2. Distributed load on elastic bar Consider an elastic bar subjected to distributed load b(x) along its length. The bar has length L, cross-sectional area A(x), Youngs modulus E(x) and boundary conditions as shown in Figure 1. L b(x)=b Figure 1: Problem 3 - distributed load. (a) Construct the strong form. (b) Derive and state the weak form. (c) Consider an approximate solution u(x) = 0101 +4202, using 01(x) = 1 and 02(x) = ?? Show that u(x) is an admissible trial solution. (d) Solve this problem using the Rayleigh Ritz method. Give an approximate solution for the displacement field Check if the solution satisfies the essential and natural boundary conditions . Find the exact solution to the problem Comment on the approximate vs the exact solution (e) Solve for the case where b(x) = box/L. Give an approximate solution for the displacement field . Check if the solution satisfies the essential and natural boundary conditions Find the exact solution to the problem Comment on the approximate vs the exact solution (f) From D and E Plot the exact vs the approximate solutions Plot the derivative of the exact vs the approximate solutions. 2. Distributed load on elastic bar Consider an elastic bar subjected to distributed load b(x) along its length. The bar has length L, cross-sectional area A(x), Youngs modulus E(x) and boundary conditions as shown in Figure 1. L b(x)=b Figure 1: Problem 3 - distributed load. (a) Construct the strong form. (b) Derive and state the weak form. (c) Consider an approximate solution u(x) = 0101 +4202, using 01(x) = 1 and 02(x) = ?? Show that u(x) is an admissible trial solution. (d) Solve this problem using the Rayleigh Ritz method. Give an approximate solution for the displacement field Check if the solution satisfies the essential and natural boundary conditions . Find the exact solution to the problem Comment on the approximate vs the exact solution (e) Solve for the case where b(x) = box/L. Give an approximate solution for the displacement field . Check if the solution satisfies the essential and natural boundary conditions Find the exact solution to the problem Comment on the approximate vs the exact solution (f) From D and E Plot the exact vs the approximate solutions Plot the derivative of the exact vs the approximate solutions