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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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36
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
11/31
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
13/31
11.3.1 問題描述
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11.3.2 ANSYS Procedure (1/3)01
02
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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
17/31
第 11.4節
實例 : 升降平台結構分析Example: Structural Analysis of a Lift Platform
18/31
11.4.1 問題描述
72
32
24
30 30
300 lb 400 lb 300 lb
24
30
30
30
6
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11.4.2 ANSYS Procedure (1/4)01
02
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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
22/31
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
23/31
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