Solve Problem 3.55 for the axial displacement in the bar using collocation, subdomain, l...

Solve Problem 3.55 for the axial displacement in the bar using collocation, subdomain, least squares, and Galerkin’s methods. Choose a quadratic polynomial u(x) = c₁x + c₂x² in each method. Compare these weighted residual method solutions to the exact solution.

Reference Problem 3.55

For the bar subjected to the uniform line load in the axial direction shown in Figure P3–55, determine the nodal displacements and axial stress distribution using (a) two equal-length elements and (b) four equal-length elements. Compare the finite element results with an exact solution. Let A = 2 in² and E = 30 10⁶ psi.