Chapter 15
結構動力分析Structural Dynamic Analysis
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Contents15.1 何謂動力分析?
What Are Dynamic Analyses? 15.2 解題方法
Solution Methods 15.3 質量與阻尼
Mass and Damping 15.4 實例:圓柱形子彈的撞擊模擬
Example: Copper Cylinder Impacting on a Rigid Wall 15.5 動態負載
Dynamic Loads 15.6 初始條件
Initial Conditions 15.7 積分時間間隔
Integration Time Steps 15.8 練習題:火箭的飛行
Exercise: Rocket Flight
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第 15.1 節
何謂動力分析?What Are Dynamic Analyses?
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Dynamic Effects
• Inertia force• Damping force• Elastic Force• External force• Dynamic Effects
FKDDCDM
FKD
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15.1.1 Transient Dynamic Analysis
FKDDCDM
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15.1.2 Modal Analysis (1/3)
0KDDCDM
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15.1.2 Modal Analysis (2/3)
0KDDCDM
0KDDM
21 ud ff
2eR
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15.1.2 Modal Analysis (3/3)
• Avoid resonance
• Exploit resonance
• Assess structural stiffness
• Structural modal degrees of freedom
• Further dynamic analyses
• etc.
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15.1.3 Harmonic Response Analysis
tsinFKDDCDM
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第 15.2 節
解題方法Solution Methods
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Solution Methods
Solution Methods for Equation of Motion
Direct Integration Mode Superposition
Implicit Explicit
ReduceFull Full Reduce
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15.2.1 Direct Integration
• Implicit method (ANSYS)
• Explicit method (LS-DYNA)
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15.2.2 Implicit vs. Explicit Methods
ttttttt DDDfD ,,...,
ttttttt DDDfD ,,..., 2
Implicit method
Explicit method
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15.2.3 Mode Superposition Method
nnCCCC MMMMD ...332211
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15.2.4 Reduced Method
FKD
s
m
s
m
sssm
msmm
F
F
D
D
KK
KK
FDK
m
msmssss DKFKD 1
smssmsmm KKKKK 1
sssmsm FKKFF 1
where
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15.2.5 Methods for Nonlinear Dynamic Analysis
• For nonlinear analysis, the only methods applicable is DIRECT INTEGRATION method.
• Reduced method can not be used for nonlinear analysis.
• Either implicit or explicit methods can be used.
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第 15.3 節
質量與阻尼Mass and Damping
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15.3.1 Consistent vs. Lumped Mass Matrices
x
x
x
x
x
x
xxxx
xxxx
xx
xxxx
xxxx
xx
ROTZ
UY
UX
ROTZ
UY
UX
j
j
j
i
i
i
00000
00000
00000
00000
00000
00000
00
00
0000
00
00
0000
Consistent mass matrix
Lumped mass matrix
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15.3.2 Damping
• Damping effects is the total of all energy dissipation mechanisms– Hysteresis (solid damping)– Viscous damping– Dry-friction (Coulomb damping)
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15.3.3 Idealization of Structural Damping
• Structural dampings are usually small (2%-7%).
• Equivalent viscous damping is assumed in ANSYS, i.e.,
DCF D
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15.3.4 How ANSYS Forms Damping Matrix?
• Alpha damping• Beta damping• Material dependent beta damping• Element damping matrices• Frequency-dependent damping matrix
CCKKMC
em N
kk
N
jjj
mjc
11
2
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第 15.4 節
實例 : 圓柱型子彈的撞擊模擬Copper Cylinder Impacting on a Rigid Wall
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15.4.1 Problem Description
x
y
L D
Initial Velocity Vo
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15.4.2 Modeling Consideration
• Material: bilinear plastic model.
• VISCO106 (2D viscoplastic solid) is used.
• Use axisymmetric model.
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15.4.3 ANSYS Procedure (1/4)01
02
03
04
05
06
07
08
09
10
11
12
13
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15
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18
19
20
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FINISH
/CLEAR
/TITLE, UNITS: SI
/PREP7
ET, 1, VISCO106,,, 1
MP, EX, 1, 117E9
MP, NUXY, 1, 0.35
MP, DENS, 1, 8930
TB, BISO, 1
TBDATA,, 400E6, 100E6
TBPLOT, BISO, 1
RECTNG, 0, 0.0032, 0, 0.0324
LESIZE, 1,,, 4
LESIZE, 2,,, 20
MSHAPE, 0, 2D
MSHKEY, 1
AMESH, ALL
FINISH
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15.4.3 ANSYS Procedure (2/4)23
24
25
26
27
28
29
30
31
32
33
34
35
36
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/SOLU
ANTYPE, TRANS
TRNOPT, FULL
NLGEOM, ON
IC, ALL, UY, 0, -227
NSEL, S, LOC, X, 0
D, ALL, UX, 0
NSEL, S, LOC, Y, 0
D, ALL, UY, 0
NSEL, ALL
/PBC, U,, ON
EPLOT
TIME, 80E-6
DELTIM, 0.4E-6
KBC, 1
OUTRES, ALL, 4
SOLVE
FINISH
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15.4.3 ANSYS Procedure (3/4)
44
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51
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55
56
57
/POST26
TOPNODE = NODE(0,0.0324,0)
NSOL, 2, TOPNODE, U, Y, DISP
DERIV, 3, 2, 1,, VELO
/GRID, 1
/AXLAB, X, TIME s
/AXLAB, Y, DISPLACEMENT m
PLVAR, 2
/AXLAB, Y, VELOCITY m/s
PLVAR, 3
FINISH
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15.4.3 ANSYS Procedure (4/4)59
60
61
62
63
64
65
/POST1
SET, LAST
PLDISP, 2
PLNSOL, EPTO, EQV
ANTIME, 30
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第 15.5 節
動態負載Dynamic Loads
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Dynamic Loads: An Example01
02
03
04
05
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07
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10
11
12
13
14
15
16
17
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/SOLU
...
F, ... ! 22.5 at the nodes
TIME, 0.5 ! Ending time
DELTIM, ... ! Integration step
KBC, 0 ! Ramped loading
AUTOTS, ON ! Option
OUTRES, ... ! Option
SOLVE ! Load step 1
F, ... ! 10 at the nodes
TIME, 1 ! Ending time
SOLVE ! Load step 2
FDELE, ... ! Zero the force
TIME, 1.5 ! Ending time
KBC, 1 ! Stepped loading
SOLVE ! Load step 3
0 0.5 1.0 1.5Time (s)
Force (N)22.5
10
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第 15.6 節
初始條件Initial Conditions
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15.6.1 Example: An Stationary Plate Subjected to an Impulse
Load
• This is the default initial condition. No input is needed.
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15.6.2 Example: Initial Velocity on a Golf Club Head
• This simple initial condition can be specified by using IC command.
NSEL, ALL
IC, ALL, UY, 0, V0
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15.6.3 Example: Plucking a Cantilever Beam
01
02
03
04
05
06
07
08
09
10
11
12
13
14
/SOLU
ANTYPE, TRANS
...
TIMINT, OFF ! Transient effects off
TIME, 0.001 ! Small time interval
D, ... ! Apply displacement at desired nodes
KBC, 1 ! Stepped loads
NSUBST, 2 ! To avoid non-zero velocity
SOLVE
TIMINT, ON ! Transient effects on
TIME, ... ! Actual time at end of load
DDELE, ... ! Delete the applied displacement
SOLVE
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15.6.4 Example: Dropping an Object from Rest
01
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/SOLU
TIMINT, OFF ! Transient effects off
TIME, 0.001 ! Small time interval
NSEL, ... ! Select all nodes on the object
D, ALL, ALL, 0 ! Temporarily fix them
NSEL, ALL
ACEL, ... ! Apply acceleration
KBC, 1 ! Stepped loads
NSUBST, 2 ! To avoid non-zero velocity
SOLVE ! Load step 1
TIMINT, ON ! Transient effects on
TIME, ... ! Actual time at end of load
NSEL, ... ! Select all nodes on the object
DDELE, ALL, ALL ! Release them
NSEL, ALL
SOLVE ! Load step 2
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第 15.7 節
積分時間間隔Integration time Steps
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15.7.1 Response Frequency
Response
Time
Minimumresponse
time
20
pt
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15.7.2 Abrupt Changes in Loading
0 0.5 1.0 1.5Time (s)
Force (N)
22.5
10
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15.7.3 Contact Frequency
30
Tt
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15.7.4 Wave Propagation
c
xt
3
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15.8 Exercise: Rocket Flight
y
140 in.
Thrust
Time
100 lb
1 sec.1
2
3