)單元、四節(jié)點(diǎn)單元n2)2)空間問題空間問題n3)3)案例案例動(dòng)力學(xué)方程：動(dòng)力學(xué)方程： 與靜態(tài)有什么不同？與靜態(tài)有什么不同？Elemental volume位移/displacements u, v, w應(yīng)變/strains zxyzxyzyx,應(yīng)力/stress zxyzxyzyx,Not-steady loads any more動(dòng)力學(xué)方程：動(dòng)力學(xué)方程： 與靜態(tài)有什么不同？與靜態(tài)有什么不同？ etNtf twtvtutf etBt etDBtDtDBdVBkT twtvtutf eTTetNdVNdVtfNtP 慣NdVNmT eetmtP 慣 e

3、TTetNdVNdVtfNtP阻NdVNcT eetctP阻1. 質(zhì)量矩陣及阻尼矩陣質(zhì)量矩陣及阻尼矩陣動(dòng)力學(xué)方程動(dòng)力學(xué)方程 質(zhì)量矩陣及阻尼矩陣質(zhì)量矩陣及阻尼矩陣eeenenenecCmMkK111 eneetPtP1 tCtMtP tCtMtPtK tPtKtCtM 特征值問題特征值問題0kM tsin0002MK0IAn紐馬克法動(dòng)力響應(yīng)和逐步積分法動(dòng)力響應(yīng)和逐步積分法PKCM 00ttttttttPKCM tttt 101ttt tttttttt 1221ttttttt ttttttttttttttttttt ) 121(21)(11022221222紐馬克法紐馬克法ttttPKCtMtKK

4、21ttttttttttttCttMPP 2211121112綜合紐馬克法計(jì)算步驟綜合紐馬克法計(jì)算步驟1 1）初始計(jì)算）初始計(jì)算（1）形成剛度矩陣K、質(zhì)量矩陣M、組逆矩陣C（2）獲得初始值000 和，（3）選擇步長(zhǎng) 參數(shù) 和 ，并計(jì)算下列有關(guān)常數(shù)t25 . 025. 05 . 0tatataaatatata7654321201221121111（4 4）形成）形成“剛度剛度”矩陣矩陣CaMaKK10（5 5）分解矩陣）分解矩陣TLDLK 2 2）對(duì)于每個(gè)時(shí)間步長(zhǎng)進(jìn)行下列計(jì)算）對(duì)于每個(gè)時(shí)間步長(zhǎng)進(jìn)行下列計(jì)算（1）計(jì)算 時(shí)刻的“載荷”矢量ttttttttttttaaaCaaaMPP 541320（2

5、）解矩陣方程求 時(shí)刻的位移位移ttttttTPLDL（3）計(jì)算 時(shí)刻的加速度、速度tttttttttaaa 320ttttttaa 76綜合紐馬克法計(jì)算步驟綜合紐馬克法計(jì)算步驟What is a modal analysis?A modal analysis is used to determine the natural frequencies and mode shapes of a structure. nThe natural frequencies and mode shapes are important parameters in the design of a structur

6、e for dynamic loading conditions. nThe natural frequencies and mode shapes are also required if you want to do a spectrum analysis or a Harmonic Response Analysis or transient analysis.What is a modal analysis?nThe equation for a static analysis:nThe equation for a dynamic analysis:nThe equation for

7、 a modal analysis:FKC MFK0MK The procedure for a modal analysisnThe procedure for a modal analysis consists of four main steps: nBuild the model.nApply loads and obtain the solution.nExpand the modes.nReview the results.Build the ModelnWhen building your model, remember these points:n1. Only linear

8、behavior is valid in a modal analysis. If you specify nonlinear elements, they are treated as linear. nFor example, if you include a contact element, its stiffness are calculated based on its initial status and never change.n2. Material properties can be linear, isotropic or orthotropic, and constan

9、t or temperature-dependent. nYou must define both Youngs modulus (EX) (or stiffness in some form) and density (DENS) (or mass in some form) for a modal analysis. nNonlinear properties are ignored. If applying element damping, you must define the required real constants for the specific element type

10、(COMBIN7, COMBIN14, COMBIN37, and so on).Applying Loads and Obtain the Solution nDefine Analysis Type and Options nOption1: New Analysis nOption2: Analysis Type: Modal nOption3: Mode-Extraction Method (Choose one of the extraction methods listed below). n1.Block Lanczos method (default)n2.Subspace m

11、ethodn3. PowerDynamics methodn4. Reduced (Householder) methodn5. Unsymmetric methodn6 .Damped methodn7. QR Damped methodnFor most applications, you will use the Block Lanczos, subspace, reduced, or PowerDynamics method. The unsymmetric, damped, and QR damped methods are meant for special application

12、s.Applying Loads and Obtain the SolutionnOption4: Number of Modes to Extract nOption5: Number of Modes to Expand nOption6: Pre-stress Effects Calculation nApply Loads nThe only loads valid in a typical modal analysis are zero-value displacement constraints. (If you input a nonzero displacement const

13、raint, the program assigns a zero-value constraint to that DOF instead.) nOther loads can be specified, but are ignored nSolve Review the ResultsnResults from a modal analysis (that is, the modal expansion pass) are written to the structural results file, Jobname.RST. nResults consist of: nNatural f

14、requencies, nExpanded mode shapesnRelative stress and force distributions.nYou can review these results in POST1, the general postprocessor. Case No. 10: A modal analysis of a cantilever beam (模態(tài)分析實(shí)例均勻直桿的縱向固有頻率分析 ) 圖10-1所示為一根長(zhǎng)度為L(zhǎng)的等截面(0.01x0.01m2)直桿，桿長(zhǎng)L=0.1 m, 一端固定，一端自由。已知桿材料的彈性模量E=21011 N/m2，密度=7800

15、 kg/m3 。要求計(jì)算直桿縱向振動(dòng)的固有頻率。圖 10-1 均勻直桿的固有頻率分析Analysis procedure n1. Change Job namen2. Define the element type n3. Define material properties n4. Build the element modelnCreate Block Generate volume mesh n5. Apply constraints to the model nApplied displacement boundary condition n6. Obtain solutionnSpe

16、cify analysis type and options Solve n7. Review the resultsnList the natural frequencies nAnimate the five mode shapes nPlease look at the details in text of this case study。n(請(qǐng)看教案中的具體操作）Conclusion（總結(jié)）nMain menun(1) PREP7:nElement typenMaterial propertiesnModeling: create Volume Meshingn(2) Solution

17、nDefine analysis typenApply loadsnSolvenMain menu:n(3) POST1nResults Summery nRead resultsnUntility Menu:n(1) PlotCtrls: animiteCommand flown/CLEARn/FILNAME, EXAMPLE10n/PREP7nET,1,SOLID186nMP,EX,1,2E11nMP,PRXY,1,0.3nMP,DENS,1,7800nBLOCK,0,0.01,0,0.01,0,0.1nLESIZE,1,3nLESIZE,2,3nLESIZE,9,15nMSHAPE,0nMSHKEY,1nVMESH,1nFINISHn/POST1nSET,LISTnSET,FIRST n/VIEW,1,-1n/REPLOTnPLDInANMODE,10,0.5,0nSET,NEXTnPLDInANMODE,10,0.5,0nFINISHn/SOLUnANTYPE, MODALnMODOPT,LANB,5nMXPAND,5nDA,1,UZnDA,3,UYnDA,5,UXnSOLVEnSAVEnFINISHHomework 作業(yè)作業(yè)n1、求解動(dòng)力學(xué)方程有限元法