Ansys release 90 002114 sas ip inc vm236 hysteresis

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Unformatted text preview: or P( Y < 0) = ∞ c2 1 ∫0 2x W exp − 1 + λ c2 x W dx W The solution of this integral is: ANSYS Verification Manual . ANSYS Release 9.0 . 002114 . © SAS IP, Inc. 1–541 VM232 c1 2 exp − 1 + λ c1 x 2 P( Y < 0) = − exp − 1 + λ x W W c1 c2 c2 x W =0 x W =∞ 1+ λ c2 1 or P( Y < 0) = 1 c 1+ λ 1 c2 For λ = 0.5, c1 = 1.0 and c2 = 0.1 the probability P(Y < 0) becomes: P( Y < 0) = 1 ≅ 0.1666667 6 In this test case, numerical results are first obtained from a Monte Carlo Simulation method using Latin Hypercube Sampling. P(Y < 0) = 0.165096 A response surface method using a central composite design is evaluated to show that it delivers an acceptable analysis. P(Y < 0) = 0.166829 Figure 232.3 Response Surface plot 1–542 ANSYS Verification Manual . ANSYS Release 9.0 . 002114 . © SAS IP, Inc. VM232 Results Comparison Target ANSYS Ratio P (Y < 0) from Monte Carlo 0.16666667 0.165096 0.9906 P (Y < 0) from Response Surface 0.16666667 0.166829 1.001 ANSYS Verification Manual . ANSYS Release 9.0 . 002114 . © SAS IP, Inc. 1–543 V...
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