Chapter 2, Problem 21E

A tapered bar with circular cross section is fixed at $x=0$, and an axial force of $0.3\times {10}^6\text{N}$ is applied at the other end. The length of the bar (L) is 0.3 m, and the radius varies as $r\left(x\right)=0.03-0.07x$, where r and x are in meters. Use three equal-length finite elements to determine the displacements, axial force resultants, and support reactions. Compare your FE solutions with the exact solution by plotting u vs. x, and P (element force) vs. x. Use $E={10}^{10}\text{Pa}$.