For a linearly elastic material, the stress () is given as where () is the displacement of the material and is a positive constant known as the Young’s modulus. The question considered here is,...

For a linearly elastic material, the stress

() is given as

where
() is the displacement of the material and

is a positive constant known as the Young’s modulus. The question considered here is, how to determine

from measurements of , as given in Table 6.10.

(a) Show that

In the following you can assume that
(0) = 0 and

= 4.

(b) Use the trapezoidal rule to find the value of
() at

= 1/4, 1/2, 3/4, 1.

(c) Use the composite midpoint rule to calculate
(1).

(d) Use the composite Simpson rule to calculate
(1).

(e) Use Romberg integration with the composite trapezoidal rule to calculate
(1).