Lin Chen Tom Nierodzinski Yan Di Lv Zhongyuan Optimum Sensitivity Analysis MAE 550 12/10/07.
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Transcript of Lin Chen Tom Nierodzinski Yan Di Lv Zhongyuan Optimum Sensitivity Analysis MAE 550 12/10/07.
Lin Chen Tom Nierodzinski
Yan Di Lv Zhongyuan
Optimum Sensitivity AnalysisMAE 55012/10/07
OutlineObjectiveProblem FormulationResults AnalysisConclusion
Objective
Better understand OSA by comparing different parameters for the same design problem
Problem FormulationParameters Chosen:
P = StressE = Young’s Modulusσ = allowable stressy = deflection
Design Variables:bi and hi i = 1,5
(Total of 10 design variables)
(Total of 21 constraints)
D.V's Value (cm)
b1 3.13118
b2 2.88012
b3 2.57744
b4 2.20456
b5 1.74969
h1 62.6236
h2 57.6024
h3 51.5488
h4 44.0911
h5 34.9915
Problem Formulation cont.DOT results of optimum
point
Active constraintsg4
g5
g6
g7
g8
g9
g10
g21
Inactive constraints Valuesg1 -0.1275g2 -0.1031g3 -0.6138g11 -2.1311g12 -1.8801g13 -1.5774g14 -1.2046g15 -0.7497g16 -57.624g17 -52.602g18 -46.549g19 -39.091g20 -29.992
OSA AnalysisLambda values
i Value
4 2855 14136 2097 1928 1729 145
10 10321 20582
* BTB 1BTF(X *)
OSA AnalysisMatrix dimensions for OSA
A1010 B108
BT 810 088
X101
81
c101
d81
0
)()(22
XgXX
XFXX
A jkiJj
jki
ik
)(XgX
B ji
ij
Jj
)()(22
XgpX
XFpX
c jiJj
ji
i
)(Xgp
d jj
Jj
Stress(P) = 50,000 N
Stress(P) = 50,000 NActive to inactive
∆p = 5.6*10^3
Inactive to Active∆p = 3.52*10^3
Minimum %7%
Young’s Modulus = 2x107 Pa
Young’s Modulus = 2x107 PaActive to inactive
∆p = 1.56*10^6
Inactive to Active∆p = 7.47*10^5
Minimum %3.7%
Sigma = 14,000 N/cm2
σ = 14,000 N/cm2
Active to inactive∆p = 3.64*10^3
Inactive to Active∆p = 345
Minimum %2.5%
Y(deflection) = 2.5 cm
Y(deflection) = 2.5 cmActive to inactive
∆p = 0.19
Inactive to Active∆p = 0.0924
Minimum %3.69%
ConclusionOSA is limited in minimum delta pIn this case inactive constraints are more
sensitive
Questions?