有限元程序設(shè)計(jì)-第九章有限元法中相關(guān)問題的處理.ppt

上傳人:za****8 文檔編號:15475796 上傳時(shí)間:2020-08-12 格式:PPT 頁數(shù):53 大?。?.26MB
收藏 版權(quán)申訴 舉報(bào) 下載
有限元程序設(shè)計(jì)-第九章有限元法中相關(guān)問題的處理.ppt_第1頁
第1頁 / 共53頁
有限元程序設(shè)計(jì)-第九章有限元法中相關(guān)問題的處理.ppt_第2頁
第2頁 / 共53頁
有限元程序設(shè)計(jì)-第九章有限元法中相關(guān)問題的處理.ppt_第3頁
第3頁 / 共53頁

下載文檔到電腦,查找使用更方便

14.9 積分

下載資源

還剩頁未讀,繼續(xù)閱讀

資源描述:

《有限元程序設(shè)計(jì)-第九章有限元法中相關(guān)問題的處理.ppt》由會員分享,可在線閱讀,更多相關(guān)《有限元程序設(shè)計(jì)-第九章有限元法中相關(guān)問題的處理.ppt(53頁珍藏版)》請?jiān)谘b配圖網(wǎng)上搜索。

1、1,Finite Element Method,有限元建模技術(shù),CHAPTER 11:,2,INTRODUCTION,保證有限元計(jì)算的結(jié)果可靠,穩(wěn)定 提高求解的精度和效率,,3,INTRODUCTION,需要考慮的主要因素: 計(jì)算量和計(jì)算規(guī)模的大小; 明確需求和問題的特點(diǎn); 根據(jù)物理性質(zhì)和幾何特征選擇合理的單元配置; 邊界條件的施加; 初始條件的加載。,4,CPU時(shí)間的估計(jì),,( ranges from 2 3),,Bandwidth, b, affects ,- 最小化帶寬值,Aim:,盡可能控制有限元建模的自由度的數(shù)目 單元密度的搭配,5,GEOMETRY MODELLING,對模型進(jìn)行適

2、當(dāng)?shù)暮喕?3D? 2D? 1D? 或者混合單元形式,,(盡可能采用低維數(shù)單元),6,MESHING,在重點(diǎn)分析的局部布置較多的單元以增加精度;,,單元密度控制,7,Element distortion,單元會存在不規(guī)則的情況,但是不能逾越有限元法的基本原理. The distortions are measured against the basic shape of the element Square Quadrilateral elements Isosceles triangle Triangle elements Cube Hexahedron elements Isosceles

3、tetrahedron Tetrahedron elements,8,Element distortion,單元的橫縱比,Rule of thumb:,9,Element distortion,角度的要求,10,Element distortion,曲率的要求,,11,Element distortion,對于面積和體積的要求,不能存在負(fù)面積,物理坐標(biāo)和自然坐標(biāo)之間的轉(zhuǎn)換,12,Element distortion,對于面積和體積的要求,13,Element distortion,中部節(jié)點(diǎn)位置,,可能導(dǎo)致應(yīng)力場的奇異,14,MESH COMPATIBILITY,最小勢能原理的要求 單元邊界的協(xié)

4、調(diào)性,15,不同階數(shù)的單元組合,,單元間隙,造成應(yīng)力場的奇異,,,16,不同階數(shù)的單元組合,解決方式: Use same type of elements throughout Use transition elements Use MPC equations 多點(diǎn)約束方程,,,17,Straddling elements 跨界單元模式,避免跨界單元建模形式,18,USE OF SYMMETRY,不同類型的對稱:,,,,Mirror symmetry,Axial symmetry,Cyclic symmetry,Repetitive symmetry,Use of symmetry redu

5、ces number of DOFs and hence computational time. Also reduces numerical error.,19,Mirror symmetry,特殊面的對稱形式,,20,Mirror symmetry,考慮二維問題,如何施加約束:,u1x = 0,u2x = 0,u3x = 0,Single point constraints (SPC) 單點(diǎn)約束,21,Mirror symmetry,,Deflection = Free 法向偏移無約束 Rotation = 0 轉(zhuǎn)角為0,對稱加載,22,Mirror symmetry,Anti-symme

6、tric loading 反對稱加載,,Deflection = 0 偏移為0 Rotation = Free 轉(zhuǎn)角自由,23,Mirror symmetry,Symmetric 對稱 No translational displacement normal to symmetry plane(垂直于對稱面) No rotational components w.r.t. axis parallel to symmetry plane(平行于對稱面),24,Mirror symmetry,Anti-symmetric 反對稱 No translational displacement para

7、llel to symmetry plane No rotational components w.r.t. axis normal to symmetry plane,25,Mirror symmetry,Any load can be decomposed to a symmetric and an anti-symmetric load 任何加載可以分解為對稱和反對稱的組合,,26,Mirror symmetry,,27,Mirror symmetry,,,28,Mirror symmetry,Dynamic problems (e.g. two half models to get f

8、ull set of eigenmodes in eigenvalue analysis) 動(dòng)態(tài)問題(模態(tài)和特征值分析),,29,Axial symmetry,采用1D,2D軸對稱單元,,,Cylindrical shell using 1D axisymmetric elements,3D structure using 2D axisymmetric elements,30,Cyclic symmetry,,uAn = uBn,uAt = uBt,Multipoint constraints (MPC),31,Repetitive symmetry,,uAx = uBx,32,MODELL

9、ING OF OFFSETS,,, offset can be safely ignored,,, offset needs to be modelled,,, ordinary beam, plate and shell elements should not be used. Use 2D or 3D solid elements.,Guidelines:,33,MODELLING OF OFFSETS,Three methods: Very stiff element 大剛性單元 Rigid element 剛體單元 MPC equations 多點(diǎn)約束方程,,,34,Creation

10、of MPC equations for offsets多點(diǎn)約束方程,,,,,,,,,,,Eliminate q1, q2, q3,,35,Creation of MPC equations for offsets,36,Creation of MPC equations for offfsets,d6 = d1 + d5 or d1 + d5 - d6 = 0 d7 = d2 - d4 or d2 - d4 - d7 = 0 d8 = d3 or d3 - d8 = 0 d9 = d5 or d5 - d9 = 0,37,MODELLING OF SUPPORTS,,

11、38,MODELLING OF SUPPORTS,,(Prop support of beam),39,MODELLING OF JOINTS,,Perfect connection ensured here,40,MODELLING OF JOINTS,,Mismatch between DOFs of beams and 2D solid beam is free to rotate (rotation not transmitted to 2D solid),,Perfect connection by artificially extending beam into 2D solid

12、(Additional mass),41,MODELLING OF JOINTS,Using MPC equations,,,,,,42,MODELLING OF JOINTS,,Similar for plate connected to 3D solid,43,OTHER APPLICATIONS OF MPC EQUATIONS,Modelling of symmetric boundary conditions,,dn = 0,ui cos + vi sin=0 or ui+vi tan =0 for i=1, 2, 3,44,Enforcement of mesh compatib

13、ility,,dx = 0.5(1-) d1 + 0.5(1+) d3,dy = 0.5(1-) d4 + 0.5(1+) d6,Substitute value of at node 3,0.5 d1 - d2 + 0.5 d3 =0,0.5 d4 - d5 + 0.5 d6 =0,Use lower order shape function to interpolate,45,Enforcement of mesh compatibility,Use shape function of longer element to interpolate,dx = -0.5 (1-) d1 + (1

14、+)(1-) d3 + 0.5 (1+) d5,Substituting the values of for the two additional nodes,d2 = 0.251.5 d1 + 1.50.5 d3 - 0.250.5 d5,d4 = -0.250.5 d1 + 0.51.5 d3 + 0.251.5 d5,46,Enforcement of mesh compatibility,In x direction,,0.375 d1 - d2 + 0.75 d3 - 0.125 d5 = 0,-0.125 d1 + 0.75 d3 - d4 + 0.375 d5 = 0,In y

15、direction,,0.375 d6- d7+0.75 d8- 0.125 d10 = 0,-0.125 d6+0.75 d8 - d9 + 0.375 d10 = 0,47,Modelling of constraints by rigid body attachment,,d1 = q1 d2 = q1+q2 l1 d3=q1+q2 l2 d4=q1+q2 l3,(l2 /l1-1) d1 - ( l2 /l1) d2 + d3 = 0 (l3 /l1-1) d1 - ( l3 /l1) d2 + d4 = 0,Eliminate q1 and q2,(DOF in x directio

16、n not considered),48,IMPLEMENTATION OF MPC EQUATIONS,,,(Matrix form of MPC equations),(Global system equation),Constant matrices,,,49,Lagrange multiplier method,,,,,(Lagrange multipliers),Multiplied to MPC equations,Added to functional,The stationary condition requires the derivatives of p with resp

17、ect to the Di and i to vanish.,,Matrix equation is solved,50,Lagrange multiplier method,Constraint equations are satisfied exactly Total number of unknowns is increased Expanded stiffness matrix is non-positive definite due to the presence of zero diagonal terms Efficiency of solving the system equa

18、tions is lower,51,Penalty method,(Constrain equations),,=1 2 ... m is a diagonal matrix of penalty numbers,Stationary condition of the modified functional requires the derivatives of p with respect to the Di to vanish,,Penalty matrix,52,Penalty method,,Zienkiewicz et al., 2000 :, = constant (1/h)p+1

19、,Characteristic size of element,,P is the order of element used,,,max (diagonal elements in the stiffness matrix),,or,Youngs modulus,53,Penalty method,The total number of unknowns is not changed. System equations generally behave well. The constraint equations can only be satisfied approximately. Right choice of may be ambiguous.,

展開閱讀全文
溫馨提示:
1: 本站所有資源如無特殊說明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請下載最新的WinRAR軟件解壓。
2: 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請聯(lián)系上傳者。文件的所有權(quán)益歸上傳用戶所有。
3.本站RAR壓縮包中若帶圖紙,網(wǎng)頁內(nèi)容里面會有圖紙預(yù)覽,若沒有圖紙預(yù)覽就沒有圖紙。
4. 未經(jīng)權(quán)益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
5. 裝配圖網(wǎng)僅提供信息存儲空間,僅對用戶上傳內(nèi)容的表現(xiàn)方式做保護(hù)處理,對用戶上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對任何下載內(nèi)容負(fù)責(zé)。
6. 下載文件中如有侵權(quán)或不適當(dāng)內(nèi)容,請與我們聯(lián)系,我們立即糾正。
7. 本站不保證下載資源的準(zhǔn)確性、安全性和完整性, 同時(shí)也不承擔(dān)用戶因使用這些下載資源對自己和他人造成任何形式的傷害或損失。

最新文檔

相關(guān)資源

更多
正為您匹配相似的精品文檔
關(guān)于我們 - 網(wǎng)站聲明 - 網(wǎng)站地圖 - 資源地圖 - 友情鏈接 - 網(wǎng)站客服 - 聯(lián)系我們

copyright@ 2023-2025  zhuangpeitu.com 裝配圖網(wǎng)版權(quán)所有   聯(lián)系電話:18123376007

備案號:ICP2024067431-1 川公網(wǎng)安備51140202000466號


本站為文檔C2C交易模式,即用戶上傳的文檔直接被用戶下載,本站只是中間服務(wù)平臺,本站所有文檔下載所得的收益歸上傳人(含作者)所有。裝配圖網(wǎng)僅提供信息存儲空間,僅對用戶上傳內(nèi)容的表現(xiàn)方式做保護(hù)處理,對上載內(nèi)容本身不做任何修改或編輯。若文檔所含內(nèi)容侵犯了您的版權(quán)或隱私,請立即通知裝配圖網(wǎng),我們立即給予刪除!

五月丁香婷婷狠狠色,亚洲日韩欧美精品久久久不卡,欧美日韩国产黄片三级,手机在线观看成人国产亚洲