667 gap stiff 20022 analysis assumptions and modeling

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Unformatted text preview: c1x 2 − c 2 xE W Next, the probability that Y is negative, i.e. P(Y < 0) is evaluated. For this case the probability is: 1–540 ANSYS Verification Manual . ANSYS Release 9.0 . 002114 . © SAS IP, Inc. VM232 P( Y < 0) = ∫∫ fW ( x W )fE ( xE )dx W dxE Y <0 The integration domain Y < 0 can be expressed as: c1x 2 − c 2 xE < 0 W or c 2 xE > c1x 2 W or c xE > 1 x 2 c2 W Therefore, the integration domain of the integral can be written as: P( Y < 0) = ∞∞ c1 2 fW ( x W )fE ( xE )dxEdx W 0 x c2 W ∫∫ Separating the product in the integrator leads to: ∞ P( Y < 0) = fW ( x W ) c1 2 fE ( xE )dxE dx W 0 c xW 2 ∫ ∞ ∫ Using eqs. 2 and 4 leads to: P( Y < 0) = ∞ 2x W exp( − x 2 ) ∫ c1 2 λ exp( −λxE )dxE dx W W x 0 c2 W ∫ ∞ Solving the inner integral is: P( Y < 0) = 2x W exp( − x 2 ) exp( −λxE ) x = c1 x 2 − exp( −λxE ) x =∞ dx W W E E 0 c2 W ∫ ∞ or P( Y < 0) = c 2x W exp( − x 2 )exp −λ 1 x 2 dx W W W 0 c2 ∫ ∞...
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This note was uploaded on 12/09/2010 for the course DEPARTMENT E301 taught by Professor Kulasinghe during the Spring '09 term at University of Peradeniya.

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