Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 14, Problem 9P
Develop a program using a programming or macro language to implement the random search method. Design the subprogram so that it is expressly designed to locate a maximum. Test the program with f(x, y) from Prob. 14.7. Use a range of
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A wheel of diameter 150.0 mm and width 37.00 mm carrying a load 2.200 kN rolls on a
flat rail. Take the wheel material as steel and the rail material as cast iron. Assume the
figure given, which is based on a Poisson's ratio of 0.3, is applicable to estimate
the depth at which the maximum shear stress occurs for these materials. At this critical
depth, calculate the Hertzian stresses σr, σy, σz, and Tmax for the wheel.
1.0
0.8
0, т
Ratio of stress to Pmax
0.4
0.6
90
69
0.2
0.5b
b
1.5b
Tmax
2b
Distance from contact surface
The Hertizian stresses are as follows:
02 = or = -23.8 psi for the wheel =|
necessary.)
σy for the wheel =|
MPa
σz for the wheel =
MPa
V4 for the wheel = |
MPa
2.5b
ཡི
3b
MPa (Include a minus sign if
Only question 3
Only question 2
Chapter 14 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 14 - 14.1 Find the directional derivative of
at in...Ch. 14 - Repeat Example 14.2 for the following function at...Ch. 14 - 14.3 Given
Construct and solve a system of...Ch. 14 - (a) Start with an initial guess of x=1 and y=1 and...Ch. 14 - 14.5 Find the gradient vector and Hessian matrix...Ch. 14 - Prob. 6PCh. 14 - Perform one iteration of the steepest ascent...Ch. 14 - Perform one iteration of the optimal gradient...Ch. 14 - Develop a program using a programming or macro...Ch. 14 - 14.10 The grid search is another brute force...
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