Download (You may use Matlab or any other computer code, but the procedure

(You may use Matlab or any other computer code, but the procedure must be given in
detail in the report)
Question:
Consider the simplest problem of a 1D bar of uniform cross-section, as shown in
Figure 1. The bar is of length l  1 and section area A  1 . It is subjected to a
uniform body force b  1 . The young’s modulus of the material is E  1.0 . Obtain
solutions in terms of displacement, strain, stress and strain energy, using the following
methods:
1. The analytical (exact) method.
2. FEM, using two equal-length linear elements. Discussion the FEM solution
with the analytic solution, in terms of important properties.
3. CS-FEM, using two equal-length linear elements and cell-based smoothing
(CS) domains. Discuss the CS-FEM solution with the linear FEM and the
analytic solutions, in terms of important properties.
4. NS-FEM, using two equal-length linear elements and node-based smoothing
(NS) domains. Discuss the NS-FEM solution with the linear FEM and the
analytic solutions, in terms of important properties.
5. CS/NS-FEM (or FEM), using two equal-length linear elements and
combined CS and NS domains. You may use a parameter  to control the
domain size of NS and CS domains. Discuss the solution with the linear FEM,
in terms of important properties.
6. Built a computer code and repeat the above using 25, 50, and 100 elements.
7. Discuss about the results obtained.
x
b
Figure 1
1