chapter 11 樑與鋼架結構分析 analysis of beams and frames

Chapter 11

樑與鋼架結構分析Analysis of Beams and Frames

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Contents

11.1 BEAM3: 2D樑元素BEAM3: 2D Elastic Beam Element

11.2 實例 : 腳踏車架設計Example: Design of a Bicycle Frame

11.3 實例 : 鋼弦的震動分析Example: Vibration of a String Under Tension

11.4 實例 : 升降平台結構分析Example: Structural Analysis of a Lift Platfor

m

11.5 樑元素瀏覽Overview of Beam Elements

11.6 練習題Exercises

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第 11.1節

BEAM3: 2D樑元素BEAM3: 2D Elastic Beam Element

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11.1.1 BEAM3元素描述

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11.1.2 BEAM3輸入資料Element Name BEAM3

Nodes I, J

Degrees of Freedom

UX, UY, ROTZ

Real Constants AREA, IZZ, HEIGHT, SHEARZ, ISTRN, ADDMAS

Material Properties EX, NUXY, GXY, ALPX, DENS, DAMP

Surface Loads Pressureface 1, face 2, face 3, face 4

Body Loads Temperature -- T1, T2, T3, T4

Special Features Stress stiffening, Large deflection, etc.

etc.

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11.1.3 BEAM3輸出資料

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第 11.2節

實例 : 腳踏車架設計Example: Design of a Bicycle Frame

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11.2.1 問題描述31

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1215

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11.2.2 ANSYS Procedure (1/3)01

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FINISH

/CLEAR

/UNITS, BIN

  D       = 1 ! Outer Diameter

  T       = 1/16 ! Thickness

  PI      = 4*ATAN(1)

  PSEAT   = 150*2.5 ! Load on seat

  PHANDLE = 25*2.5 ! Load on handle

/PREP7

  ET, 1, BEAM3

  MP, EX, 1, 30E6

  MP, NUXY, 1, 0.3

  AREA = PI*(D**2-(D-T)**2)/4

  IZZ  = PI*(D**4-(D-T)**4)/64

  R, 1, AREA, IZZ, D

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11.2.2 ANSYS Procedure (2/3)20

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  K, 1,  0,  0

  K, 2, 18,  0

  K, 3, 36,  0

  K, 4, 10, 15

  K, 5, 31, 15

  K, 6, 32, 12

  L, 1, 2

  L, 4, 5

  L, 1, 4

  L, 2, 4

  L, 2, 6

  L, 5, 6

  L, 6, 3

  ESIZE, 2

  LMESH, ALL

  FINISH

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/SOLU

  NLEFT   = NODE(0,0,0) ! Left support

  NRIGHT  = NODE(36,0,0) ! Right support

  NSEAT   = NODE(10,15,0) ! Seat

  NHANDLE = NODE(31,15,0) ! Handle

  D, NLEFT,  UX, 0

  D, NLEFT,  UY, 0

  D, NRIGHT, UY, 0

  F, NSEAT,   FY, -PSEAT

  F, NHANDLE, FY, -PHANDLE

  /PBC, ALL,, ON

  EPLOT

  SOLVE

  FINISH

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11.2.2 ANSYS Procedure (3/3)53

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/POST1

  PLDISP, 2

  ETABLE, MFORX, SMISC, 1

  ETABLE, MFORY, SMISC, 2

  ETABLE, MMOMZ, SMISC, 6

  ETABLE, SDIR,  LS,    1

  ETABLE, SBYT,  LS,    2

  ETABLE, SBYB,  LS,    3

  ETABLE, SMAX,  NMISC, 1

  ETABLE, SMIN,  NMISC, 2

  PRETAB, MFORX, MFORY, MMOMZ

  PRETAB, SDIR, SBYT, SBYB, SMAX, SMIN

  PLETAB, SDIR

  PLETAB, SBYT

  PLETAB, SMAX

  PLETAB, SMIN

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第 11.3節

實例 : 鋼弦的震動分析Example: Vibration of a String Under Tension

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11.3.1 問題描述

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11.3.2 ANSYS Procedure (1/3)01

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FINISH

/CLEAR

/TITLE, VM53 (lb-in-s)

  D     = 1/16 ! Diameter

  PI    = 4*ATAN(1) ! Constant

  AREA  = PI*D**2/4 ! Cross section

  IZZ   = PI*D**4/64 ! Moment of inertia

  ISTRN = 0.00543228 ! Initial strain

  E     = 30E6 ! Steel

  NU    = 0.3 ! Steel

  RO    = 0.00073 ! Steel

  L     = 100 ! Length of string

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11.3.2 ANSYS Procedure (2/3)15

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/PREP7

  ET, 1, BEAM3

  R, 1, AREA, IZZ, D,, ISTRN

  MP, EX, 1, E

  MP, NUXY, 1, NU

  MP, DENS, 1, RO

  N,  1, 0, 0

  N, 14, L, 0

  FILL

  E, 1, 2

  EGEN, 13, 1, -1

  FINISH

/SOLU

  D,   1, ALL, 0

  D,  14, ALL, 0

  PSTRES,ON 

  SOLVE

  FINISH

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/POST1

  ETABLE, STRESS, LS, 1

  PRETAB, STRESS

  FINISH

/SOLU

  ANTYPE, MODAL

  MODOPT, SUBSP, 3

  PSTRES, ON

  SOLVE

  FINISH

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11.3.2 ANSYS Procedure (3/3)51

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/POST1

  SET, LIST

  /TRIAD, OFF

  /COLOR, PBAK, OFF

  SET, 1, 1

  /WINDOW, 1, -1, 1.67, 0.4, 1.0

  PLDISP, 2

  /NOERASE

  /WINDOW, 1, OFF

  SET, 1, 2

  /WINDOW, 2, -1, 1.67, -0.3, 0.3

  PLDISP, 2

  /WINDOW, 2, OFF

  SET, 1, 3

  /WINDOW, 3, -1, 1.67, -1.0, -0.4

  PLDISP, 2

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第 11.4節

實例 : 升降平台結構分析Example: Structural Analysis of a Lift Platform

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11.4.1 問題描述

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11.4.2 ANSYS Procedure (1/4)01

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FINISH

/CLEAR

/TITLE, Lift Platform (lb-in-s)

  B     = 1 ! Width for all members

  E     = 30E6 ! Steel

  NU    = 0.3 ! Steel

/PREP7

  ET, 1, BEAM3

  MP, EX, 1, E

  MP, NUXY, 1, NU

  R, 1, B*8, B*8**3/12, 8 ! Arms

  R, 2, B*4, B*4**3/12, 4 ! Platform

  R, 3, B*2, B*2**3/12, 2 ! Connector

  R, 4, B*2, B*2**3/12, 2 ! Actuator

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11.4.2 ANSYS Procedure (2/4)19

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  N, 101,   0,  0

  N, 102,   0, 24

  N, 103,  32, 24

  N, 104,  32, 48

  N, 105,  72, 54

  N, 106,  72, 78

  N, 201,  72, 54

  N, 202,  72, 78

  N, 203, 102, 54

  N, 204, 102, 78

  N, 205, 132, 54

  N, 206, 132, 78

  N, 301,  32, 24

  N, 302,  32, 48

  N, 401,  32, 24

  N, 402,  62, -6

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  REAL, 1

  E, 101, 103

  E, 103, 105

  E, 102, 104

  E, 104, 106

  REAL, 2

  E, 201, 203

  E, 203, 205

  E, 202, 204

  E, 204, 206

  E, 201, 202

  E, 203, 204

  E, 205, 206

  REAL, 3

  E, 301, 302

  REAL, 4

  E, 401, 402

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11.4.2 ANSYS Procedure (3/4)54

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  CP, 1, UX, 105, 201

  CP, 2, UY, 105, 201

  CP, 3, UX, 106, 202

  CP, 4, UY, 106, 202

  CP, 5, UX, 103, 301, 401

  CP, 6, UY, 103, 301, 401

  CP, 7, UX, 104, 302

  CP, 8, UY, 104, 302

  D, 101, UX, 0

  D, 101, UY, 0

  D, 102, UX, 0

  D, 102, UY, 0

  D, 402, UX, 0

  D, 402, UY, 0

  F, 202, FY, -300

  F, 204, FY, -400

  F, 206, FY, -300

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  /PNUM, NODE, ON

  EPLOT

  /PNUM, DEFAULT

  FINISH

/SOLU

  SOLVE

  FINISH

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11.4.2 ANSYS Procedure (4/4)84

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/POST1

  PLDISP, 2

  ETABLE, MFORX, SMISC, 1

  ETABLE, MFORY, SMISC, 2

  ETABLE, MMOMZ, SMISC, 6

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第 11.5節

樑元素瀏覽Overview of Beam Elements

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11.5.1 Elastic Beams

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11.5.2 Plastic Beams

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11.5.3 Finite Strain Beams

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11.5.4 Unsymmetric Beams

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11.5.5 Elastic Pipes

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11.5.6 Plastic Pipes

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11.5.7 Explicit Dynamics

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第 11.6節

練習題Exercises