The exact solution to the boundary value problem

, ,  

for y(4) is

-234.66

0.00

16.000

37.333

Given

, , ,

The value of  at y(4) using finite difference method and a step size of h=4 can be approximated by

Given

, , ,

 The value of  using finite difference method with a second order accurate central divided difference method and a step size of  is

 0.000

37.333

-234.67

-256.00

The transverse deflection, u of a cable of length, L, fixed at both ends, is given as a solution to

where

T = tension in cable

R = flexural stiffness

q = distributed transverse load

Using finite difference method modeling with second order central divided difference accuracy and a step size of , the value of the deflection of the center (, , ,  ) most nearly is

0.072737"

0.08832"

0.081380"

0.084843"

The radial displacement, u is a pressurized hollow thick cylinder (inner radius=5″, outer radius=8″) is given at different radial locations.

The maximum normal stress, in psi, on the cylinder is given by

The maximum stress, in psi, with second order accuracy is

Hint:     , and

where

2079.3

2104.5

2130.7

2182.0

For a simply supported beam (at  and ) with a uniform load q, the vertical deflection v(x) is described by the boundary value ordinary differential equation as

                                                                        ,

where

            E = Young’s modulus of elasticity of beam

            I = second moment of area.

This ordinary differential equations is based on assuming that  is small.  If  is not small, then the ordinary differential equation is

Multiple choice questions on other topics

Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468 and 0717624.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.