Chapter 2, Problem 18E

A vertical rod of elastic material is fixed at both ends with constant cross-sectional area A, Young’s modulus E, and height of L under the distributed load f per unit length. The vertical deflection $u\left(x\right)$ of the rod is governed by the following differential equation:

$AE\frac{d^{2}u}{d{x}^2}+f=0$.

Using three elements of equal length, solve for $u\left(x\right)$ and compare it with the exact solution. Use the following numerical values: $A={10}^{-4}{\text{m}}^{\text{2}},E=\text{ 1}0\text{ GPa},L=0.\text{3m}, \text{N}/\text{m}$.