Chapter 2, Problem 28E

Consider a finite element with three nodes, as shown in the figure. When the solution is approximated using $u\left(x\right)=N_1\left(x\right)u_1+N_2\left(x\right)u_2+N_3\left(x\right)u_3$.

a. calculate the interpolation functions $N_1\left(x\right)$, $N_2\left(x\right)$, and $N_3\left(x\right)$, if it is intended to obtain the displacement field in the following form: $u\left(x\right)=c_0+c_1\sqrt{x}+c_{2}x$; and

b. when the nodal displacements are given as: $u_1=0,u_2=0.5$, and $u_3=1$, sketch the function $u\left(x\right)$.