Solve for the axial displacement and stress in the tapered bar shown in Figure P3-12 using one and then two constant-area elements. Evaluate the area at the center of each element length. Use that area for each element. Let A0 = 2 in2, L = 20 in., E = 10 × 106 psi, and P = 1000 lb. Compare your finite element solutions with the exact solution.

Figure P3-12,

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A(x) = Ao(1 + E) -L-