j HP L 11h Figure 1 Question 1. Figure 1 shows a cantilever beam A3 with length i. and flexural rigidityr El, leaded by a compressive force F'. An approximate finite element analysis (using just one element] predicts critical buckling when (K PKQD = o {1) where _E 12 sL _} 1.2 o_1L _ WE K_ L3 6L 4L2} K3_L o.1L 0.1333,:21' D [63]\" and er]; and SB are the vertical displacement and rotation at B. (a) By making the substitution PL? it = E1 formulate equation (1} as a linear eigenvalue problem in the form E! L3[A}LB)D = {l (b) Find the two eigenvalues H. and the corresponding two eigenveotors D. [Hint: in the characteristic equation a common factor of L2 can be ignored] to} Compare your eigenvalues with the exact classical solutions IL _ 112 El. _ 9H2 _ 4 ' _ 4 and comment on the accuracy of your finite element solution