Essentials of Materials Science and Engineering, SI Edition
4th Edition
ISBN: 9781337672078
Author: ASKELAND, Donald R., WRIGHT, Wendelin J.
Publisher: Cengage Learning
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Question
Chapter 16, Problem 16.36P
Interpretation Introduction
Interpretation:
The term thermosetting polymer needs to be explained. Also, it is to be explained why this polymer cannot be produced using only ethylene glycol and adipic acid.
Concept Introduction:
Polymers are the large molecules which are made up of many small repeating units bonded together in linear, branched or cross-linked manner.
They are of two types: natural and synthetic. Natural polymers are those which occur naturally, and synthetic polymers are those which are synthesized or man-made.
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Please find Vo using Mesh analysis
(a) Determine the Nataf model for the joint PDF fxx, (xx) of the basic (physical) random variables X₁
and X, with marginal PDF's
fx(x)=e, 0≤x
(Exponential distribution)
fx₁ (x2)=x2e-0.5x, 0≤x (Rayleigh distribution)
and correlation coefficient
Pxx=0.50
Note: Use Table 6 of paper by Liu and Der Kiureghian, 1986.
(b) Generate a 3D surface plot and contour plot of the joint PDF fxx, (x,x) using Matlab or any other
software of your choice.
(c) What is the standard deviation of X2?
(d) Construct a transformation from the physical X space (defined by random variables X, and X,) to the
standard normal U space (defined by the statistically independent standard normal random variables
(U, and U₂), i.e., U=T(X). Also describe the inverse transform X=T(U) and the Jacobian
matrices J
=
ди
θα
and Ju
Ox
ди
(e) According to the inverse transformation X = T¹ (U) and using Matlab, generate 1,000 samples from
the Nataf joint PDF fxx, (x1,x2) derived in part (a). Start by generating samples of U using a…
Based on the results obtained, comment on the relative importance of the body and the tails of thedistributions of R and S on the probability of failure with increasing central safety factor CSF .
Chapter 16 Solutions
Essentials of Materials Science and Engineering, SI Edition
Ch. 16 - Prob. 16.1PCh. 16 - Prob. 16.2PCh. 16 - Prob. 16.3PCh. 16 - Prob. 16.4PCh. 16 - Prob. 16.5PCh. 16 - Prob. 16.6PCh. 16 - Prob. 16.7PCh. 16 - Prob. 16.8PCh. 16 - Prob. 16.9PCh. 16 - Prob. 16.10P
Ch. 16 - Prob. 16.11PCh. 16 - Prob. 16.12PCh. 16 - Prob. 16.13PCh. 16 - Prob. 16.14PCh. 16 - Prob. 16.15PCh. 16 - Prob. 16.16PCh. 16 - Prob. 16.17PCh. 16 - Prob. 16.18PCh. 16 - Prob. 16.19PCh. 16 - Prob. 16.20PCh. 16 - Prob. 16.21PCh. 16 - Prob. 16.22PCh. 16 - Prob. 16.23PCh. 16 - Prob. 16.24PCh. 16 - Prob. 16.25PCh. 16 - Prob. 16.26PCh. 16 - Prob. 16.27PCh. 16 - Prob. 16.28PCh. 16 - Prob. 16.29PCh. 16 - Prob. 16.30PCh. 16 - Prob. 16.31PCh. 16 - Prob. 16.32PCh. 16 - Prob. 16.33PCh. 16 - Prob. 16.34PCh. 16 - Prob. 16.35PCh. 16 - Prob. 16.36PCh. 16 - Prob. 16.37PCh. 16 - Prob. 16.38PCh. 16 - Prob. 16.39PCh. 16 - Prob. 16.41DPCh. 16 - Prob. 16.42DPCh. 16 - Prob. 16.43DPCh. 16 - Prob. 16.44CPCh. 16 - Prob. K16.1KPCh. 16 - Prob. K16.2KPCh. 16 - Prob. K16.3KP
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