第09章 周期对称结构的静力分析.pdf

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第九章 周期对称结构的静力分析 如果结构绕其轴旋转一个角度α ,结构(包括材料常数)与旋转前完全相同,则将这 种结构称为周期对称结构(循环对称结构)。符合这一条件的最小旋转角α 称为旋转周期, 从结构中任意取出夹角为α 的部分都可以称为结构的基本扇区。由基本扇区绕其轴旋转复 N(= α π / 2 N 必为整数)份,则可得到整个完整的结构。 ANSYS 中可以利用结构的周期对称性,在建立模型和求解时,只对一个基本扇区 建模和分析,在后处理中再进行扩展,也可得到整个结构的结果。这样可以降低分析的规 模,节省计算费用。 本章中介绍的实例依然是第八章的轮盘,区别是此处考虑了轮盘上的 6 个均压孔。 91 问题描述 某型压气机盘如图 9.1 所示,其截面图如图 9.2 所示。盘上 6 个均压孔均布。将叶片的 引起的离心效果均匀施加于轮盘的边缘。 9.1 带有均压孔的压气机盘

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  • N /2 N

    ANSYS

    6

    91

    9.1 9.2 6

    9.1

  • 9.2 9.1 9.1

    1 2 3 4 5 6 7 8 X 226 226 157 237.5 229.2 237.5 126 138 Z 208.8 258.7 258.7 220.3 220.3 208.8 276.7 276.7

    9 10 11 12 13 14 15 16 17 X 102.5 102.5 237.5 237.5 135 243.85 243.85 229.2 162.5 Z 263 248.7 273.8 264.1 248.7 273.8 254.8 254.8 264.1

    11373 / TC4 1.1510 MPa

    0.30782 4.4810 /

    5

    9

    74 628232N

    6 10mm 200mm

    92

    MPa N mm

  • 921

    ANSYS6.1

    ANSYS6.1 1 Utility Menu >File >Change Jobname Change Jobname 9.3

    9.3 2 Enter new jobnameCH09

    3 4 Utility Menu >File >Change Title Change Title 9.4

    9.4 5 Enter new titlesstatic analysis of compressor

    structure with hole 6 7 Utility Menu>Plot>Replotstatic analysis of compressor

    structure with hole 8Main Menu >Preference Preference of GUI Filtering Structural

    922

  • 8 SOLID45SOLID45

    1Main Menu >Preprocessor >Element Type >Add/Edit/DeleteElement Types 9.5

    9.7 2 Library of Element Types, 9.6

    9.6 3Solid

    4Brick 8node 45 8 SOLID45

    5 SOLID45

    6

    923

    1 Main Menu>Preprocessor>Material Props>Material Models

    Define Material Model Behavior 9.7

  • 9.7 2 Structural>Linear>Elastic>Isotropic

    1 EX PRXY 9.8

    9.8 3 EX 1.15e5 PRXY 0.30782

    4 1

    5 Structural>Density 9.9

    9.9 6 DENS4.48e-9/ 7

  • 1 8 Define Material Model BehaviorMaterial >Exit

    924

    1 Main Menu>Preprocessor>Modeling>Create>Keypoints>In Active CSCreate Keypoint in Active Coordinate System9.10

    9.10 2 Keypoint number 1

    3 X,Y,Z Location in active CS 1 XZ 226 208.8

    4 1 5 2 4 9.1 17

    6 Utility Menu>PlotCtrls>Numbering Plot Numbering Controls 9.11

  • 9.11 7 Keypoint numbers

    8 Line numbers 9 Numbering shown with Numbers only

    10 11 Utility Menu>PlotCtrls>Pan-Zoom-Rotate Pan-Zoom-Rotate

    12 Pan-Zoom-Rotate 13 Pan-Zoom-Rotate 9.12

    9.12

  • 14Main Menu>Modeling>Create>Lines>Lines>Straight Line

    15 1 21,2 12

    16 231664455161615151414111112121787799101013

    17 18 Utility Menu>Plot>Multi-Plots 9.13

    9.13 19Main Menu>Modeling>Create>Lines>Lines>Tangent to Line

    20 9.13 L11

    21 17

    22 8 Line Tangent to Line 9.14

  • 9.14 23

    24 L2 25 3

    26 13 9.14 27 28 Main Menu>Preprocessor>Modeling>Create>Areas>Arbitrary>By

    Lines 9.15

    9.15 29 Loop

    30ANSYS

    31 32 Utility Menu>PlotCtrls>Numbering Plot Numbering Controls Line numbers Keypoint numbers

    33 Utility Menu>Plot>Areas 9.16

  • 9.16

    925

    60 Z 60

    1 Main Menu>Preprocessor>Modeling>Create>Keypoints>In Active CSCreate Keypoint in Active Coordinate System 9.10

    2 18 19

    X 0 0 Z 0 300 3Main Menu>Preprocessor>Modeling>Operate>Extrude>Areas>About Axis

    4 9.2.4

    5 181918,19 Sweep Area about Axis 9.17

  • 9.17 6 Arc length in degrees60 7 ANSYS 60

    8 Utility Menu>Plot>Volumes 9 Utility Menu>PlotCtrls>Pan-Zoom-Rotate Pan-Zoom-Rotate

    10 Pan-Zoom-Rotate 11 Pan-Zoom-Rotate 9.18

    9.18 15

    926

    ANSYS 6030

    1 Utility Menu>WorkPlane>Offset WP by Increments Offset WP

  • 9.19

    9.19 2 XY,YZ,ZX Angles30 XY Z 30 30

    3

    4 Main Menu>Preprocessor>Modeling>Create>Cylinder>Solid CylinderSolid Cylinder 9.20

  • 9.20 5WP X X200

    6WP Y 0 7 Radius10 8 Depth300

    9 ANSYS 9.21

    9.21 10Main Menu>Preprocessor>Modeling>Operate>Subtract>Volumes

    11

    12 ANSYS 9.22

  • 9.22 13

    927

    9271 1 Utility Menu>PlotCtrls>Pan-Zoom-Rotate Pan-Zoom-Rotate

    2 Pan-Zoom-Rotate 3 Pan-Zoom-Rotate

    4 Utility Menu>WorkPlane>Align WP with>Global Cartesian

    5Main Menu>Modeling>Create>Lines>Lines>Straight Line

    618,19 7 8Main Menu>Preprocessor>Modeling>Create>Arcs>By Cent & Radius

    90,0 10220

  • 220mm Arc by Center & Radius 9.23

    9.23 11 Arc length in degrees60 12 ANSYS 60

    130,0 14180

    180mm Arc by Center & Radius 9.23 15 Arc length in degrees60 16 17 Utility Menu>Select>Entities Select Entities 9.24

    18 Lines 19 Attached to

    9.24 20 Areas 21 Unselect

    22 5 11

  • 23 Menu>PlotCtrls>NumberingUtility 24 25 Utility Menu>Plot>Lines 9.25

    9.25 26Main Menu>Preprocessor>Modeling>Operate>Extrude>Along Lines

    27 53

    9.25 L53

    28 L52 ANSYS

    29 54

    9.25 L54

    28 L52 ANSYS

    ering Controls

    ct Entities

    Unsele

    29 Utility Menu>PlotCtrls>Numbering Plot NumbLine numbers 30 Utility Menu>Select>Everything

    31 Utility Menu>Select>Entities Sele32 Areas

    33 Attached to 34 Volumes 35 ct

    36

  • 37Main Menu>Preprocessor>Modeling>Operate>Divide>Volume by Area

    38 39 ,ANSYS

    41 Utility Menu>Plot>Volumes 9.26

    40 Utility Menu>Select>Everything

    9.26

    9

    ne>Offset WP by Increments Offset WP 9.27

    271 1 Utility Menu>WorkPla

  • 9.27 2 Degrees 90 9.27 3 X 90

    4 XY,YZ,ZX Angles,,21 Y Y Y Z 21

    5Main Menu>Preprocessor>Modeling>Operate>Divide>Volu by WrkPlane

    6 7 XY,YZ,ZX Angles,,9 Y 9

    8Main Menu>Preprocessor>Modeling>Operate>Divide>Volu by WrkPlane

    9 10 XY,YZ,ZX Angles,,9 Y 9

    11Main Menu>Preprocessor>Modeling>Operate>Divide>Volu by WrkPlane

    12 13Main Menu>Preprocessor>Modeling>Delete>Line and below

    14

  • 15 Utility Menu>WorkPlane>Change Active CS to>Global cylindrical

    16 Utility Menu>Select>Entities Select Entities 17 Volumes

    18 By Location 19 X coordinateX

    20180,220 180 220 21 From Full

    22 23 Utility Menu>Select>Comp/Assembly>Create Component Create

    Component 9.28

    9.28 24 Component nameHOLEVol

    25 Component is made of Volumes 26 27 Utility Menu>Select>Everything

    28 Utility Menu>Plot>Volumes 9.29

  • 9.29 29

    928

    ANSYS CYCLIC ANSYS

    ANSYS CYCLIC ANSYS ANSYS CYCLIC

    1 Utility Menu>Select>Entities Select Entities

    2 Areas 3 By Location

    4 Y coordinateY

    50 6 From Full

    7

  • 8 Utility Menu>Select>Comp/Assembly>Create Component Create Component 9.28

    9 Component nameCYCLIC_M01L CYCLIC M01L M Match01

    L 10 Component is made of Areas 11

    12 Utility Menu>Select>Entities Select Entities 1360

    14 15 Utility Menu>Select>Comp/Assembly>Create Component Create

    Component 16 Component nameCYCLIC_M01H H

    17 Component is made of Areas 18 19 Utility Menu>Select>Everything

    20 Main Menu>Preprocessor>Modeling>Cyclic Sector>User DefinedUser-specified Cyclic Section Definition 9.30

    9.30 21 Root name of components 16CYCLIC

    22 NO. of sectors6 23 Sector Angle60 24 Cyclic Coordinate System1

    25

    929

  • ANSYS6.1

    9291 1 Main Menu>Preprocessor>Meshing>Size Cntrls>Global>Size Global

    Element Sizes 9.31

    9.31 2 Element edge length 3

    3 4 Utility Menu>Select>Comp/Assembly>Select Comp/Assembly Select

    Component or Assembly 9.32

    9.32 5 Comp/Assemb to be selected HOLEVOL

    6

  • 7 Utility Menu>Select>Entities Select Entities 8 Volumes 9 By Location 10 Y coordinateY

    1121,30 12 Reselct

    13

    14 Areas 15 Attached to

    16 Volumes 17 From Full

    18

    19 Utility Menu>WorkPlane>align WP with>Global Cartesian

    20 Utility Menu>WorkPlane>Offset WP by Increments Offset WP

    21 XY,YZ,ZX Angles30 XY Z 30 30

    22 X.Y.Z Offsets200 X 200

    23 Offset WP 24 Utility Menu>WorkPlane>Local Coordinate Systems>Create Local CS>At WP

    Origin Create Local CS at WP Origin 9.33

    9.33 25 Ref number of new coord sys11

  • 26 Type of coordinate system Cylindrical 1

    27

    28 Utility Menu>Select>Entities Select Entities 29 Areas

    30 By Location 31 Z coordinateZ 32264.1

    33 Unselect 34 35258.7

    36 37 X coordinateX

    3810 39 40 Utility Menu>WorkPlane>Change Active CS to>Global Cylindrical

    41 Utility Menu>Select>Entities Select Entities 42 Areas

    43 By Location 44 Y coordinateY

    4530 46 Unselect

    47 48Main Menu>Preprocessor>Meshing>Concatenate>Areas

    49

    9292

    1 Utility Menu>Select>Entities Select Entities 2 Lines

    3 Attached to 4 Areas 5 From Full

    6 7 By Location

  • 8 Z coordinateZ 9264.1 10 Reselect

    11

    12Main Menu>Preprocessor>Meshing>Concatenate>Lines

    13 14 Attached to

    15 Areas 16 From Full

    17 18 By Location

    19 Z coordinateZ 20258.7

    21 Reselect 22

    23Main Menu>Preprocessor>Meshing>Concatenate>Lines

    24

    9293

    1 Utility Menu>Select>Entities Select Entities 2 Volumes 3 By Location 4 Y coordinateY

    50,21 6 From Full

    7 8Main Menu>Preprocessor>Meshing>Mesh>Volume Sweep>Sweep

    9 10 Utility Menu>Select>Entities

    11 Volumes 12 By Location

  • 13 Y coordinateY

    1421,30 15 From Full

    16 17 X coordinateX

    18180,220 19 Ueselect

    20 21Main Menu>Preprocessor>Meshing>Mesh>Volume Sweep>Sweep

    22 23 Utility Menu>Select>Comp/Assembly>Select Comp/Assembly Select

    Component or Assembly 9.32 24 Comp/Assemb to be selected HOLEVOL

    25 26 Utility Menu>Select>Entities Select Entities

    27 Y coordinateY

    2821,30 29 Reselect

    30 31Main Menu>Preprocessor>Meshing>Mesh>Volume Sweep>Sweep

    32

    9294 ANSYS

    1 Utility Menu>Select>Entities Select Entities 2 Y coordinateY

    30,30 4 From Full

    5 6Main Menu>Preprocessor>Meshing>Concatenate>Del Contas>Lines

    7Main Menu>Preprocessor>Meshing>Concatenate>Del Contas>Areas

  • 8 Utility Menu>WorkPlane>Change Active CS to>Working Planing

    9Main Menu>Preprocessor>Modeling>Reflect>Volumes

    10 Reflect Volumes 9.34

    9.34 11 Plane of symmetry X-Z plane Y XZ

    12 Items to be reflected Volumes and mesh

    13 Existing volumes will be Copied 14 ANSYS XZ

    15 Utility Menu>Select>Everything 16 Main Menu>Preprocessor>Numbering Ctrls>Merge Items Merge

    Coincident or Equivalently Defined Items 9.35

    9.35 17 Type of item to be merge All

  • 18 ANSYS

    19 Main Menu>Preprocessor>Numbering Ctrls>Compress NumbersCompress Numbers 9.36

    9.36 20 Item to be compressed ALL 21 ANSYS

    22 Utility Menu>Plot>Elements 9.37

    9.37 23

    93

    ANSYSANSYS

  • ANSYS

    931

    1 Utility Menu>WorkPlane>Change Active CS to>Global cylindrical

    2Main Menu>Preprocessor>Modeling>Move / Modify>To Active CS

    3 4 Utility Menu>Select>Entities Select Entities

    5 Nodes 6 By Location

    7 X coordinatesX

    8237.5

    9 From Full 10 11 Z coordinates

    12220.3,208.8

    13 Reselect 14 15Main Menu> Solution> Define Loads> Apply> Structural> Displacement> On

    Nodes 16 Apply UROT on Nodes 9.38

  • 9.38 17 UX UY X Y

    18 ANSYS 19 Utility Menu>Select>Everything

    20 Utility Menu>Select>Entities Select Entities 21 Nodes

    22 By Location 23 Z coordinates Z

    24208.8

    25 From Full 26 27Main Menu> Solution> Define Loads> Apply> Structural> Displacement> On

    Nodes 28 9.38 Apply U

    ROT on Nodes 29 UZZ UYY

    30 ANSYS 31 Utility Menu>Select>Everything

    32 Utility Menu>Plot>Elements 9.39

  • 9.39 33

    932

    1 Main Menu>Solution>Define Loads>Apply>Other>Angular VelocityApply Angular velocity 9.40

    9.40 2 Global Cartesian Z-compZ1191.11/

    3

  • 4 Utility Menu>Select>Entities Select Entities 5 Nodes

    6 By Location 7 X coordinates X

    8243.5

    9 From Full 10 11 Utility Menu>Parameters>Get Scalar Data Get Scalar Data 9.41

    9.41 12Model data 9.41

    13 For selected set 9.41 14 Get Data for Selected Set 9.42

    9.42 15 Name of parameter to be definedNo_Nodes

    16 Data to be retrieved Current node set

    17 No. of nodes

  • 18 ANSYS

    19 Main Menu>Solution>Define Loads>Apply>Structural>Force/Moment>On Nodes

    20 Apply F/M on Nodes 9.43

    9.43 21 Direction of force/mom FXX

    22 Force/moment value628232/NO_Nodes/6

    23 ANSYS 24 Utility Menu>Select>Everything

    25 Utility Menu>Plot>Elements 9.44

    9.44 26

    27Main Menu> Solution> Solve> Current LS 9.45

  • 9.45 28 9.46

    9.46 ANSYS 29 ANSYS

    29 9.47

    9.47 30

    94

    ANSYS Jobname.RST POST1

  • 941

    1Main Menu>General Postproc>Options for Outp Options for Output 9.48

    9.48 2 Results coord system Global cylindrical

    3

    942

    1Main Menu>General Postproc>Plot Results>Contour Plot>Nodal Solu Contour Nodal Solution Data 9.49

  • 9.49 2 Item to be contouredDOF solution

    3 Translation UXXX

    4 Def + undef edge 5 9.50

  • 9.50 6Main Menu>General Postproc>Plot Results>Contour Plot>Nodal Solu Contour Nodal Solution Data 9.49

    7 UYY 8 9.51

    9.51 9Main Menu>General Postproc>Plot Results>Contour Plot>Nodal Solu Contour Nodal Solution Data 9.49

    10 UZZ

  • 11 9.52

    9.52 12Main Menu>General Postproc>Plot Results>Contour Plot>Nodal Solu Contour Nodal Solution Data 9.49

    13 USUM 14 9.53

    9.53

  • 943

    1Main Menu> General Postproc> Plot Results> Contour Plot> Nodal SoluContour Nodal Solution Data 9.54

    9.54 2 Item to be contoured Stress

    3 X-direction SXX 4 Def shape only

    5 X 9.55

  • 9.55 6Main Menu> General Postproc> Plot Results> Contour Plot> Nodal Solu

    Contour Nodal Solution Data 9.54 7 Item to be contoured Stress

    8 Y-direction SYY 9 9.56

    9.56 10Main Menu> General Postproc> Plot Results> Contour Plot> Nodal Solu

  • Contour Nodal Solution Data 9.54 11 Item to be contoured Stress

    12 Z-direction SZZ 13 9.57

    9.57 14Main Menu> General Postproc> Plot Results> Contour Plot> Nodal Solu

    Contour Nodal Solution Data 9.54 15 Item to be contoured Stress

    16 von Mises SEQVvon Mises 17 Def shape only

    10 von Mises 9.58

  • 9.58 von Mises

    95

    GUI

    ! /FILNAME,CH09 /TITLE,static analysis of compressor structure with hole ! /PREP7 ET,1,SOLID45 ! 8 SOLID45 MP,EX,1, 1.15e5 ! 1.15e5MPa MP,PRXY,1,0.30782 ! 0.30782 MP,DENS,1,4.48e-9 ! 4.48e-9/ ! K,1,226,,208.8 K,2,226,,258.7 K,3,157,,258.7

  • K,4,237.5,,220.3 K,5,229.2,,220.3 K,6,237.5,,208.8 K,7,126,,276.7 K,8,138,,276.7 K,9,102.5,,263 K,10,102.5,,248.7 K,11,237.5,,273.8 K,12,237.5,,264.1 K,13,135,,248.7 K,14,243.85,,273.8 K,15,243.85,,254.8 K,16,229.2,,254.8 K,17,162.5,,264.1 /PNUM,KP,1 ! /PNUM,LINE,1 ! /NUMBER,2 ! /VIEW, 1 ,,-1 /AUTO, 1 ! Bottom ! LSTR,1,2 LSTR,2,3 LSTR,1,6 LSTR,6,4 LSTR,4,5 LSTR,5,16 LSTR,16,15 LSTR,15,14 LSTR,14,11 LSTR,11,12 LSTR,12,17 LSTR,8,7 LSTR,7,9 LSTR,9,10 LSTR,10,13 LPLOT !

  • LTAN,11,8 ! LTAN,2,13 AL,ALL ! /PNUM,LINE,0 ! /PNUM,KP,0 ! ! K,18,,,, K,19,,,300 ! VROTAT,ALL,,,,,,18,19,60 ! 1819 60 /VIEW, 1 ,1,1,1 /AUTO, 1 ! iso SAVE ! wprot,30 ! Z 30 CYL4,200,0,10,,,,300 !200,0 10 300

    VSBV,1,2 ! SAVE ! /VIEW, 1 ,,,-1 /AUTO, 1 ! BACK WPCSYS,-1,0 ! LSTR,18,19 ! FLST,2,2,8 FITEM,2,0,0,0 FITEM,2,220,0,0 CIRCLE,P51X,,,,60 ! 220 FLST,2,2,8 FITEM,2,0,0,0 FITEM,2,180,0,0 CIRCLE,P51X,,,,60 ! 180 LSLA,U ! /PNUM,LINE,1 ! ADRAG,53,,,,,,52 ! 220 ADRAG,54,,,,,,52 ! 180 /PNUM,LINE,0

  • ALLSEL ! ASLV,U ! VSBA,ALL,ALL ! ALLSEL wprot,,90 ! X 90 wprot,,,21 ! Y 21 VSBW,ALL ! wprot,,,9 ! Y 9 VSBW,ALL ! wprot,,,9 ! Y 9 VSBW,ALL ! LDELE,52,,,1 ! CSYS,1 ! VSEL,S,LOC,X,180,220 ! CM,HOLEVOL,VOLU ! HOLEVOL ALLSEL VPLOT ! SAVE ! ASEL,S,LOC,Y,0 ! CM,CYCLIC_M01L,AREA ! ASEL,S,LOC,Y,60 ! CM,CYCLIC_M01h,AREA ! ALLSEL CYCLIC,6,60,1,'CYCLIC' ! ESIZE,3 ! CMSEL,S,HOLEVOL HOLEVOL VSEL,R,LOC,Y,21,30 ! ASLV,S WPCSYS,-1,0 wprot,30 wpoff,200 CSWPLA,11,1 !

  • ASEL,U,LOC,Z,264.1 ! ASEL,U,LOC,Z,258.7 ! ASEL,U,LOC,X,10 ! CSYS,1 ASEL,U,LOC,Y,30 ! ACCAT,ALL LSLA,S LSEL,R,LOC,Z,264.1 ! LCCAT,ALL ! LSLA,S LSEL,R,LOC,Z,258.7 ! LCCAT,ALL ! ! TYPE,1 MSHAPE,0,3D ! VSEL,S,LOC,Y,0,21 ! VSWEEP,ALL ! VSEL,S,LOC,Y,21,30 ! VSEL,U,LOC,X,180,220 ! VSWEEP,ALL ! CMSEL,S,HOLEVOL VSEL,R,LOC,Y,21,30 ! VSWEEP,ALL ! VSEL,S,LOC,Y,0,30 ! ASEL,S,ACCA ! ADELE,ALL ! LSEL,S,LCCA ! LDELE,ALL ! CSYS,4 ! VSYMM,Y,ALL,,,,0,0 ! XZ ALLSEL ! NUMMRG,ALL ! NUMCMP,ALL ! CSYS,1 NROTAT,ALL SAVE

  • ! /SOLU ANTYPE,STATIC !ANSYS ! NSEL,S,LOC,X,237.5 NSEL,R,LOC,Z,220.3,208.8 D,ALL,,,,,,UX,UY ALLSEL ! NSEL,S,LOC,Z,208.8 D,ALL,,,,,,UY,UZ ALLSEL EPLOT SAVE OMEGA,,,1191.11 ! ! NSEL,S,LOC,X,243.5 ! *GET,NO_Nodes,NODE,,COUNT ! F,ALL,FX,628232/NO_Nodes/6 ! ALLSEL SAVE ! SOLVE ! FINISH ! /POST1 PLNSOL,U,X,2,1 ! PLNSOL,U,Y,2,1 ! PLNSOL,U,Z,2,1 !

  • PLNSOL,U,SUM,2,1 ! PLNSOL,S,X,0,1 ! PLNSOL,S,Y,0,1 ! PLNSOL,S,Z,0,1 ! PLNSOL,S,EQV,0,1 ! FINISH