Let?s consider a cylindrical bar or rod that has a Young's modulus of 1 pa. For now, let's assume we can model the part in one-dimension, like we have been doing in class. Assume also that a finite element solution using one-dimensional, two-noded elements as been obtained for a rod (shown in figure). The area of each element is 0.001 m ² , the lengths of each element are 0.05, 0.08 and 0.1 meters for elements 1, 2 and 3, respectively.

The displacements are as follows:

a) According to the finite element theory, plot the displacement u(x) vs. x.

b) According to the finite element theory plot the strain vs x.

c) Determine the B matrix for element e ₂ .

d) Determine that strain energy in element e ₁ .

(e) 2 (e) (e3) X -Q= -0.002 0 0.006 -0.001