A tapered rod is subjected to a body force f = x2 acting in the x -direction and also a point load P = 2 as shown in Fig. P3.14 .

(a) Use the Rayleigh–Ritz method with an assumed displacement field u = a0 + a1x + a2x2 to determine expressions for displacement u1x2 and stress s1x2 . (b) Solve this problem using a finite element solution with two (2) two-noded elements. Show all work such as element matrices, assembly, boundary conditions, and solution. Compare finite element and Rayleigh–Ritz solutions by providing plots of u1x2 vs. x and s1x2 vs. x by the two methods.

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