弹性力学基础及有限元法-12

1、内蒙古科技大学内蒙古科技大学 机械工程学院机械工程学院 刘学杰刘学杰 2015-052015-05动力学问题的有限元法，动态分析动力学问题的有限元法，动态分析FEM & ANSYS-12有限元法及实践有限元法及实践-12Finite Element Method (FEM) & the PracticeOutline 概要概要n1. Review 回顾回顾n2. 有限元法有限元法:动力学问题动力学问题n3.动态分析实例动态分析实例 模态分析模态分析Review 回顾：回顾：n1 1 学习报告：学习报告：1313组组- -王炎王炎n2 2 静态分析小结静态分析小结n1 1）平面问

2、题：三节点单元、四节点单元）平面问题：三节点单元、四节点单元n2)2)空间问题空间问题n3)3)案例案例动力学方程：动力学方程： 与静态有什么不同？与静态有什么不同？Elemental volume位移/displacements u, v, w应变/strains zxyzxyzyx,应力/stress zxyzxyzyx,Not-steady loads any more动力学方程：动力学方程： 与静态有什么不同？与静态有什么不同？ etNtf twtvtutf etBt etDBtDtDBdVBkT twtvtutf eTTetNdVNdVtfNtP 惯NdVNmT eetmtP 惯 e

3、TTetNdVNdVtfNtP阻NdVNcT eetctP阻1. 质量矩阵及阻尼矩阵质量矩阵及阻尼矩阵动力学方程动力学方程 质量矩阵及阻尼矩阵质量矩阵及阻尼矩阵eeenenenecCmMkK111 eneetPtP1 tCtMtP tCtMtPtK tPtKtCtM 特征值问题特征值问题0kM tsin0002MK0IAn纽马克法动力响应和逐步积分法动力响应和逐步积分法PKCM 00ttttttttPKCM tttt 101ttt tttttttt 1221ttttttt ttttttttttttttttttt ) 121(21)(11022221222纽马克法纽马克法ttttPKCtMtKK

4、21ttttttttttttCttMPP 2211121112综合纽马克法计算步骤综合纽马克法计算步骤1 1）初始计算）初始计算（1）形成刚度矩阵K、质量矩阵M、组逆矩阵C（2）获得初始值000 和，（3）选择步长 参数 和 ，并计算下列有关常数t25 . 025. 05 . 0tatataaatatata7654321201221121111（4 4）形成）形成“刚度刚度”矩阵矩阵CaMaKK10（5 5）分解矩阵）分解矩阵TLDLK 2 2）对于每个时间步长进行下列计算）对于每个时间步长进行下列计算（1）计算 时刻的“载荷”矢量ttttttttttttaaaCaaaMPP 541320（2

5、）解矩阵方程求 时刻的位移位移ttttttTPLDL（3）计算 时刻的加速度、速度tttttttttaaa 320ttttttaa 76综合纽马克法计算步骤综合纽马克法计算步骤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 (模态分析实例均匀直杆的纵向固有频率分析 ) 图10-1所示为一根长度为L的等截面(0.01x0.01m2)直杆，杆长L=0.1 m, 一端固定，一端自由。已知杆材料的弹性模量E=21011 N/m2，密度=7800

15、 kg/m3 。要求计算直杆纵向振动的固有频率。图 10-1 均匀直杆的固有频率分析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(请看教案中的具体操作）Conclusion（总结）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 作业作业n1、求解动力学方程有限元法