Multiple Choice test on Finite Difference Method for ...
Multiple-Choice Test
Chapter 08.07
Finite Difference Method
1. The exact solution to the boundary value problem
[pic], [pic], [pic]
for [pic] is
A) [pic]
B) 0.00
C) 16.000
D) 37.333
2. Given
[pic], [pic], [pic]
the value of [pic] at [pic] using the finite difference method and a step size of [pic] can be approximated by
A) [pic]
E) [pic]
F) [pic]
G) [pic]
3. Given
[pic], [pic], [pic],
the value of [pic] using the finite difference method with a second order accurate central divided difference method and a step size of [pic] is
A) 0.000
H) 37.333
I) [pic]
J) [pic]
4. The transverse deflection [pic] of a cable of length [pic] that is fixed at both ends, is given as a solution to
[pic]
where
[pic] = tension in cable
[pic] = flexural stiffness
[pic] = distributed transverse load
[pic]
Given [pic], [pic], [pic], and [pic]
Using finite difference method modeling with second order central divided difference accuracy and a step size of [pic], the value of the deflection at the center of the cable most nearly is
A) 0.072737″
K) 0.080832″
L) 0.081380″
M) 0.084843″
5. The radial displacement u of a pressurized hollow thick cylinder (inner radius = 5″, outer radius = 8″) is given at different radial locations.
|Radius |Radial Displacement |
|(in) |(in) |
|5.0 |0.0038731 |
|5.6 |0.0036165 |
|6.2 |0.0034222 |
|6.8 |0.0032743 |
|7.4 |0.0031618 |
|8.0 |0.0030769 |
The maximum normal stress, in psi, on the cylinder is given by
[pic][pic][pic]
The maximum stress, in psi, with second order accuracy is
A) 2079.6
B) 2104.5
C) 2130.7
D) 2182.0
6. For a simply supported beam (at [pic] and [pic]) with a uniform load q, the vertical deflection [pic] is described by the boundary value ordinary differential equation as [pic], [pic]
where
[pic] = Young’s modulus of the beam
[pic] = second moment of area
This ordinary differential equation is based on assuming that [pic] is small. If [pic] is not small, then the ordinary differential equation is given by [pic]
A) [pic]
B) [pic]
C) [pic]
D) [pic]
For a complete solution, refer to the links at the end of the book.
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