11. A cantilevered beam structure shown in the figure is under the distributed load. When q =

l,000N/m, Lt = 1.5 m, E — 207GPa, and the radius of the circular cross-section r = 0.1m, solve the displacement of the neutral axis and stress on the top surface. Use three equal-length beam finite elements and the MATLAB program in Appendix. Compare the finite element sol¬

ution with the exact solution. Provide the bending moment and shear force diagram from the finite element method and compare them with the exact solution. Explain why the finite ele¬

ment solutions are different from the exact solutions.

I i \ ^

Lt 12. Model the beam shown in the figure using a two-node beam finite element.

L = 1 m EI = 0.15 N'm2

/= 1 N/m

(a) Using a beam stiffness matrix, set up the equation for this beam: ([K]{Q} = {F}).

(b) Compute the angle of rotation at node 1, and write the equation of deformed shape of the beam using the shape functions.

(c) Explain why the answer obtained above is not likely to be very accurate. If you want to obtain a better answer for this problem using the finite element method, what would you do?