The equation governing the deflection y of a simply supported beam of length L under uniform loading w is EI d^2y/dx^2 = wLx/2 - wx^2/2
with boundary conditions y(0) = y(L) = 0. Let E = 150GPa, I = 20000cm, w = 20kN/m, and L = 2m.
(a) Determine the discretized template equation by substituting in a central finite difference approximation. Put all terms involving the dependent variable on the left side, and other terms on the right. Eliminate the denominators on the left side if possible.
(b) Use the template equation (similar to Eq 9.4 in the lecture notes), along with the boundary condition equations to write a set of equations in matrix form that could be solved for the nodal values of y. Use 5 nodes, such that Ac = 0.5.