The strong form of governing equation for a simply supported beam under a distributed load p, shown in the figure above, is as follows d'v M(x) = 0 dx2 ELU where v is the deflection in y direction, E is Young's modulus, I is the second moment of inertia, M(x) is the internal bending moment and is given by M(x) = px(L-X) The boundary conditions are v(O)=0 v(L)=0 Derive the weak form of the problem similar to eqn. (3.11) in Lecture 3. Pay attention to the treatment of boundary conditions and body loads. The physical problem is the same as in 2.1, but we wish to find the numerical solution using hat functions. Divide the beam evenly into 4 sections with 5 nodes (3 nodes are internal, see the figure below), use the hat function method introduced in lecture 4 to solve the problem. Find the deflections at nodes 2, 3 and 4, and compare the results with HW1.2. Assume E = 29x100 lb/in?, 1=3100 in, L=20 ft=240 in, p=5000 lb/ft=5000 lb/(12 in). node 1 node 2 node 3 node 4 node 5 O The strong form of governing equation for a simply supported beam under a distributed load p, shown in the figure above, is as follows d'v M(x) = 0 dx2 ELU where v is the deflection in y direction, E is Young's modulus, I is the second moment of inertia, M(x) is the internal bending moment and is given by M(x) = px(L-X) The boundary conditions are v(O)=0 v(L)=0 Derive the weak form of the problem similar to eqn. (3.11) in Lecture 3. Pay attention to the treatment of boundary conditions and body loads. The physical problem is the same as in 2.1, but we wish to find the numerical solution using hat functions. Divide the beam evenly into 4 sections with 5 nodes (3 nodes are internal, see the figure below), use the hat function method introduced in lecture 4 to solve the problem. Find the deflections at nodes 2, 3 and 4, and compare the results with HW1.2. Assume E = 29x100 lb/in?, 1=3100 in, L=20 ft=240 in, p=5000 lb/ft=5000 lb/(12 in). node 1 node 2 node 3 node 4 node 5 O