Imperfection sensitivity of Frame buckling loads

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Imperfection sensitivity of Frame buckling loads

• Random Fields Project
• Badri Hiriyur

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Frame Structure Random Variable 1. Nodal
Imperfection 2. Youngs Modulus of
Elasticity Response Study of First eigenvalue
(Critical Load) By Monte Carlo
simulation KeµKgUF Ke has random component
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Random Variable E E0Ek E0 is mean value of E
(deterministic) Ek is the random component of
E Modeled as a Zero-mean RV with various standard
deviations Varying spatially as well as across
realizations
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Ek generated using normrnd function in MATLAB Pcr
calculated for each realization The output Pcr
histogram shows that the output is also
Gaussian. Hypothesis testing was done to check
Gaussian using jbtest. Signficance level of 5
and got affirmative result. Also Normplot shows
gaussian output
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Problem on hand - Pcr should be greater that a
particular limit. So treated as a Level crossing
problem for 1/Pcr. To limit dE so that
Prob1/Pcrgt Limit is acceptable. Imperfection
sensitivity is related to the number of times
1/Pcr crosses a set limit in a given number of
realizations.
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Sample 1/Pcr-Signal 1/Pcr variation with
Standard deviation of 10
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Pcr signal is generated for various values of
standard deviation in Ek (Uniformly distibuted in
(0,0.1) The Pdf of peaks crossing level is
generated for each standard deviation This would
help in correlating Pcr sensitivity to
imperfection in material properties
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Sample histogram of Expectation of Peaks
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• Yet to get-
• The variation of Peaks-pdf with std deviation in
  Random input parameter EK
• Generating an imperfection sensitivity index-one
  number that quantifies the dependency of Critical
  load on randomness of Input.

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Any Questions?